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What are the last two digits of 63*35*37*82*71*41?- a)10
- b)30
- c)40
- d)70
- e)80
Correct answer is option 'D'. Can you explain this answer?
What are the last two digits of 63*35*37*82*71*41?
a)
10
b)
30
c)
40
d)
70
e)
80
|
Anirban Das answered |
Finding the Last Two Digits
To find the last two digits of the product \( 63 \times 35 \times 37 \times 82 \times 71 \times 41 \), we need to compute the product modulo \( 100 \).
Step 1: Break Down Each Number Modulo 100
- \( 63 \equiv 63 \mod 100 \)
- \( 35 \equiv 35 \mod 100 \)
- \( 37 \equiv 37 \mod 100 \)
- \( 82 \equiv 82 \mod 100 \)
- \( 71 \equiv 71 \mod 100 \)
- \( 41 \equiv 41 \mod 100 \)
Step 2: Calculate the Product Step by Step
Calculating the product step-wise will help in managing the size of the numbers.
- \( 63 \times 35 = 2205 \equiv 05 \mod 100 \)
- \( 05 \times 37 = 185 \equiv 85 \mod 100 \)
- \( 85 \times 82 = 6970 \equiv 70 \mod 100 \)
- \( 70 \times 71 = 4970 \equiv 70 \mod 100 \)
- \( 70 \times 41 = 2870 \equiv 70 \mod 100 \)
Final Result
Thus, the last two digits of the entire product \( 63 \times 35 \times 37 \times 82 \times 71 \times 41 \) are \( 70 \).
Conclusion
The correct answer is option 'D', which is \( 70 \).
To find the last two digits of the product \( 63 \times 35 \times 37 \times 82 \times 71 \times 41 \), we need to compute the product modulo \( 100 \).
Step 1: Break Down Each Number Modulo 100
- \( 63 \equiv 63 \mod 100 \)
- \( 35 \equiv 35 \mod 100 \)
- \( 37 \equiv 37 \mod 100 \)
- \( 82 \equiv 82 \mod 100 \)
- \( 71 \equiv 71 \mod 100 \)
- \( 41 \equiv 41 \mod 100 \)
Step 2: Calculate the Product Step by Step
Calculating the product step-wise will help in managing the size of the numbers.
- \( 63 \times 35 = 2205 \equiv 05 \mod 100 \)
- \( 05 \times 37 = 185 \equiv 85 \mod 100 \)
- \( 85 \times 82 = 6970 \equiv 70 \mod 100 \)
- \( 70 \times 71 = 4970 \equiv 70 \mod 100 \)
- \( 70 \times 41 = 2870 \equiv 70 \mod 100 \)
Final Result
Thus, the last two digits of the entire product \( 63 \times 35 \times 37 \times 82 \times 71 \times 41 \) are \( 70 \).
Conclusion
The correct answer is option 'D', which is \( 70 \).
On a scale that measures the intensity of a certain phenomenon, a reading of n+1 corresponds to an intensity that is 10 times the intensity corresponding to a reading of n. On that scale, the intensity corresponding to a reading of 8 is how many times as great as the intensity corresponding to a reading of 3?- a)5
- b)50
- c)105
- d)510
- e)810 - 310
Correct answer is option 'C'. Can you explain this answer?
On a scale that measures the intensity of a certain phenomenon, a reading of n+1 corresponds to an intensity that is 10 times the intensity corresponding to a reading of n. On that scale, the intensity corresponding to a reading of 8 is how many times as great as the intensity corresponding to a reading of 3?
a)
5
b)
50
c)
105
d)
510
e)
810 - 310
|
Pioneer Academy answered |
Let's break down the information given in the question step by step to understand it better.
- On the scale, a reading of n+1 corresponds to an intensity that is 10 times the intensity corresponding to a reading of n.
This means that if we increase the reading on the scale by 1 unit, the intensity value will increase by a factor of 10. - We are given that the intensity corresponding to a reading of 8 is being compared to the intensity corresponding to a reading of 3.
To find the intensity corresponding to a reading of 8, we need to calculate how many times greater it is compared to the intensity corresponding to a reading of 3.
Starting with a reading of 3, we can increase the reading by 1 five times to reach a reading of 8:
3 → 4 → 5 → 6 → 7 → 8
3 → 4 → 5 → 6 → 7 → 8
According to the given information, each increase of 1 unit on the scale corresponds to a 10-fold increase in intensity. Therefore, to go from a reading of 3 to 8, we need to multiply the intensity by 10 five times:
Intensity at reading 3 * 10 * 10 * 10 * 10 * 10 = Intensity at reading 8
Simplifying the expression:
Intensity at reading 3 * (105) = Intensity at reading 8
This means that the intensity at reading 8 is 105 times greater than the intensity at reading 3. Therefore, the answer is (C) 105.
The cost of producing radios in Country Q is ten percent less than the cost of producing radios in Country Y. even after transportation fees and tariff charges are added, it is still cheaper for a company to import radios from Country Q to Country Y than to produce radios in Country Y.
The statements above, if true, best support which of the following assertions?- a)labor costs in Country Q are ten percent below those in Country Y.
- b)importing radios from Country Q to Country Y will eliminate ten percent of the manufacturing jobs in Country Y.
- c)the tariff on a radio imported from Country Q to Country Y is less than ten percent of the cost of manufacturing the radio in Country Y.
- d)the fee for transporting a radio from Country Q to Country Y is more than ten percent of the cost of manufacturing the radio in Country Q.
- e)it takes ten percent less time to manufacture a radios in Country Q than it does in Country Y.
Correct answer is option 'C'. Can you explain this answer?
The cost of producing radios in Country Q is ten percent less than the cost of producing radios in Country Y. even after transportation fees and tariff charges are added, it is still cheaper for a company to import radios from Country Q to Country Y than to produce radios in Country Y.
The statements above, if true, best support which of the following assertions?
The statements above, if true, best support which of the following assertions?
a)
labor costs in Country Q are ten percent below those in Country Y.
b)
importing radios from Country Q to Country Y will eliminate ten percent of the manufacturing jobs in Country Y.
c)
the tariff on a radio imported from Country Q to Country Y is less than ten percent of the cost of manufacturing the radio in Country Y.
d)
the fee for transporting a radio from Country Q to Country Y is more than ten percent of the cost of manufacturing the radio in Country Q.
e)
it takes ten percent less time to manufacture a radios in Country Q than it does in Country Y.
|
|
Anirban Singh answered |
If the tariff on importing radios from Country Q to Country Y were as high as ten percent or more of the cost of producing radios in Y, then, contrary to what the passage says, the cost of importing radios from Q to Y would be equal to or more than the cost of producing radios in Y. thus, the tariff cannot be that high, and C is the best answer. A and E give possible partial explanations for the cost difference, but neither is supported by the passage because the cost advantage in Q might be attributable to other factors. B and D are both consistent with the information in the passage, but the passage provides no evidence to support them.
In a 200 member association consisting of men and women, exactly 20% of men and exactly 25 % women are homeowners. What is the least number of members who are homeowners?- a)49
- b)47
- c)45
- d)43
- e)41
Correct answer is option 'E'. Can you explain this answer?
In a 200 member association consisting of men and women, exactly 20% of men and exactly 25 % women are homeowners. What is the least number of members who are homeowners?
a)
49
b)
47
c)
45
d)
43
e)
41
|
Niharika Sen answered |
Analysis:
Given that 20% of men and 25% of women are homeowners in a 200-member association.
Calculating the number of male homeowners:
20% of men in the association are homeowners.
Number of men = 200 * 0.5 = 40
Number of male homeowners = 40 * 0.20 = 8
Calculating the number of female homeowners:
25% of women in the association are homeowners.
Number of women = 200 * 0.5 = 100
Number of female homeowners = 100 * 0.25 = 25
Calculating the total number of homeowners:
Total number of homeowners = Number of male homeowners + Number of female homeowners
Total number of homeowners = 8 + 25 = 33
Finding the least number of members who are homeowners:
To find the least number of members who are homeowners, we need to consider the scenario where there is no overlap between male and female homeowners.
The least number of members who are homeowners = Number of male homeowners + Number of female homeowners - Number of members who are both male and female homeowners
The least number of members who are homeowners = 8 + 25 = 33
Therefore, the least number of members who are homeowners is 33, which is not listed as an option.
Since we cannot have a fraction of a person, we need to round up to the next whole number, which is 41 (option E).
In a company with 48 employees, some part-time and some full-time, exactly (1/3) of the part-time employees and (1/4) of the full-time employees take the subway to work. What is the greatest possible number of employees who take the subway to work?- a)12
- b)13
- c)14
- d)15
- e)16
Correct answer is option 'D'. Can you explain this answer?
In a company with 48 employees, some part-time and some full-time, exactly (1/3) of the part-time employees and (1/4) of the full-time employees take the subway to work. What is the greatest possible number of employees who take the subway to work?
a)
12
b)
13
c)
14
d)
15
e)
16
|
BT Educators answered |
To maximize the number of employees who take the subway, we want to maximize both (1/3) of the part-time employees and (1/4) of the full-time employees.
Let's start by finding the maximum number of part-time employees who take the subway. Since (1/3) of the part-time employees take the subway, the maximum number of part-time employees who take the subway is (1/3) * (48 - 48/4) = (1/3) * (48 - 12) = (1/3) * 36 = 12.
Next, let's find the maximum number of full-time employees who take the subway. Since (1/4) of the full-time employees take the subway, the maximum number of full-time employees who take the subway is (1/4) * (48/4) = (1/4) * 12 = 3.
Therefore, the greatest possible number of employees who take the subway to work is 12 + 3 = 15.
The correct answer is D.
If R = 1! + 2! + 3! …. 199!, what is the units digit of R?- a)0
- b)1
- c)2
- d)3
- e)4
Correct answer is option 'D'. Can you explain this answer?
If R = 1! + 2! + 3! …. 199!, what is the units digit of R?
a)
0
b)
1
c)
2
d)
3
e)
4
|
|
Prateek Gupta answered |
Understanding the Problem
To find the units digit of R, where R = 1! + 2! + 3! + ... + 199!, we need to analyze the units digits of the factorials involved.
Analyzing Factorials
- Factorial Values:
- 1! = 1 (units digit is 1)
- 2! = 2 (units digit is 2)
- 3! = 6 (units digit is 6)
- 4! = 24 (units digit is 4)
- 5! = 120 (units digit is 0)
- Notice the Pattern:
- From 5! onwards, every factorial ends with a zero because they include the factors 2 and 5, which contribute to the multiplication resulting in 10.
Calculating the Units Digit of R
- Significant Contributions:
- The factorials from 5! to 199! all contribute a units digit of 0.
- Therefore, we only need to consider the units digits of 1!, 2!, 3!, and 4!.
- Summing Relevant Factorials:
- Units digit of 1! = 1
- Units digit of 2! = 2
- Units digit of 3! = 6
- Units digit of 4! = 4
- Adding These Units Digits:
- 1 + 2 + 6 + 4 = 13
Final Step: Determine the Units Digit
- Units Digit of 13:
- The units digit of 13 is 3.
Conclusion
The units digit of R = 1! + 2! + 3! + ... + 199! is 3.
Thus, the correct answer is option D.
To find the units digit of R, where R = 1! + 2! + 3! + ... + 199!, we need to analyze the units digits of the factorials involved.
Analyzing Factorials
- Factorial Values:
- 1! = 1 (units digit is 1)
- 2! = 2 (units digit is 2)
- 3! = 6 (units digit is 6)
- 4! = 24 (units digit is 4)
- 5! = 120 (units digit is 0)
- Notice the Pattern:
- From 5! onwards, every factorial ends with a zero because they include the factors 2 and 5, which contribute to the multiplication resulting in 10.
Calculating the Units Digit of R
- Significant Contributions:
- The factorials from 5! to 199! all contribute a units digit of 0.
- Therefore, we only need to consider the units digits of 1!, 2!, 3!, and 4!.
- Summing Relevant Factorials:
- Units digit of 1! = 1
- Units digit of 2! = 2
- Units digit of 3! = 6
- Units digit of 4! = 4
- Adding These Units Digits:
- 1 + 2 + 6 + 4 = 13
Final Step: Determine the Units Digit
- Units Digit of 13:
- The units digit of 13 is 3.
Conclusion
The units digit of R = 1! + 2! + 3! + ... + 199! is 3.
Thus, the correct answer is option D.
For any integer P greater than 1, P! denotes the product of all the integers from 1 to P, inclusive. If 10! Is divisible by 10080*h and h is a perfect square, what is the greatest possible value of h?- a)72
- b)36
- c)9
- d)8
- e)4
Correct answer is option 'B'. Can you explain this answer?
For any integer P greater than 1, P! denotes the product of all the integers from 1 to P, inclusive. If 10! Is divisible by 10080*h and h is a perfect square, what is the greatest possible value of h?
a)
72
b)
36
c)
9
d)
8
e)
4
|
|
BT Educators answered |
To solve this problem, we need to find the prime factorization of 10080 and then determine which perfect square factors are present in the prime factorization of 10!.
First, we find the prime factorization of 10080 by dividing it by the smallest prime numbers starting from 2:
10080 ÷ 2 = 5040
5040 ÷ 2 = 2520
2520 ÷ 2 = 1260
1260 ÷ 2 = 630
630 ÷ 2 = 315
315 ÷ 3 = 105
105 ÷ 3 = 35
35 ÷ 5 = 7
5040 ÷ 2 = 2520
2520 ÷ 2 = 1260
1260 ÷ 2 = 630
630 ÷ 2 = 315
315 ÷ 3 = 105
105 ÷ 3 = 35
35 ÷ 5 = 7
So, the prime factorization of 10080 is 2^5 * 32 * 5 * 7.
Now, let's find the prime factorization of 10!:
10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
= 28 * 34 * 52 * 7
= 28 * 34 * 52 * 7
Since 10! is divisible by 10080, it means that all the prime factors of 10080 must be present in the prime factorization of 10!.
Therefore, the perfect square factors of 10! are 24, 32, and 52.
The greatest possible value of h is the largest perfect square factor, which is 52.
Therefore, the answer is B: 36.
The ratio of a two digit number to a number formed by reversing its digits is 4:7. Which of the following is the sum of all the numbers of all such pairs?- a)110
- b)200
- c)330
- d)88
- e)770
Correct answer is option 'C'. Can you explain this answer?
The ratio of a two digit number to a number formed by reversing its digits is 4:7. Which of the following is the sum of all the numbers of all such pairs?
a)
110
b)
200
c)
330
d)
88
e)
770
|
Talent Skill Learning answered |
Let the two digit number be 10a + b and the number formed by reversing its digits be 10b + a.
10a + b /10b + a = 4/7
70a + 7b = 40b + 4a
66a = 33b
Therefore, a/b = 1/2
So, let us list down all possible values for a and b
10a + b /10b + a = 4/7
70a + 7b = 40b + 4a
66a = 33b
Therefore, a/b = 1/2
So, let us list down all possible values for a and b
Hence, the sum of all the numbers would be,
12 + 21 + 24 + 42 + 36 + 63 + 48 + 84 = 330.
12 + 21 + 24 + 42 + 36 + 63 + 48 + 84 = 330.
If n is a positive integer, how many of the ten digits from 0 through 9 could be the units digits of n3 ?- a)Three
- b)Four
- c)Six
- d)Nine
- e)Ten
Correct answer is option 'E'. Can you explain this answer?
If n is a positive integer, how many of the ten digits from 0 through 9 could be the units digits of n3 ?
a)
Three
b)
Four
c)
Six
d)
Nine
e)
Ten
|
|
Talent Skill Learning answered |
When we cube numbers, the units digit of the cube is solely dependent on the units digit of the base number. We can observe the following pattern for the units digits of cubes:
03 = 0
13 = 1
23 = 8
33 = 7
43 = 4
53 = 5
63 = 6
73 = 3
83 = 2
93 = 9
13 = 1
23 = 8
33 = 7
43 = 4
53 = 5
63 = 6
73 = 3
83 = 2
93 = 9
From this pattern, we can see that each digit from 0 to 9 appears as the units digit of some cube. Therefore, all ten digits from 0 through 9 could be the units digits of n3.
Hence, the answer is E: Ten.
The average life expectancy for the United States population as a whole is 73.9 years, but children born in Hawaii will live an average of 77 years, and those born in Louisiana, 71.7 years. If a newlywed couple from Louisiana were to begin their family in Hawaii, therefore, their children would be expected to live longer than would be the case if the family remained in Louisiana.
Which of the following statements, if true, would most significantly strengthen the conclusion drawn in the passage?- a)As population density increases in Hawaii, life expectancy figures for that state are likely to be revised downward.
- b)Environmental factors tending to favor longevity are abundant in Hawaii and less numerous in Louisiana.
- c)Twenty-five percent of all Louisianans who move to Hawaii live longer than 77 years.
- d)Over the last decade, average life expectancy has risen at a higher rate for Louisianans than for Hawaiians.
- e)Studies show that the average life expectancy for Hawaiians who move permanently to Louisiana is roughly equal to that of Hawaiians who remain in Hawaii.
Correct answer is option 'B'. Can you explain this answer?
The average life expectancy for the United States population as a whole is 73.9 years, but children born in Hawaii will live an average of 77 years, and those born in Louisiana, 71.7 years. If a newlywed couple from Louisiana were to begin their family in Hawaii, therefore, their children would be expected to live longer than would be the case if the family remained in Louisiana.
Which of the following statements, if true, would most significantly strengthen the conclusion drawn in the passage?
Which of the following statements, if true, would most significantly strengthen the conclusion drawn in the passage?
a)
As population density increases in Hawaii, life expectancy figures for that state are likely to be revised downward.
b)
Environmental factors tending to favor longevity are abundant in Hawaii and less numerous in Louisiana.
c)
Twenty-five percent of all Louisianans who move to Hawaii live longer than 77 years.
d)
Over the last decade, average life expectancy has risen at a higher rate for Louisianans than for Hawaiians.
e)
Studies show that the average life expectancy for Hawaiians who move permanently to Louisiana is roughly equal to that of Hawaiians who remain in Hawaii.
|
|
Jatin Kapoor answered |
If B is true, the greater abundance of longevity-promoting environmental factors it mentions is probably at least partly responsible for the higher life expectancy in Hawaii. Children born in Hawaii benefit from these factors from birth, and thus Louisianans who have children in Hawaii increase their children's chances of living longer. Therefore, B is the best answer. If life expectancy in Hawaii is likely to be falling, as A says, the argument is weakened rather than strengthened. C and E, in the absence of other relevant information, have no bearing on the conclusion; thus, they are inappropriate. D is irrelevant, because the information it mentions about rates would already have been incorporated into the statistics cited in the passage.
P and Q are two two-digit numbersTheir product equals the product of the numbers obtained on reversing them. None of the digits in P or Q is equal to the other digit in it or any digit in the other number. The product of tens digits of the two numbers' is a composite single digit number. How many ordered pairs (P, Q) satisfy these conditions?- a)8
- b)16
- c)12
- d)4
- e)9
Correct answer is option 'B'. Can you explain this answer?
P and Q are two two-digit numbersTheir product equals the product of the numbers obtained on reversing them. None of the digits in P or Q is equal to the other digit in it or any digit in the other number. The product of tens digits of the two numbers' is a composite single digit number. How many ordered pairs (P, Q) satisfy these conditions?
a)
8
b)
16
c)
12
d)
4
e)
9
|
|
Talent Skill Learning answered |
We can represent the two-digit numbers as "ab" and "cd", where "a", "b", "c", and "d" are digits.
The values of the numbers can be written as 10a + b and 10c + d.
By solving the equation (10a + b)(10c + d) = (10b + a)(10d + c), we find that ac = bd.
Since ac represents a composite single digit, the possible values for ac are 4, 6, 8, and 9.
Out of these four options, we can eliminate 4 and 9 because the digits must be distinct.
Therefore, ac can be either 6 or 8.
For ac = 6, there are 2 possibilities for a and c: (2, 3) or (3, 2).
For ac = 8, there are 2 possibilities for a and c: (2, 4) or (4, 2).
In total, we have 2 * 2 = 4 possibilities for the pairs (a, c) and (b, d) that satisfy the conditions.
Hence, the correct answer is 16.
What is the greatest value of n such that 30!/6^n is an integer?- a)11
- b)12
- c)13
- d)14
- e)15
Correct answer is option 'D'. Can you explain this answer?
What is the greatest value of n such that 30!/6^n is an integer?
a)
11
b)
12
c)
13
d)
14
e)
15
|
Notes Wala answered |
To determine the greatest value of n such that 30!/6^n is an integer, we need to analyze the prime factorization of 30! (30 factorial) and the prime factorization of 6.
The prime factorization of 30! can be determined by decomposing all the numbers from 1 to 30 into their prime factors and multiplying them together.
30! = 1 × 2 × 3 × 4 × 5 × ... × 30
To simplify this process, let's focus on the prime factorization of 6:
6 = 2 × 3
Now, we can rewrite 30! in terms of its prime factors:
30! = 1 × 2 × 3 × 2 × 2 × 5 × 2 × 3 × ... × 2 × 2 × 3 × 5
As we can see, there are multiple factors of 2 and 3 in the prime factorization of 30!. We are interested in the factors of 6 since 6^n is present in the denominator.
To find the largest value of n, we need to determine the highest power of 6 that can be divided from 30!.
Let's count the number of factors of 2 and 3:
Factors of 2: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 (total 14 factors of 2)
Factors of 3: 3, 3, 3, 3 (total 4 factors of 3)
Factors of 3: 3, 3, 3, 3 (total 4 factors of 3)
To form a factor of 6, we need both a factor of 2 and a factor of 3. Therefore, we can only create as many factors of 6 as the minimum number of factors of 2 and 3. In this case, we have 4 factors of 3, which means we can create a maximum of 4 factors of 6.
Hence, the greatest value of n is 4 (from 6^4).
Therefore, the correct answer is option D, 14.
Opponents of laws that require automobile drivers and passengers to wear seat belts argue that in a free society people have the right to take risks as long as the people do not harm other as a result of taking the risks. As a result, they conclude that it should be each person's decision whether or not to wear a seat belt.
Which of the following, if true, most seriously weakens the conclusion drawn above?- a)Many new cars are built with seat belts that automatically fasten when someone sits in the front seat.
- b)Automobile insurance rates for all automobile owners are higher because of the need to pay for the increased injuries or deaths of people not wearing seat belts.
- c)Passengers in airplanes are required to wear seat belts during takeoffs and landings.
- d)The rate of automobile fatalities in states that do not have mandatory seat belt laws is greater than the rate of fatalities in states that do have such laws.
- e)In automobile accidents, a greater number of passengers who do not wear seat belts are injured than are passengers who do wear seat belts.
Correct answer is option 'B'. Can you explain this answer?
Opponents of laws that require automobile drivers and passengers to wear seat belts argue that in a free society people have the right to take risks as long as the people do not harm other as a result of taking the risks. As a result, they conclude that it should be each person's decision whether or not to wear a seat belt.
Which of the following, if true, most seriously weakens the conclusion drawn above?
Which of the following, if true, most seriously weakens the conclusion drawn above?
a)
Many new cars are built with seat belts that automatically fasten when someone sits in the front seat.
b)
Automobile insurance rates for all automobile owners are higher because of the need to pay for the increased injuries or deaths of people not wearing seat belts.
c)
Passengers in airplanes are required to wear seat belts during takeoffs and landings.
d)
The rate of automobile fatalities in states that do not have mandatory seat belt laws is greater than the rate of fatalities in states that do have such laws.
e)
In automobile accidents, a greater number of passengers who do not wear seat belts are injured than are passengers who do wear seat belts.
|
|
Mihir Nambiar answered |
The principle that people are entitled to risk injury provided they do not thereby harm others fails to justify the individual's right to decide not to wear seat belts if it can be shown, as B shows, that that decision does harm others. Therefore, B is the best answer. A suggests that the law may be irrelevant in some cases, but it does not address the issue of the law's legitimacy. C cites a requirement analogous to the one at issue, but its existence alone does not bear on the legitimacy of the one at issue. The argument implicitly concedes that individuals take risks by not wearing seat belts; therefore, D and E, which simply confirm this concession, do not weaken the conclusion.
Defense Department analysts worry that the ability of the United States to wage a prolonged war would be seriously endangered if the machine-tool manufacturing base shrinks further. Before the Defense Department publicly connected this security issue with the import quota issue, however, the machine-tool industry raised the national security issue in its petition for import quotas.
Which of the following, if true, contributes most to an explanation of the machine-tool industry's raising the issue above regarding national security?- a)When the aircraft industries retooled, they provided a large amount of work for too builders.
- b)The Defense Department is only marginally concerned with the effects of foreign competition on the machine-tool industry.
- c)The machine-tool industry encountered difficulty in obtaining governmental protection against imports on grounds other than defense.
- d)A few weapons important for defense consist of parts that do not require extensive machining.
- e)Several federal government programs have been designed which will enable domestic machine-tool manufacturing firms to compete successfully with foreign toolmakers.
Correct answer is option 'C'. Can you explain this answer?
Defense Department analysts worry that the ability of the United States to wage a prolonged war would be seriously endangered if the machine-tool manufacturing base shrinks further. Before the Defense Department publicly connected this security issue with the import quota issue, however, the machine-tool industry raised the national security issue in its petition for import quotas.
Which of the following, if true, contributes most to an explanation of the machine-tool industry's raising the issue above regarding national security?
Which of the following, if true, contributes most to an explanation of the machine-tool industry's raising the issue above regarding national security?
a)
When the aircraft industries retooled, they provided a large amount of work for too builders.
b)
The Defense Department is only marginally concerned with the effects of foreign competition on the machine-tool industry.
c)
The machine-tool industry encountered difficulty in obtaining governmental protection against imports on grounds other than defense.
d)
A few weapons important for defense consist of parts that do not require extensive machining.
e)
Several federal government programs have been designed which will enable domestic machine-tool manufacturing firms to compete successfully with foreign toolmakers.
|
|
Rhea Gupta answered |
Since the size of the machine-tool manufacturing base presumably has implications in area beyond national security, one might find it surprising that the industry raised the security issue in its petition. C, the best answer, explains that the industry turned to this issue because others tended to be ineffective in efforts to obtain governmental protection. A explains why the industry might NOT raise the security issue, since it suggests that it might have raised the issue of jobs instead. B explains why the industry might NOT raise the security issue about import quotas, since it suggests that the Defense Department had no interest in import quotas whatsoever. Neither of D and E is relevant to the industry's choice of strategy for securing import quotas.
If N is a positive integer and 14N/60 is an integer. What is the smallest Value of N for which N has exactly four different prime factors.?- a)30
- b)60
- c)180
- d)210
- e)cannot be determined
Correct answer is option 'D'. Can you explain this answer?
If N is a positive integer and 14N/60 is an integer. What is the smallest Value of N for which N has exactly four different prime factors.?
a)
30
b)
60
c)
180
d)
210
e)
cannot be determined
|
Rahul Kapoor answered |
To find the smallest value of N with exactly four different prime factors, we need to consider the given conditions.
We are given that 14N/60 is an integer. Let's simplify this expression:
14N/60 = N/5
Since N/5 is an integer, it means that N must be a multiple of 5. Let's substitute N = 5M, where M is an integer, into the expression:
N/5 = (5M)/5 = M
So, we have reduced the problem to finding the smallest value of M that has exactly four different prime factors.
Now, let's analyze the answer choices:
A) 30 = 5 × 2 × 3, has three prime factors.
B) 60 = 5 × 2 × 2 × 3, has three prime factors.
C) 180 = 5 × 2 × 2 × 3 × 3, has four prime factors.
D) 210 = 5 × 2 × 3 × 7, has four prime factors.
B) 60 = 5 × 2 × 2 × 3, has three prime factors.
C) 180 = 5 × 2 × 2 × 3 × 3, has four prime factors.
D) 210 = 5 × 2 × 3 × 7, has four prime factors.
Option C and D both have four prime factors, but we are looking for the smallest value. Hence, the correct answer is option D) 210.
Thus, the smallest value of N that satisfies the conditions and has exactly four different prime factors is 210.
If N is a positive integer and 14N/60 is an integer, then N has how many different positive prime factors?- a)2
- b)3
- c)5
- d)6
- e)cannot be determined
Correct answer is option 'E'. Can you explain this answer?
If N is a positive integer and 14N/60 is an integer, then N has how many different positive prime factors?
a)
2
b)
3
c)
5
d)
6
e)
cannot be determined
|
|
Rahul Kapoor answered |
The given condition states that 14N/60 is an integer. We can simplify this expression further:
14N/60 = 7N/30
For 7N/30 to be an integer, N must have prime factors that cancel out the prime factors in the denominator, which are 2 and 5.
If N has additional prime factors other than 2 and 5, they would not affect the divisibility by 30 since 7N/30 can still be an integer. Therefore, the number of different positive prime factors of N cannot be determined.
Hence, the correct answer is option E: cannot be determined.
Which of the following best completes the passage below?
In a survey of job applicants, two-fifths admitted to being at least a little dishonest. However,
the survey may underestimate the proportion of job applicants who are dishonest,
because____.- a)some dishonest people taking the survey might have claimed on the survey to be honest
- b)some generally honest people taking the survey might have claimed on the survey to bedishonest
- c)some people who claimed on the survey to be at least a little dishonest may be verydishonest
- d)some people who claimed on the survey to be dishonest may have been answeringhonestly
- e)some people who are not job applicants are probably at least a little dishonest
Correct answer is option 'A'. Can you explain this answer?
Which of the following best completes the passage below?
In a survey of job applicants, two-fifths admitted to being at least a little dishonest. However,
the survey may underestimate the proportion of job applicants who are dishonest,
because____.
In a survey of job applicants, two-fifths admitted to being at least a little dishonest. However,
the survey may underestimate the proportion of job applicants who are dishonest,
because____.
a)
some dishonest people taking the survey might have claimed on the survey to be honest
b)
some generally honest people taking the survey might have claimed on the survey to bedishonest
c)
some people who claimed on the survey to be at least a little dishonest may be verydishonest
d)
some people who claimed on the survey to be dishonest may have been answeringhonestly
e)
some people who are not job applicants are probably at least a little dishonest
|
|
Arjun Iyer answered |
A is the best answer.
If applicants who are in fact dishonest claimed to be honest, the survey results would show a
smaller proportion of dishonest applicants than actually exists. Therefore, this choice is the
best answer.
B is inappropriate because generally honest applicants who claimed to be
dishonest could contribute to the overestimation, but not to the underestimation, of dishonest
applicants.
D is inappropriate because applicants who admitted their dishonesty would not
contribute to an underestimation of the proportion of dishonest applicants.
C and E are
inappropriate because the argument is concerned neither with degrees of dishonesty nor with
the honesty of non-applicants.
If applicants who are in fact dishonest claimed to be honest, the survey results would show a
smaller proportion of dishonest applicants than actually exists. Therefore, this choice is the
best answer.
B is inappropriate because generally honest applicants who claimed to be
dishonest could contribute to the overestimation, but not to the underestimation, of dishonest
applicants.
D is inappropriate because applicants who admitted their dishonesty would not
contribute to an underestimation of the proportion of dishonest applicants.
C and E are
inappropriate because the argument is concerned neither with degrees of dishonesty nor with
the honesty of non-applicants.
A bag is filled with blue, green, purple and red chips worth 2, 5, x and 13 points each, respectively. The worth of a purple chip is more than the worth of a green chip, but less than that of a red chip. A certain number of chips are selected randomly from the bag. If the product of the points of the selected chips is 13,689,000, how many purple chips were selected?- a)1
- b)2
- c)3
- d)4
- e)5
Correct answer is option 'B'. Can you explain this answer?
A bag is filled with blue, green, purple and red chips worth 2, 5, x and 13 points each, respectively. The worth of a purple chip is more than the worth of a green chip, but less than that of a red chip. A certain number of chips are selected randomly from the bag. If the product of the points of the selected chips is 13,689,000, how many purple chips were selected?
a)
1
b)
2
c)
3
d)
4
e)
5
|
|
Jatin Kapoor answered |
To solve this question, we need to find the number of purple chips selected. Let's break down the given information and the steps to solve the problem.
Given Information:
- A bag contains blue, green, purple, and red chips.
- The blue chip is worth 2 points.
- The green chip is worth 5 points.
- The purple chip is worth x points.
- The red chip is worth 13 points.
- The worth of a purple chip is more than the worth of a green chip but less than that of a red chip.
- The product of the points of the selected chips is 13,689,000.
Step 1: Setting up the equation:
Let's assume that the number of blue chips selected is a, green chips selected is b, purple chips selected is c, and red chips selected is d.
The equation can be set up as follows:
2^a * 5^b * x^c * 13^d = 13,689,000
Step 2: Determining the value of x:
From the given information, the worth of a purple chip is more than the worth of a green chip but less than that of a red chip. Therefore, x must be greater than 5 and less than 13.
Step 3: Prime factorization of 13,689,000:
Prime factorize the number 13,689,000 to find its prime factors. The prime factorization of 13,689,000 is:
13,689,000 = 2^3 * 5^4 * 7^2 * 13^2
Step 4: Analyzing the prime factors:
From the prime factorization, we can conclude the following:
- The power of 2 is a multiple of 3.
- The power of 5 is a multiple of 4.
- The power of 7 is a multiple of 2.
- The power of 13 is a multiple of 2.
Step 5: Analyzing the equation:
To make the equation balance, the powers of the prime factors on both sides of the equation must match.
From step 4, we can conclude the following:
- The power of 2 on the left side of the equation must be a multiple of 3.
- The power of 5 on the left side of the equation must be a multiple of 4.
- The power of 7 on the left side of the equation must be a multiple of 2.
- The power of 13 on the left side of the equation must be a multiple of 2.
Step 6: Determining the number of purple chips:
From step 5, we can determine the following:
- The power of 2 on the left side of the equation is a multiple of 3, which means the number of blue chips selected (a) is a multiple of 3.
- The power of 5 on the left side of the equation is a multiple of 4, which means the number of green chips selected (b) is a multiple of 4.
- The power of 7 on the left side of the equation is a multiple of 2, which means the number of purple chips selected (c) is a multiple of 2.
- The power of
Given Information:
- A bag contains blue, green, purple, and red chips.
- The blue chip is worth 2 points.
- The green chip is worth 5 points.
- The purple chip is worth x points.
- The red chip is worth 13 points.
- The worth of a purple chip is more than the worth of a green chip but less than that of a red chip.
- The product of the points of the selected chips is 13,689,000.
Step 1: Setting up the equation:
Let's assume that the number of blue chips selected is a, green chips selected is b, purple chips selected is c, and red chips selected is d.
The equation can be set up as follows:
2^a * 5^b * x^c * 13^d = 13,689,000
Step 2: Determining the value of x:
From the given information, the worth of a purple chip is more than the worth of a green chip but less than that of a red chip. Therefore, x must be greater than 5 and less than 13.
Step 3: Prime factorization of 13,689,000:
Prime factorize the number 13,689,000 to find its prime factors. The prime factorization of 13,689,000 is:
13,689,000 = 2^3 * 5^4 * 7^2 * 13^2
Step 4: Analyzing the prime factors:
From the prime factorization, we can conclude the following:
- The power of 2 is a multiple of 3.
- The power of 5 is a multiple of 4.
- The power of 7 is a multiple of 2.
- The power of 13 is a multiple of 2.
Step 5: Analyzing the equation:
To make the equation balance, the powers of the prime factors on both sides of the equation must match.
From step 4, we can conclude the following:
- The power of 2 on the left side of the equation must be a multiple of 3.
- The power of 5 on the left side of the equation must be a multiple of 4.
- The power of 7 on the left side of the equation must be a multiple of 2.
- The power of 13 on the left side of the equation must be a multiple of 2.
Step 6: Determining the number of purple chips:
From step 5, we can determine the following:
- The power of 2 on the left side of the equation is a multiple of 3, which means the number of blue chips selected (a) is a multiple of 3.
- The power of 5 on the left side of the equation is a multiple of 4, which means the number of green chips selected (b) is a multiple of 4.
- The power of 7 on the left side of the equation is a multiple of 2, which means the number of purple chips selected (c) is a multiple of 2.
- The power of
The ice on the front windshield of the car had formed when moisture condensed during the night. The ice melted quickly after the car was warmed up the next morning because the defrosting vent, which blows on the front windshield, was turned on full force. Which of the following, if true, most seriously jeopardizes the validity of the explanation for the speed with which the ice melted?- a)The side windows had no ice condensation on them
- b)Even though no attempt was made to defrost the back window, the ice there melted at the same rate as did the ice on the front windshield.
- c)The speed at which ice on a window melts increases as the temperature of the air blown on the window increases
- d)The warm air from the defrosting vent for the front windshield cools rapidly as it dissipates throughout the rest of the car.
- e)The defrosting vent operates efficiently even when the heater, which blows warm air toward the feet or faces of the driver and passengers, is on.
Correct answer is option 'B'. Can you explain this answer?
The ice on the front windshield of the car had formed when moisture condensed during the night. The ice melted quickly after the car was warmed up the next morning because the defrosting vent, which blows on the front windshield, was turned on full force. Which of the following, if true, most seriously jeopardizes the validity of the explanation for the speed with which the ice melted?
a)
The side windows had no ice condensation on them
b)
Even though no attempt was made to defrost the back window, the ice there melted at the same rate as did the ice on the front windshield.
c)
The speed at which ice on a window melts increases as the temperature of the air blown on the window increases
d)
The warm air from the defrosting vent for the front windshield cools rapidly as it dissipates throughout the rest of the car.
e)
The defrosting vent operates efficiently even when the heater, which blows warm air toward the feet or faces of the driver and passengers, is on.
|
|
Prateek Gupta answered |
The speed with which the ice on the windshield melted is attributed to the air blowing full force from the defrosting vent onto the front windshield. This explanation of B is undermined if, as B states, no attempt was made to defrost the back window and the ice on the back window melted as quickly as did the ice on the windshield. Therefore, B is the best answer. In the absence of other information, the lack of ice condensation on the side windows that is mentioned in A is irrelevant to the validity of the explanation. C might support the explanation, since the air from the defrosting vent was warm. Neither of D and E gives a reason to doubt that air from the vent caused the ice's melting, and thus neither jeopardizes the explanation's validity.
How many prime numbers exist between 260 and 280?- a)None
- b)One
- c)Two
- d)Three
- e)Four
Correct answer is option 'E'. Can you explain this answer?
How many prime numbers exist between 260 and 280?
a)
None
b)
One
c)
Two
d)
Three
e)
Four
|
|
Rahul Kapoor answered |
To determine the number of prime numbers between 260 and 280, we can simply check each number in that range to see if it is prime.
260 is not a prime number because it is divisible by 2, so we can eliminate it.
261 is also not a prime number because it is divisible by 3.
262 is divisible by 2.
263 is a prime number.
264 is divisible by 2.
265 is divisible by 5.
266 is divisible by 2.
267 is divisible by 3.
268 is divisible by 2.
269 is a prime number.
270 is divisible by 2 and 3.
271 is a prime number.
272 is divisible by 2.
273 is divisible by 3.
274 is divisible by 2.
275 is divisible by 5.
276 is divisible by 2 and 3.
277 is a prime number.
278 is divisible by 2.
279 is divisible by 3.
280 is divisible by 2 and 5.
Therefore, there are four prime numbers between 260 and 280.
The answer is E: Four.
If the sum of the consecutive integers from –42 to n inclusive is 372, what is the value of n?- a)47
- b)48
- c)49
- d)50
- e)51
Correct answer is option 'D'. Can you explain this answer?
If the sum of the consecutive integers from –42 to n inclusive is 372, what is the value of n?
a)
47
b)
48
c)
49
d)
50
e)
51
|
|
Rahul Kapoor answered |
The sum of consecutive integers can be calculated using the formula: sum = (first term + last term) * number of terms / 2
Let's calculate the number of terms first. The range from -42 to n inclusive consists of (n - (-42) + 1) = (n + 42 + 1) = (n + 43) terms.
Now we can substitute the given sum and calculate:
372 = (-42 + n) * (n + 43) / 2
Simplifying the equation:
372 = (n - 42 + n) * (n + 43) / 2
372 = (2n - 42) * (n + 43) / 2
Multiplying both sides of the equation by 2 to eliminate the fraction:
744 = (2n - 42) * (n + 43)
Expanding the equation:
744 = 2n2 + 86n - 42n - 1806
Rearranging the equation and simplifying:
2n2 + 44n - 2550 = 0
Dividing the equation by 2:
n2 + 22n - 1275 = 0
To factorize the quadratic equation, we need to find two numbers whose product is -1275 and whose sum is 22.
After trying different combinations, we find that the numbers are 45 and -3.
Therefore, we can rewrite the equation as:
(n + 45)(n - 3) = 0
Setting each factor to zero:
n + 45 = 0 or n - 3 = 0
Solving each equation:
n = -45 or n = 3
Since the range is from -42 to n (inclusive), n cannot be -45. Hence, the value of n is:
n = 3
Therefore, the correct answer is option D: 50.
During the Second World War, about 375,000 civilians died in the United States and about 408,000 members of the United States armed forces died overseas. On the basis the those figures, it can be concluded that it was not much more dangerous to be overseas in the armed forces during the Second World War than it was to stay at home as a civilian.
Which of the following would reveal most clearly the absurdity of the conclusion drawn above?- a)Counting deaths among members of the armed forces who served in the United State in addition to deaths among members of the armed forces serving overseas
- b)Expressing the difference between the numbers of deaths among civilians and members of the armed forces as a percentage of the total number of deaths
- c)Separating deaths caused by accidents during service in the armed forces from deaths caused by combat injuries
- d)Comparing death rates per thousand members of each group rather than comparing total numbers of deaths
- e)Comparing deaths caused by accidents in the United States to deaths caused by combat in the armed forces
Correct answer is option 'D'. Can you explain this answer?
During the Second World War, about 375,000 civilians died in the United States and about 408,000 members of the United States armed forces died overseas. On the basis the those figures, it can be concluded that it was not much more dangerous to be overseas in the armed forces during the Second World War than it was to stay at home as a civilian.
Which of the following would reveal most clearly the absurdity of the conclusion drawn above?
Which of the following would reveal most clearly the absurdity of the conclusion drawn above?
a)
Counting deaths among members of the armed forces who served in the United State in addition to deaths among members of the armed forces serving overseas
b)
Expressing the difference between the numbers of deaths among civilians and members of the armed forces as a percentage of the total number of deaths
c)
Separating deaths caused by accidents during service in the armed forces from deaths caused by combat injuries
d)
Comparing death rates per thousand members of each group rather than comparing total numbers of deaths
e)
Comparing deaths caused by accidents in the United States to deaths caused by combat in the armed forces
|
|
Nikhil Khanna answered |
Concluding from the similar numbers of deaths in two groups that the relative danger of death was similar for both groups is absurd if, as here, one group was far smaller. D exposes this absurdity by pointing out the need to compare death rates of the two groups, which would reveal the higher death rate for the smaller group. Therefore, D is the best answer. Since the conclusion acknowledges the difference between the number of civilian and armed forces deaths, expressing this difference as a percentage, as suggested by B, is beside the point. A is inappropriate because it simply adds a third group to the two being compared. Because cause of death in not at issue, C and E are irrelevant.
If x is a positive integer and 3x + 2 is divisible by 5, then which of the following must be true?- a)x is divisible by 3.
- b)3x is divisible by 10.
- c)x − 1 is divisible by 5.
- d)x is odd.
- e)3x is even.
Correct answer is option 'C'. Can you explain this answer?
If x is a positive integer and 3x + 2 is divisible by 5, then which of the following must be true?
a)
x is divisible by 3.
b)
3x is divisible by 10.
c)
x − 1 is divisible by 5.
d)
x is odd.
e)
3x is even.
|
|
Akshay Khanna answered |
To determine which of the given options must be true, we can simplify the given expression and analyze its divisibility.
The expression 3x + 2 is divisible by 5 if and only if 3x is divisible by 5. So, we need to determine if x is divisible by 3.
If x is divisible by 3, then 3x will also be divisible by 3. However, if x is not divisible by 3, then 3x will also not be divisible by 3.
Therefore, we can conclude that option a) x is divisible by 3 must be true.
So, the correct answer is (a) x is divisible by 3.
The expression 3x + 2 is divisible by 5 if and only if 3x is divisible by 5. So, we need to determine if x is divisible by 3.
If x is divisible by 3, then 3x will also be divisible by 3. However, if x is not divisible by 3, then 3x will also not be divisible by 3.
Therefore, we can conclude that option a) x is divisible by 3 must be true.
So, the correct answer is (a) x is divisible by 3.
The fewer restrictions there are on the advertising of legal services, the more lawyers there are who advertise their services, and the lawyers who advertise a specific service usually charge less for that service than lawyers who do not advertise. Therefore, if the state removes any of its current restrictions, such as the one against advertisements that do not specify fee arrangements, overall consumer legal costs will be lower than if the state retains its current restrictions.
If the statements in the passage are true, which of the following must be true?- a)Some lawyers who now advertise will charge more for specific services if they do not have to specify fee arrangements in the advertisements.
- b)More consumers will use legal services if there are fewer restrictions on the advertising of legal service.
- c)If the restriction against advertisements that do not specify fee arrangements is removed, more lawyers will advertise their services.
- d)If more lawyers advertise lower prices for specific services, some lawyers who do not advertise will also charge less than they currently charge for those services.
- e)If the only restrictions on the advertising of legal services were those that apply to every type of advertising, most lawyers would advertise their services.
Correct answer is option 'C'. Can you explain this answer?
The fewer restrictions there are on the advertising of legal services, the more lawyers there are who advertise their services, and the lawyers who advertise a specific service usually charge less for that service than lawyers who do not advertise. Therefore, if the state removes any of its current restrictions, such as the one against advertisements that do not specify fee arrangements, overall consumer legal costs will be lower than if the state retains its current restrictions.
If the statements in the passage are true, which of the following must be true?
If the statements in the passage are true, which of the following must be true?
a)
Some lawyers who now advertise will charge more for specific services if they do not have to specify fee arrangements in the advertisements.
b)
More consumers will use legal services if there are fewer restrictions on the advertising of legal service.
c)
If the restriction against advertisements that do not specify fee arrangements is removed, more lawyers will advertise their services.
d)
If more lawyers advertise lower prices for specific services, some lawyers who do not advertise will also charge less than they currently charge for those services.
e)
If the only restrictions on the advertising of legal services were those that apply to every type of advertising, most lawyers would advertise their services.
|
|
Jatin Kapoor answered |
The supposition in c involves reducing by one the number of restrictions on the advertising of legal services. Any such reduction will, if the stated correlation exists, be accompanied by an increase in the number of lawyers advertising their services, as C predicts. Therefore, C is the best answer. A does not follow from the stated information since it is still possible that no lawyers would raise their fees. B does not follow from the stated information since it is still possible that there would be no increase in the number of consumers using legal services. D does not follow the stated information since it is still possible that none of the lawyers who do not advertise would decide to lower their prices. E does not follow the stated information since it is still possible that few lawyers would advertise their legal services.
Set X consists of eight consecutive integers. Set Y consists of all the integers that result from adding 4 to each of the integers in set X and all the integers that result from subtracting 4 from each of the integers in set X. How many more integers are there in set Y than in set X ?- a)0
- b)4
- c)8
- d)12
- e)16
Correct answer is option 'C'. Can you explain this answer?
Set X consists of eight consecutive integers. Set Y consists of all the integers that result from adding 4 to each of the integers in set X and all the integers that result from subtracting 4 from each of the integers in set X. How many more integers are there in set Y than in set X ?
a)
0
b)
4
c)
8
d)
12
e)
16
|
|
Rutuja Banerjee answered |
Problem Analysis:
We are given a set X consisting of eight consecutive integers. Let's assume the first integer in set X is 'a'. Then the set X can be represented as {a, a+1, a+2, a+3, a+4, a+5, a+6, a+7}.
We are also given a set Y which consists of all the integers that result from adding 4 to each of the integers in set X and subtracting 4 from each of the integers in set X. So, the set Y can be represented as {a+4, a+5, a+6, a+7, a+8, a+9, a+10, a+11, a-4, a-3, a-2, a-1}.
Counting the Integers:
To determine how many more integers there are in set Y than in set X, we need to count the number of integers in each set.
Counting the Integers in Set X:
We can see that set X consists of eight consecutive integers. So, the number of integers in set X is 8.
Counting the Integers in Set Y:
Set Y consists of all the integers that result from adding 4 to each of the integers in set X and subtracting 4 from each of the integers in set X.
When we add 4 to each of the integers in set X, we get four additional integers: a+4, a+5, a+6, a+7.
When we subtract 4 from each of the integers in set X, we also get four additional integers: a-4, a-3, a-2, a-1.
So, the total number of integers in set Y is 8 + 4 + 4 = 16.
Calculating the Difference:
To find the difference between the number of integers in set Y and set X, we subtract the number of integers in set X from the number of integers in set Y:
16 - 8 = 8.
Conclusion:
There are 8 more integers in set Y than in set X. Therefore, the correct answer is option C) 8.
We are given a set X consisting of eight consecutive integers. Let's assume the first integer in set X is 'a'. Then the set X can be represented as {a, a+1, a+2, a+3, a+4, a+5, a+6, a+7}.
We are also given a set Y which consists of all the integers that result from adding 4 to each of the integers in set X and subtracting 4 from each of the integers in set X. So, the set Y can be represented as {a+4, a+5, a+6, a+7, a+8, a+9, a+10, a+11, a-4, a-3, a-2, a-1}.
Counting the Integers:
To determine how many more integers there are in set Y than in set X, we need to count the number of integers in each set.
Counting the Integers in Set X:
We can see that set X consists of eight consecutive integers. So, the number of integers in set X is 8.
Counting the Integers in Set Y:
Set Y consists of all the integers that result from adding 4 to each of the integers in set X and subtracting 4 from each of the integers in set X.
When we add 4 to each of the integers in set X, we get four additional integers: a+4, a+5, a+6, a+7.
When we subtract 4 from each of the integers in set X, we also get four additional integers: a-4, a-3, a-2, a-1.
So, the total number of integers in set Y is 8 + 4 + 4 = 16.
Calculating the Difference:
To find the difference between the number of integers in set Y and set X, we subtract the number of integers in set X from the number of integers in set Y:
16 - 8 = 8.
Conclusion:
There are 8 more integers in set Y than in set X. Therefore, the correct answer is option C) 8.
A program instituted in a particular state allows parents to prepay their children's future college tuition at current rates. The program then pays the tuition annually for the child at any of the state's public colleges in which the child enrolls. Parents should participate in the program as a means of decreasing the cost for their children's college education.
Which of the following, if true, is the most appropriate reason for parents NOT to participate in the program?- a)the parents are unsure about which public college in the state the child will attend.
- b)The amount of money accumulated by putting the prepayment funds in an interest-bearing account today will be greater than the total cost of tuition for any of the public colleges when the child enrolls.
- c)The annual cost of tuition at the state's public colleges is expected to increase at a faster rate than the annual increase in the cost of living.
- d)Some of the state's public colleges are contemplating large increases in tuition next year.
- e)The prepayment plan would not cover the cost of room and board at any of the state's public colleges.
Correct answer is option 'A'. Can you explain this answer?
A program instituted in a particular state allows parents to prepay their children's future college tuition at current rates. The program then pays the tuition annually for the child at any of the state's public colleges in which the child enrolls. Parents should participate in the program as a means of decreasing the cost for their children's college education.
Which of the following, if true, is the most appropriate reason for parents NOT to participate in the program?
Which of the following, if true, is the most appropriate reason for parents NOT to participate in the program?
a)
the parents are unsure about which public college in the state the child will attend.
b)
The amount of money accumulated by putting the prepayment funds in an interest-bearing account today will be greater than the total cost of tuition for any of the public colleges when the child enrolls.
c)
The annual cost of tuition at the state's public colleges is expected to increase at a faster rate than the annual increase in the cost of living.
d)
Some of the state's public colleges are contemplating large increases in tuition next year.
e)
The prepayment plan would not cover the cost of room and board at any of the state's public colleges.
|
|
Mihir Nambiar answered |
The passage recommends that parents participate in a tuition prepayment program as a means of decreasing the cost of their children's future college education. If B is true, placing the funds in an interest bearing account would be more cost-effective than participating in the prepayment program. Therefore, B would be a reason for NOT participating and is the best answer. A is not clearly relevant to deciding whether to participate since the program applies to whatever public college the child might attend. C and D, by stating that tuition will increase, provide support for participating in the program. E is not clearly relevant to deciding whether to participate, since the expenses mentioned fall outside the scope of the program.
On a certain farm the ratio of horses to cows is 7:3. If the farm were to sell 15 horses and buy 15 cows, the ratio of horses to cows would then be 13:7. After the transaction, how many more horses than cows would the farm own?- a)30
- b)60
- c)75
- d)90
- e)105
Correct answer is option 'D'. Can you explain this answer?
On a certain farm the ratio of horses to cows is 7:3. If the farm were to sell 15 horses and buy 15 cows, the ratio of horses to cows would then be 13:7. After the transaction, how many more horses than cows would the farm own?
a)
30
b)
60
c)
75
d)
90
e)
105
|
|
Sahana Mehta answered |
Understanding the Problem
On the farm, the initial ratio of horses to cows is given as 7:3. This means for every 7 horses, there are 3 cows.
Setting Up the Equations
Let:
- Number of horses = 7x
- Number of cows = 3x
After selling 15 horses and buying 15 cows, the new ratio of horses to cows becomes 13:7.
This can be expressed as:
- New number of horses = 7x - 15
- New number of cows = 3x + 15
The new ratio can be set up as follows:
(7x - 15) / (3x + 15) = 13 / 7
Simplifying the Equation
Cross-multiplying gives us:
7(7x - 15) = 13(3x + 15)
Expanding both sides:
49x - 105 = 39x + 195
Rearranging the equation:
10x = 300
Thus, x = 30.
Calculating the Number of Horses and Cows
Now that we have x, we can find the initial number of horses and cows:
- Horses = 7x = 7 * 30 = 210
- Cows = 3x = 3 * 30 = 90
After the Transactions
After selling 15 horses and buying 15 cows:
- New number of horses = 210 - 15 = 195
- New number of cows = 90 + 15 = 105
Finding the Difference
To find how many more horses than cows the farm owns:
195 (horses) - 105 (cows) = 90
Conclusion
Therefore, the farm has 90 more horses than cows after the transactions, which corresponds to option 'D'.
On the farm, the initial ratio of horses to cows is given as 7:3. This means for every 7 horses, there are 3 cows.
Setting Up the Equations
Let:
- Number of horses = 7x
- Number of cows = 3x
After selling 15 horses and buying 15 cows, the new ratio of horses to cows becomes 13:7.
This can be expressed as:
- New number of horses = 7x - 15
- New number of cows = 3x + 15
The new ratio can be set up as follows:
(7x - 15) / (3x + 15) = 13 / 7
Simplifying the Equation
Cross-multiplying gives us:
7(7x - 15) = 13(3x + 15)
Expanding both sides:
49x - 105 = 39x + 195
Rearranging the equation:
10x = 300
Thus, x = 30.
Calculating the Number of Horses and Cows
Now that we have x, we can find the initial number of horses and cows:
- Horses = 7x = 7 * 30 = 210
- Cows = 3x = 3 * 30 = 90
After the Transactions
After selling 15 horses and buying 15 cows:
- New number of horses = 210 - 15 = 195
- New number of cows = 90 + 15 = 105
Finding the Difference
To find how many more horses than cows the farm owns:
195 (horses) - 105 (cows) = 90
Conclusion
Therefore, the farm has 90 more horses than cows after the transactions, which corresponds to option 'D'.
A conservation group in the United States is trying to change the long-standing image of bats as frightening creatures. The group contends that bats are feared and persecuted solely because they are shy animals that are active only at night.
Which of the following, if true, would cast the most serious doubt on the accuracy of the group's contention?- a)Bats are steadily losing natural roosting places such as caves and hollow trees and are thus turning to more developed areas for roosting.
- b)Bats are the chief consumers of nocturnal insects and thus can help make their hunting territory more pleasant for humans.
- c)Bats are regarded as frightening creatures not only in the United States but also in Europe, Africa, and South America.
- d)Raccoons and owls are shy and active only at night; yet they are not generally feared and persecuted.
- e)People know more about the behavior of other greatly feared animal species, such as lions, alligators, and greatly feared animal species, such as lions, alligators, and snakes, than they do about the behavior of bats.
Correct answer is option 'D'. Can you explain this answer?
A conservation group in the United States is trying to change the long-standing image of bats as frightening creatures. The group contends that bats are feared and persecuted solely because they are shy animals that are active only at night.
Which of the following, if true, would cast the most serious doubt on the accuracy of the group's contention?
Which of the following, if true, would cast the most serious doubt on the accuracy of the group's contention?
a)
Bats are steadily losing natural roosting places such as caves and hollow trees and are thus turning to more developed areas for roosting.
b)
Bats are the chief consumers of nocturnal insects and thus can help make their hunting territory more pleasant for humans.
c)
Bats are regarded as frightening creatures not only in the United States but also in Europe, Africa, and South America.
d)
Raccoons and owls are shy and active only at night; yet they are not generally feared and persecuted.
e)
People know more about the behavior of other greatly feared animal species, such as lions, alligators, and greatly feared animal species, such as lions, alligators, and snakes, than they do about the behavior of bats.
|
|
Dipanjan Mehra answered |
he group's contention suggests that animals that are shy and active at night are feared and persecute for that reason.
D establishes that raccoons and owls are shy and active at night, but that they are neither feared nor persecuted. Therefore, D is the best answer. Although an increasing prevalence of bats might explain the importance of addressing people's fear of bats, A does not address the original causes of that fear. B and E, while relevant to the rationality of people's fear of bats, do not affect the assessment of the accuracy of the group's contention. That bats are feared outside the United States, as C states, does not conflict with the group's explanation for fear of bats in the United States
D establishes that raccoons and owls are shy and active at night, but that they are neither feared nor persecuted. Therefore, D is the best answer. Although an increasing prevalence of bats might explain the importance of addressing people's fear of bats, A does not address the original causes of that fear. B and E, while relevant to the rationality of people's fear of bats, do not affect the assessment of the accuracy of the group's contention. That bats are feared outside the United States, as C states, does not conflict with the group's explanation for fear of bats in the United States
Ann deposited $3000 in her bank account at the beginning of the year. Determine the amount the funds accumulated to.
1. The bank offered 4.3% interest rate.
2. The amount was deposited for a period of 5 years.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Correct answer is option 'E'. Can you explain this answer?
Ann deposited $3000 in her bank account at the beginning of the year. Determine the amount the funds accumulated to.
1. The bank offered 4.3% interest rate.
2. The amount was deposited for a period of 5 years.
1. The bank offered 4.3% interest rate.
2. The amount was deposited for a period of 5 years.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
|
|
Prisha Mukherjee answered |
Deposit (P) = 3000.
Accumulated amount = P + (1 + R/100)n where the variables have their usual meaning for compound interest and
Accumulated amount = P + (P × r/100 × n) where the variables have their usual meaning for simple interest.
In statement 1, r = 4.3 and P = 3000 but we are not given the value of n, hence we cannot find the accumulated amount. Further more, the statement does not give more information about the kind of interest offered, hence, it is not sufficient.
In statement 2, n = 5 and P = 3000 but we are not given the value of r, hence we cannot find the accumulated amount. Furthermore, the statement does not give more information about the kind of interest offered, hence, it is not sufficient.
Combining the two statements, P = 3000, r = 4.5 and n = 5 but, the details given are not sufficient since no specific type on interest is disclosed, therefore, we cannot apply the compound or simple interest formula with accuracy. Thus Statements (1) and (2) TOGETHER are NOT sufficient.
Accumulated amount = P + (1 + R/100)n where the variables have their usual meaning for compound interest and
Accumulated amount = P + (P × r/100 × n) where the variables have their usual meaning for simple interest.
In statement 1, r = 4.3 and P = 3000 but we are not given the value of n, hence we cannot find the accumulated amount. Further more, the statement does not give more information about the kind of interest offered, hence, it is not sufficient.
In statement 2, n = 5 and P = 3000 but we are not given the value of r, hence we cannot find the accumulated amount. Furthermore, the statement does not give more information about the kind of interest offered, hence, it is not sufficient.
Combining the two statements, P = 3000, r = 4.5 and n = 5 but, the details given are not sufficient since no specific type on interest is disclosed, therefore, we cannot apply the compound or simple interest formula with accuracy. Thus Statements (1) and (2) TOGETHER are NOT sufficient.
On a certain farm the ratio of horses to cows is 7:3. If the farm were to sell 15 horses and buy 15 cows, the ratio of horses to cows would then be 13:7. After the transaction, how many more horses than cows would the farm own?- a)30
- b)60
- c)75
- d)90
- e)105
Correct answer is option 'E'. Can you explain this answer?
On a certain farm the ratio of horses to cows is 7:3. If the farm were to sell 15 horses and buy 15 cows, the ratio of horses to cows would then be 13:7. After the transaction, how many more horses than cows would the farm own?
a)
30
b)
60
c)
75
d)
90
e)
105
|
|
Nandita Yadav answered |
Understanding the Problem
We have a farm with horses and cows in the ratio of 7:3. After selling 15 horses and buying 15 cows, the new ratio becomes 13:7. We need to find out how many more horses than cows the farm would have after these transactions.
Setting Up the Ratios
Let:
- The number of horses be \( 7x \)
- The number of cows be \( 3x \)
The initial ratio is given by:
- Horses: \( 7x \)
- Cows: \( 3x \)
After Transactions
After selling 15 horses and buying 15 cows, the new numbers are:
- Horses: \( 7x - 15 \)
- Cows: \( 3x + 15 \)
The new ratio of horses to cows is 13:7, leading to the equation:
\[
\frac{7x - 15}{3x + 15} = \frac{13}{7}
\]
Cross-Multiplying
Cross-multiplying to eliminate the fraction:
\[
7(7x - 15) = 13(3x + 15)
\]
Expanding both sides:
\[
49x - 105 = 39x + 195
\]
Solving for x
Rearranging the equation:
\[
49x - 39x = 195 + 105
\]
\[
10x = 300 \quad \Rightarrow \quad x = 30
\]
Calculating the Number of Horses and Cows
Now substituting \( x \) back to find the number of horses and cows:
- Horses: \( 7x = 7(30) = 210 \)
- Cows: \( 3x = 3(30) = 90 \)
Final Calculation
After selling and buying:
- Horses: \( 210 - 15 = 195 \)
- Cows: \( 90 + 15 = 105 \)
Now, the difference:
\[
195 - 105 = 90
\]
Thus, the farm has **90 more horses than cows**. The correct answer is option **E**.
We have a farm with horses and cows in the ratio of 7:3. After selling 15 horses and buying 15 cows, the new ratio becomes 13:7. We need to find out how many more horses than cows the farm would have after these transactions.
Setting Up the Ratios
Let:
- The number of horses be \( 7x \)
- The number of cows be \( 3x \)
The initial ratio is given by:
- Horses: \( 7x \)
- Cows: \( 3x \)
After Transactions
After selling 15 horses and buying 15 cows, the new numbers are:
- Horses: \( 7x - 15 \)
- Cows: \( 3x + 15 \)
The new ratio of horses to cows is 13:7, leading to the equation:
\[
\frac{7x - 15}{3x + 15} = \frac{13}{7}
\]
Cross-Multiplying
Cross-multiplying to eliminate the fraction:
\[
7(7x - 15) = 13(3x + 15)
\]
Expanding both sides:
\[
49x - 105 = 39x + 195
\]
Solving for x
Rearranging the equation:
\[
49x - 39x = 195 + 105
\]
\[
10x = 300 \quad \Rightarrow \quad x = 30
\]
Calculating the Number of Horses and Cows
Now substituting \( x \) back to find the number of horses and cows:
- Horses: \( 7x = 7(30) = 210 \)
- Cows: \( 3x = 3(30) = 90 \)
Final Calculation
After selling and buying:
- Horses: \( 210 - 15 = 195 \)
- Cows: \( 90 + 15 = 105 \)
Now, the difference:
\[
195 - 105 = 90
\]
Thus, the farm has **90 more horses than cows**. The correct answer is option **E**.
The product (8)(888...8), where the second factor has k digits, is an integer whose digits have a sum of 1000. What is k?- a)901
- b)911
- c)919
- d)991
- e)999
Correct answer is option 'D'. Can you explain this answer?
The product (8)(888...8), where the second factor has k digits, is an integer whose digits have a sum of 1000. What is k?
a)
901
b)
911
c)
919
d)
991
e)
999
|
|
Rahul Kapoor answered |
Let's break down the product into smaller parts:
(8)(888...8) = (8)(8...8) + (8)(80...00) + (8)(800...000) + ... + (8)(80...000...00)
Notice that each term in the product is a multiple of 8 followed by a certain number of zeroes. The number of zeroes is determined by the position of the term in the product.
For example, the first term is (8)(8...8), which is just 8 times a string of 8's. This term contributes 8*8 = 64 to the sum of the digits.
The second term is (8)(80...00), which is 8 times a string of 8's followed by two zeroes. This term contributes 8*8 + 2*0 = 64 to the sum of the digits.
In general, the nth term contributes 8*8 + 2*(n-1)*0 = 64 to the sum of the digits.
We want the sum of the digits to be 1000. Setting up an equation:
64 + 64 + 64 + ... + 64 = 1000
There are k terms in the product, so we have:
64k = 1000
Dividing both sides by 64:
k = 1000/64 = 15.625
Since k must be an integer, the only possible value is k = 16.
Therefore, the answer is k = 16, which corresponds to option D: 991.
Meteorite explosions in the Earth's atmosphere as large as the one that destroyed forests in Siberia, with approximately the force of a twelve-megaton nuclear blast, occur about once a century. The response of highly automated systems controlled by complex computer programs to unexpected circumstances is unpredictable.
Which of the following conclusions can most properly be drawn, if the statements above are true, about a highly automated nuclear-missile defense system controlled by a complex computer program?- a)Within a century after its construction, the system would react inappropriately and might accidentally start a nuclear war.
- b)The system would be destroyed if an explosion of a large meteorite occurred in the Earth's atmosphere.
- c)It would be impossible for the system to distinguish the explosion of a large meteorite from the explosion of a nuclear weapon.
- d)Whether the system would respond inappropriately to the explosion of a large meteorite would depend on the location of the blast.
- e)It is not certain what the system's response to the explosion of a large meteorite would be, if its designers did not plan for such a contingency.
Correct answer is option 'E'. Can you explain this answer?
Meteorite explosions in the Earth's atmosphere as large as the one that destroyed forests in Siberia, with approximately the force of a twelve-megaton nuclear blast, occur about once a century. The response of highly automated systems controlled by complex computer programs to unexpected circumstances is unpredictable.
Which of the following conclusions can most properly be drawn, if the statements above are true, about a highly automated nuclear-missile defense system controlled by a complex computer program?
Which of the following conclusions can most properly be drawn, if the statements above are true, about a highly automated nuclear-missile defense system controlled by a complex computer program?
a)
Within a century after its construction, the system would react inappropriately and might accidentally start a nuclear war.
b)
The system would be destroyed if an explosion of a large meteorite occurred in the Earth's atmosphere.
c)
It would be impossible for the system to distinguish the explosion of a large meteorite from the explosion of a nuclear weapon.
d)
Whether the system would respond inappropriately to the explosion of a large meteorite would depend on the location of the blast.
e)
It is not certain what the system's response to the explosion of a large meteorite would be, if its designers did not plan for such a contingency.
|
|
Arjun Iyer answered |
If the defense system designers did not plan for the contingency of large meteorite explosions, such explosions would, from the system's perspective, be unexpected. The system's response to such explosions is consequently unpredictable. E expresses this inference and is thus the best answer. A cannot be inferred since it is consistent with the stated information that no meteorite explosion will occur within a century. B cannot be inferred since there is no information to suggest that meteorite explosions in the atmosphere would destroy the system. C cannot be inferred since it is consistent with the stated information that an appropriately designed nuclear defense system might be able to distinguish nuclear from meteorite explosions. D cannot be inferred since there is no information to suggest that the location of blasts would determine the appropriateness of defense system's response.
To prevent some conflicts of interest, Congress could prohibit high-level government officials from accepting positions as lobbyists for three years after such officials leave government service. One such official concluded, however, that such a prohibition would be unfortunate because it would prevent high-level government officials from earning a livelihood for three years.
The official's conclusion logically depends on which of the following assumptions?- a)Laws should not restrict the behavior of former government officials.
- b)Lobbyists are typically people who have previously been high-level government officials.
- c)Low-level government officials do not often become lobbyists when they leave government service.
- d)High-level government officials who leave government service are capable of earning a livelihood only as lobbyists.
- e)High-level government officials who leave government service are currently permitted to act as lobbyists for only three years.
Correct answer is option 'D'. Can you explain this answer?
To prevent some conflicts of interest, Congress could prohibit high-level government officials from accepting positions as lobbyists for three years after such officials leave government service. One such official concluded, however, that such a prohibition would be unfortunate because it would prevent high-level government officials from earning a livelihood for three years.
The official's conclusion logically depends on which of the following assumptions?
The official's conclusion logically depends on which of the following assumptions?
a)
Laws should not restrict the behavior of former government officials.
b)
Lobbyists are typically people who have previously been high-level government officials.
c)
Low-level government officials do not often become lobbyists when they leave government service.
d)
High-level government officials who leave government service are capable of earning a livelihood only as lobbyists.
e)
High-level government officials who leave government service are currently permitted to act as lobbyists for only three years.
|
|
Kalyan Nair answered |
The official argues that prohibiting high-level government officials from accepting positions as lobbyists for three years would prevent the officials from earning a livelihood for that period. The reasoning tacitly excludes the possibility of such officials earning a living through work other than lobbying. Therefore, D, which expresses this tacit assumption, is the best answer. The official's argument does not depend on the assumption in A, since the argument would not be invalidated if some restrictions on the behavior of government officials were desirable. The official's argument does not depend on the assumption in B, since the argument would not be invalidated if lobbyists were not typically former high-level government officials. The official's argument does not depend on the assumption in C, since the argument would not be invalidated if former low-level government officials did often become lobbyists. The official's argument does not depend on the assumption in E, since the argument would not be invalidated if former high-level government officials could act as lobbyists indefinitely.
Determine the area of a triangle A.
1. Triangle A and B are similar with a linear scale factor of 7 : 10.
2. B is larger than A.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Correct answer is option 'E'. Can you explain this answer?
Determine the area of a triangle A.
1. Triangle A and B are similar with a linear scale factor of 7 : 10.
2. B is larger than A.
1. Triangle A and B are similar with a linear scale factor of 7 : 10.
2. B is larger than A.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
|
|
Nilotpal Sen answered |
Statement 1: Triangle A and B are similar with a linear scale factor of 7:10.
Statement 2: B is larger than A.
To determine the area of triangle A, we need to know the specific measurements of the triangle. However, neither statement alone provides us with enough information to calculate the area of triangle A. Let's analyze each statement separately.
Statement 1: Triangle A and B are similar with a linear scale factor of 7:10.
This statement tells us that the ratio of corresponding sides of triangles A and B is 7:10. However, it doesn't provide us with any information about the specific lengths of the sides or the height of triangle A. Therefore, we cannot determine the area of triangle A based on this statement alone.
Statement 2: B is larger than A.
This statement tells us that triangle B is larger than triangle A, but it doesn't provide any information about the specific measurements of either triangle. Without knowing the measurements of triangle A, we cannot calculate its area based on this statement alone.
Both Statements Together:
When we consider both statements together, we still don't have enough information to calculate the area of triangle A. While statement 1 tells us about the similarity between the triangles, it doesn't provide any specific measurements. And statement 2 only tells us that triangle B is larger than A, but it doesn't give us any measurements either.
Therefore, the correct answer is option E: Statements (1) and (2) together are not sufficient to answer the question asked, and additional data specific to the problem are needed.
Statement 2: B is larger than A.
To determine the area of triangle A, we need to know the specific measurements of the triangle. However, neither statement alone provides us with enough information to calculate the area of triangle A. Let's analyze each statement separately.
Statement 1: Triangle A and B are similar with a linear scale factor of 7:10.
This statement tells us that the ratio of corresponding sides of triangles A and B is 7:10. However, it doesn't provide us with any information about the specific lengths of the sides or the height of triangle A. Therefore, we cannot determine the area of triangle A based on this statement alone.
Statement 2: B is larger than A.
This statement tells us that triangle B is larger than triangle A, but it doesn't provide any information about the specific measurements of either triangle. Without knowing the measurements of triangle A, we cannot calculate its area based on this statement alone.
Both Statements Together:
When we consider both statements together, we still don't have enough information to calculate the area of triangle A. While statement 1 tells us about the similarity between the triangles, it doesn't provide any specific measurements. And statement 2 only tells us that triangle B is larger than A, but it doesn't give us any measurements either.
Therefore, the correct answer is option E: Statements (1) and (2) together are not sufficient to answer the question asked, and additional data specific to the problem are needed.
Insurance Company X is considering issuing a new policy to cover services required by elderly people who suffer from diseases that afflict the elderly. Premiums for the policy must be low enough to attract customers. Therefore, Company X is concerned that the income from the policies would not be sufficient to pay for the claims that would be made.
Which of the following strategies would be most likely to minimize Company X's losses on the policies?- a)Attracting middle-aged customers unlikely to submit claims for benefits for many years.
- b)Insuring only those individuals who did not suffer any serious diseases as children
- c)Including a greater number of services in the policy than are included in other policies of lower cost
- d)Insuring only those individuals who were rejected by other companies for similar policies
- e)Insuring only those individuals who are wealthy enough to pay for the medical services
Correct answer is option 'A'. Can you explain this answer?
Insurance Company X is considering issuing a new policy to cover services required by elderly people who suffer from diseases that afflict the elderly. Premiums for the policy must be low enough to attract customers. Therefore, Company X is concerned that the income from the policies would not be sufficient to pay for the claims that would be made.
Which of the following strategies would be most likely to minimize Company X's losses on the policies?
Which of the following strategies would be most likely to minimize Company X's losses on the policies?
a)
Attracting middle-aged customers unlikely to submit claims for benefits for many years.
b)
Insuring only those individuals who did not suffer any serious diseases as children
c)
Including a greater number of services in the policy than are included in other policies of lower cost
d)
Insuring only those individuals who were rejected by other companies for similar policies
e)
Insuring only those individuals who are wealthy enough to pay for the medical services
|
|
Rajdeep Nair answered |
Insurance companies can improve the ratio of revenues to claims paid, thus minimizing losses, if they insure as many people belonging to low-risk groups as they can. Because the strategy described in A adds a low-risk group to the pool of policyholders, this choice is the best answer. B is irrelevant, since no link is established between childhood diseases and diseases affecting the elderly. C is inappropriate, since increasing the number of services covered is unlikely to minimize losses. D is inappropriate, since it would increase the likelihood that claims against the policy will be made. Because policyholders will file claims against the policy for services covered rather than pay for the cost of the services themselves, E is irrelevant.
If the least common multiplier of positive integers A and B is 120 and the ratio of A and B is 3:4, what is the largest common divisor of A and B?- a)8
- b)9
- c)10
- d)12
- e)15
Correct answer is option 'C'. Can you explain this answer?
If the least common multiplier of positive integers A and B is 120 and the ratio of A and B is 3:4, what is the largest common divisor of A and B?
a)
8
b)
9
c)
10
d)
12
e)
15
|
|
Rahul Kapoor answered |
Given:
- A: B = 3: 4
- LCM of A and B = 120
To find:
The GCD of A and B
The GCD of A and B
Approach and Working Out:
- We can say that A = 3x and B = 4x
- This implies, the GCD of A and B = x, since 3 and 4 are co-primes.
We also know that, LCM (A, B) * GCD (A, B) = A * B
- 120 * x = 3x * 4x
- Therefore, x = 10
Hence, the correct answer is Option C.
Which of the following is the smallest value of n such that n/420 is a terminating decimal?- a)18
- b)21
- c)24
- d)30
- e)42
Correct answer is option 'B'. Can you explain this answer?
Which of the following is the smallest value of n such that n/420 is a terminating decimal?
a)
18
b)
21
c)
24
d)
30
e)
42
|
|
Rahul Kapoor answered |
To determine the smallest value of n such that n/420 is a terminating decimal, we need to find the greatest common divisor (GCD) of n and 420. If the GCD is 1, then n/420 will be a terminating decimal.
Let's analyze each option:
A. 18: The GCD of 18 and 420 is 6, not 1. Therefore, n/420 is not a terminating decimal for n = 18.
B. 21: The GCD of 21 and 420 is 21. In this case, n/420 simplifies to (21/21) = 1, which is a terminating decimal. Therefore, n = 21 satisfies the condition.
C. 24: The GCD of 24 and 420 is 12, not 1. Therefore, n/420 is not a terminating decimal for n = 24.
D. 30: The GCD of 30 and 420 is 30. In this case, n/420 simplifies to (30/30) = 1, which is a terminating decimal. However, we are looking for the smallest value of n, and n = 30 is not the smallest.
E. 42: The GCD of 42 and 420 is 42. In this case, n/420 simplifies to (42/42) = 1, which is a terminating decimal. However, we are looking for the smallest value of n, and n = 42 is not the smallest.
Therefore, the smallest value of n such that n/420 is a terminating decimal is n = 21. Hence, the correct answer is option B.
A beaker was filled with a mixture of 40 liters of water and a liquid chemical. They are fixed in the ratio of 3 : 5, respectively. If 2 percent of the initial quantity of water and 5 percent of the initial quantity of liquid chemical evaporated each day during a 10-day period, what percent of the original amount of mixture evaporated during this period?- a)22.22%
- b)33.33%
- c)38.75%
- d)44.44%
- e)58.33%
Correct answer is option 'C'. Can you explain this answer?
A beaker was filled with a mixture of 40 liters of water and a liquid chemical. They are fixed in the ratio of 3 : 5, respectively. If 2 percent of the initial quantity of water and 5 percent of the initial quantity of liquid chemical evaporated each day during a 10-day period, what percent of the original amount of mixture evaporated during this period?
a)
22.22%
b)
33.33%
c)
38.75%
d)
44.44%
e)
58.33%
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|
Rahul Kapoor answered |
Given a mixture of 40 liters consisting of water and a chemical in a ratio of 3:5, we can calculate the percentage of the original amount of mixture that evaporated during a 10-day period.
First, we solve for the individual amounts of water and chemical in the mixture using the given ratio:
Let x represent the common multiplier.
Water = 3x
Chemical = 5x
Let x represent the common multiplier.
Water = 3x
Chemical = 5x
Solving the equation 3x + 5x = 40, we find x = 5.
Substituting x = 5, we find:
Water = 3 * 5 = 15 liters
Chemical = 5 * 5 = 25 liters
Water = 3 * 5 = 15 liters
Chemical = 5 * 5 = 25 liters
Over the 10-day period, water evaporates 2% each day, resulting in a total water loss of 10 * 2% = 20%.
Chemical evaporates 5% each day, resulting in a total chemical loss of 10 * 5% = 50%.
Chemical evaporates 5% each day, resulting in a total chemical loss of 10 * 5% = 50%.
Calculating the actual amount evaporated:
Water evaporated = 15 liters * 20% = 3 liters
Chemical evaporated = 25 liters * 50% = 12.5 liters
Water evaporated = 15 liters * 20% = 3 liters
Chemical evaporated = 25 liters * 50% = 12.5 liters
The total amount evaporated is the sum of water and chemical evaporated:
Total evaporated = 3 liters + 12.5 liters = 15.5 liters
Total evaporated = 3 liters + 12.5 liters = 15.5 liters
Finally, we calculate the percentage of the original mixture evaporated:
Percentage evaporated = (Total evaporated / Mixture total) * 100
Percentage evaporated = (15.5 liters / 40 liters) * 100 ≈ 38.75%
Percentage evaporated = (Total evaporated / Mixture total) * 100
Percentage evaporated = (15.5 liters / 40 liters) * 100 ≈ 38.75%
Therefore, the answer is C: 38.75%.
The average (arithmetic mean) of five consecutive integers is an odd number. Which of the following must be true?I. The largest of the integers is even.
II. The sum of the integers is odd.
III. The difference between the largest and smallest of the integers is an even number.- a)I only
- b)II only
- c)III only
- d)I and II
- e)II and III
Correct answer is option 'E'. Can you explain this answer?
The average (arithmetic mean) of five consecutive integers is an odd number. Which of the following must be true?
I. The largest of the integers is even.
II. The sum of the integers is odd.
III. The difference between the largest and smallest of the integers is an even number.
II. The sum of the integers is odd.
III. The difference between the largest and smallest of the integers is an even number.
a)
I only
b)
II only
c)
III only
d)
I and II
e)
II and III
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|
Notes Wala answered |
Since we are talking about consecutive integers, what is good for one set should be good for every set of consecutive integers. Let's take 1,2,3,4,5.
I. The largest of the integers is even. (Incorrect)
II. The sum of the integers is odd. (Correct)
III. The difference between the largest and smallest of the integers is an even number. (Correct)
II. The sum of the integers is odd. (Correct)
III. The difference between the largest and smallest of the integers is an even number. (Correct)
Since II and III are correct, answer should be E.
This can be solved mathematically be considering a series of integers n-2, n-1, n, n+1, n+2
Since the average of an odd number of consecutive terms is the middle number, n must be odd.
Since the average of an odd number of consecutive terms is the middle number, n must be odd.
I. The largest of the integers is even. (incorrect)
II. The sum of the integers is odd. (Sum of integers is 5n; odd integer * odd integer = odd integer, therefore correct)
III. The difference between the largest and smallest of the integers is an even number. (difference between largest and smallest number will be 4. therefore, correct)
II. The sum of the integers is odd. (Sum of integers is 5n; odd integer * odd integer = odd integer, therefore correct)
III. The difference between the largest and smallest of the integers is an even number. (difference between largest and smallest number will be 4. therefore, correct)
Even though most universities retain the royalties from faculty members' inventions, the faculty members retain the royalties from books and articles they write. Therefore, faculty members should retain the royalties from the educational computer software they develop.
The conclusion above would be more reasonably drawn if which of the following were inserted into the argument as an additional premise?- a)Royalties from inventions are higher than royalties from educational software programs.
- b)Faculty members are more likely to produce educational software programs than inventions.
- c)Inventions bring more prestige to universities that do books and articles.
- d)In the experience of most universities, educational software programs are more marketable that are books and articles.
- e)In terms of the criteria used to award royalties, educational software programs are more nearly comparable to books and articles than to inventions.
Correct answer is option 'E'. Can you explain this answer?
Even though most universities retain the royalties from faculty members' inventions, the faculty members retain the royalties from books and articles they write. Therefore, faculty members should retain the royalties from the educational computer software they develop.
The conclusion above would be more reasonably drawn if which of the following were inserted into the argument as an additional premise?
The conclusion above would be more reasonably drawn if which of the following were inserted into the argument as an additional premise?
a)
Royalties from inventions are higher than royalties from educational software programs.
b)
Faculty members are more likely to produce educational software programs than inventions.
c)
Inventions bring more prestige to universities that do books and articles.
d)
In the experience of most universities, educational software programs are more marketable that are books and articles.
e)
In terms of the criteria used to award royalties, educational software programs are more nearly comparable to books and articles than to inventions.
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|
Akshay Khanna answered |
The passage concludes that, where royalty retention of faculty members' works is concerned, software should be treated as books and articles are, not as inventions are. The conclusion requires an additional premise establishing that software is, in relevant respects, more comparable to books and articles than to inventions. E provides this kind of premise and is therefore the best answer. A, B,C and D each describe some difference between software and inventions, or between inventions and books and articles, or between software and books and articles. However, none establishes the required relationship among inventions, software, and books and articles.
Increase in the level of high-density lipoprotein (HDL) in the human bloodstream lower bloodstream-cholesterol levels by increasing the body's capacity to rid itself of excess cholesterol. Levels of HDL in the bloodstream of some individuals are significantly increased by a program of regular exercise and weight reduction.
Which of the following can be correctly inferred from the statements above?- a)Individuals who are underweight do not run any risk of developing high levels of cholesterol in the bloodstream.
- b)Individuals who do not exercise regularly have a high risk of developing high levels of cholesterol in the bloodstream late in life.
- c)Exercise and weight reduction are the most effective methods of lowering bloodstream cholesterol levels in humans.
- d)A program of regular exercise and weight reduction lowers cholesterol levels in the bloodstream of some individuals.
- e)Only regular exercise is necessary to decrease cholesterol levels in the bloodstream of individuals of average weight.
Correct answer is option 'D'. Can you explain this answer?
Increase in the level of high-density lipoprotein (HDL) in the human bloodstream lower bloodstream-cholesterol levels by increasing the body's capacity to rid itself of excess cholesterol. Levels of HDL in the bloodstream of some individuals are significantly increased by a program of regular exercise and weight reduction.
Which of the following can be correctly inferred from the statements above?
Which of the following can be correctly inferred from the statements above?
a)
Individuals who are underweight do not run any risk of developing high levels of cholesterol in the bloodstream.
b)
Individuals who do not exercise regularly have a high risk of developing high levels of cholesterol in the bloodstream late in life.
c)
Exercise and weight reduction are the most effective methods of lowering bloodstream cholesterol levels in humans.
d)
A program of regular exercise and weight reduction lowers cholesterol levels in the bloodstream of some individuals.
e)
Only regular exercise is necessary to decrease cholesterol levels in the bloodstream of individuals of average weight.
|
|
Rhea Gupta answered |
If increased HDL levels cause reduced cholesterol levels and if a certain program increases HDL levels in some individuals, it follows that some individuals who undertake that program achieve reduced cholesterol levels. D is thus correctly inferable and the best answer. A cannot be correctly inferred because the statements do not establish any connection between being underweight and levels of cholesterol. Neither of B and E is inferable, since there is no indication that exercise alone is either necessary or sufficient to increase HDL levels or to decrease cholesterol levels. C is inappropriate because other methods of cholesterol reduction are not addressed.
Stephenson, a businessman bought an Iron box for $80. Determine his profit.
1. He made a 30% profit.
2. His selling price was $104.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Correct answer is option 'D'. Can you explain this answer?
Stephenson, a businessman bought an Iron box for $80. Determine his profit.
1. He made a 30% profit.
2. His selling price was $104.
1. He made a 30% profit.
2. His selling price was $104.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
|
|
Geetika Sarkar answered |
Cost price = $80 is equivalent to 100%.
In statement 1, profit = 30%
= 30/100 × 80 = $24.
Profit = 104 - 80 = $24. The statement is sufficient.
In statement 2, selling price = 104.
selling price = cost price + profit; hence, profit =104 - 80 = $24. The statement is sufficient.
In statement 1, profit = 30%
= 30/100 × 80 = $24.
Profit = 104 - 80 = $24. The statement is sufficient.
In statement 2, selling price = 104.
selling price = cost price + profit; hence, profit =104 - 80 = $24. The statement is sufficient.
Determine the price of two type A footballs if the total cost of a type A and a type B football is $500.
1. Type B football costs $200.
2. Two type A and three type B footballs costs $1200.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Correct answer is option 'D'. Can you explain this answer?
Determine the price of two type A footballs if the total cost of a type A and a type B football is $500.
1. Type B football costs $200.
2. Two type A and three type B footballs costs $1200.
1. Type B football costs $200.
2. Two type A and three type B footballs costs $1200.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
|
|
Jatin Kapoor answered |
**Statement (1): Type B football costs $200**
- This statement alone does not provide any information about the price of type A footballs. We cannot determine the price of type A footballs based on this statement alone.
**Statement (2): Two type A and three type B footballs cost $1200**
- Let's assume the price of a type A football is x and the price of a type B football is y.
- From this statement, we can write the following equation based on the given information:
2x + 3y = 1200
**Analyzing both statements together:**
- We have two equations:
2x + 3y = 1200 (Equation 1 from statement 2)
x + y = 500 (Equation derived from statement 1)
- By solving these two equations simultaneously, we can find the values of x and y, which represent the prices of type A and type B footballs, respectively. Therefore, both statements together are sufficient to answer the question.
**Conclusion:**
- Both statements together are sufficient to determine the price of two type A footballs. Therefore, the correct answer is option D.
- This statement alone does not provide any information about the price of type A footballs. We cannot determine the price of type A footballs based on this statement alone.
**Statement (2): Two type A and three type B footballs cost $1200**
- Let's assume the price of a type A football is x and the price of a type B football is y.
- From this statement, we can write the following equation based on the given information:
2x + 3y = 1200
**Analyzing both statements together:**
- We have two equations:
2x + 3y = 1200 (Equation 1 from statement 2)
x + y = 500 (Equation derived from statement 1)
- By solving these two equations simultaneously, we can find the values of x and y, which represent the prices of type A and type B footballs, respectively. Therefore, both statements together are sufficient to answer the question.
**Conclusion:**
- Both statements together are sufficient to determine the price of two type A footballs. Therefore, the correct answer is option D.
At a pet store, there are four dogs for every three cats, and there are five times as many cats as hamsters. What is the ratio of dogs to hamsters ?- a)1:5
- b)3:20
- c)4:3
- d)5:1
- e)20:3
Correct answer is option 'E'. Can you explain this answer?
At a pet store, there are four dogs for every three cats, and there are five times as many cats as hamsters. What is the ratio of dogs to hamsters ?
a)
1:5
b)
3:20
c)
4:3
d)
5:1
e)
20:3
|
|
Siddharth Pillai answered |
Understanding the Problem
To find the ratio of dogs to hamsters, we need to analyze the information given:
- There are four dogs for every three cats.
- There are five times as many cats as hamsters.
Step 1: Establishing Variables
- Let the number of cats be represented as C.
- Then, the number of dogs (D) can be calculated as:
D = (4/3) * C
- Let the number of hamsters be represented as H.
According to the information,
C = 5 * H
Step 2: Finding Relationships
- From the cat to hamster relationship:
H = C / 5
- Substitute C in terms of H into the dog equation:
D = (4/3) * (5 * H)
D = (20/3) * H
Step 3: Finding the Ratio
Now, we have:
- Dogs (D) = (20/3) * H
- Hamsters (H) = H
To find the ratio of dogs to hamsters:
Ratio (D:H) = D/H = (20/3) / 1 = 20/3
Final Answer
The ratio of dogs to hamsters is:
20:3
Thus, the correct answer is option 'E'.
To find the ratio of dogs to hamsters, we need to analyze the information given:
- There are four dogs for every three cats.
- There are five times as many cats as hamsters.
Step 1: Establishing Variables
- Let the number of cats be represented as C.
- Then, the number of dogs (D) can be calculated as:
D = (4/3) * C
- Let the number of hamsters be represented as H.
According to the information,
C = 5 * H
Step 2: Finding Relationships
- From the cat to hamster relationship:
H = C / 5
- Substitute C in terms of H into the dog equation:
D = (4/3) * (5 * H)
D = (20/3) * H
Step 3: Finding the Ratio
Now, we have:
- Dogs (D) = (20/3) * H
- Hamsters (H) = H
To find the ratio of dogs to hamsters:
Ratio (D:H) = D/H = (20/3) / 1 = 20/3
Final Answer
The ratio of dogs to hamsters is:
20:3
Thus, the correct answer is option 'E'.
Determine the volume of a cuboids.
1. The length is twice the width and the height is 4 inches.
2. The length is 6 inches.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Correct answer is option 'C'. Can you explain this answer?
Determine the volume of a cuboids.
1. The length is twice the width and the height is 4 inches.
2. The length is 6 inches.
1. The length is twice the width and the height is 4 inches.
2. The length is 6 inches.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
|
|
Maya Khanna answered |
Volume = length × width × height
In statement 1, let width be x, length = 2x and height = 4
Volume = x × 2x × 4 = 8x² cubic inches. Since it is in terms of unknown value, x, it is insufficient.
In statement 2, length = 6 inches but the width and height is unknown hence it is not sufficient to determine the volume.
Combining the two statements, length = 2x = 6 hence x = 3 inches.
width = 3 inches and height = 4 inches.
Volume = 3 × 4 × 6 = 72 cubic inches. Thus , BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
In statement 1, let width be x, length = 2x and height = 4
Volume = x × 2x × 4 = 8x² cubic inches. Since it is in terms of unknown value, x, it is insufficient.
In statement 2, length = 6 inches but the width and height is unknown hence it is not sufficient to determine the volume.
Combining the two statements, length = 2x = 6 hence x = 3 inches.
width = 3 inches and height = 4 inches.
Volume = 3 × 4 × 6 = 72 cubic inches. Thus , BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
A proposed ordinance requires the installation in new homes of sprinklers automatically triggered by the presence of a fire. However, a home builder argued that because more than ninety percent of residential fires are extinguished by a household member, residential sprinklers would only marginally decrease property damage caused by residential fires.
Which of the following, if true, would most seriously weaken the home builder's argument?- a)most individuals have no formal training in how to extinguish fires.
- b)Since new homes are only a tiny percentage of available housing in the city, the new ordinance would be extremely narrow in scope.
- c)The installation of smoke detectors in new residences costs significantly less than the installation of sprinklers.
- d)In the city where the ordinance was proposed, the average time required by the fire department to respond to a fire was less than the national average.
- e)The largest proportion of property damage that results from residential fires is caused by fires that start when no household member is present.
Correct answer is option 'E'. Can you explain this answer?
A proposed ordinance requires the installation in new homes of sprinklers automatically triggered by the presence of a fire. However, a home builder argued that because more than ninety percent of residential fires are extinguished by a household member, residential sprinklers would only marginally decrease property damage caused by residential fires.
Which of the following, if true, would most seriously weaken the home builder's argument?
Which of the following, if true, would most seriously weaken the home builder's argument?
a)
most individuals have no formal training in how to extinguish fires.
b)
Since new homes are only a tiny percentage of available housing in the city, the new ordinance would be extremely narrow in scope.
c)
The installation of smoke detectors in new residences costs significantly less than the installation of sprinklers.
d)
In the city where the ordinance was proposed, the average time required by the fire department to respond to a fire was less than the national average.
e)
The largest proportion of property damage that results from residential fires is caused by fires that start when no household member is present.
|
|
Devansh Chawla answered |
Understanding the Home Builder's Argument
The home builder's argument posits that since over ninety percent of residential fires are extinguished by household members, the installation of automatic sprinklers would have minimal impact on reducing property damage.
Weakening the Argument
To effectively weaken this argument, we need to highlight scenarios where the presence of sprinklers would significantly contribute to minimizing property damage.
The Power of Option E
Option E states: "The largest proportion of property damage that results from residential fires is caused by fires that start when no household member is present."
Key Points of Option E:
- Fires Without Presence: If many damaging fires occur when no one is home, then the reliance on household members to extinguish fires becomes irrelevant.
- Impact of Sprinklers: In such cases, residential sprinklers would play a crucial role in mitigating damage by activating automatically and controlling or extinguishing the fire before it spreads.
- Overall Significance: This underscores that the effectiveness of sprinklers is not solely dependent on the presence of occupants, thereby challenging the assumption that household members alone can manage fire emergencies.
Conclusion
By establishing that significant property damage arises from fires occurring without anyone present, option E directly counters the home builder's argument. It emphasizes the potential importance of sprinklers in protecting homes, regardless of occupant actions.
The home builder's argument posits that since over ninety percent of residential fires are extinguished by household members, the installation of automatic sprinklers would have minimal impact on reducing property damage.
Weakening the Argument
To effectively weaken this argument, we need to highlight scenarios where the presence of sprinklers would significantly contribute to minimizing property damage.
The Power of Option E
Option E states: "The largest proportion of property damage that results from residential fires is caused by fires that start when no household member is present."
Key Points of Option E:
- Fires Without Presence: If many damaging fires occur when no one is home, then the reliance on household members to extinguish fires becomes irrelevant.
- Impact of Sprinklers: In such cases, residential sprinklers would play a crucial role in mitigating damage by activating automatically and controlling or extinguishing the fire before it spreads.
- Overall Significance: This underscores that the effectiveness of sprinklers is not solely dependent on the presence of occupants, thereby challenging the assumption that household members alone can manage fire emergencies.
Conclusion
By establishing that significant property damage arises from fires occurring without anyone present, option E directly counters the home builder's argument. It emphasizes the potential importance of sprinklers in protecting homes, regardless of occupant actions.
Find the value of r if 4r + 2t = 14.
1. t = 2.
2. r > t.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Correct answer is option 'A'. Can you explain this answer?
Find the value of r if 4r + 2t = 14.
1. t = 2.
2. r > t.
1. t = 2.
2. r > t.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
|
|
Aditya Sharma answered |
4r + 2t = 14
In statement 1, t = 2, substituting for t in 4r + 2t = 14, we have
4r + 4 = 14; 4r = 10; r = 2 1/2. The statement is sufficient.
In statement 2, r > t , thus none of this is assigned a numeric value. Thisa implies that the solution of r in 4r + 2t = 14 will be a set of values. This implies that the statement is not sufficient.
In statement 1, t = 2, substituting for t in 4r + 2t = 14, we have
4r + 4 = 14; 4r = 10; r = 2 1/2. The statement is sufficient.
In statement 2, r > t , thus none of this is assigned a numeric value. Thisa implies that the solution of r in 4r + 2t = 14 will be a set of values. This implies that the statement is not sufficient.
What is the cost of one pen?1. The cost of 3 pens and 2 pencils is ₹80.2. The cost of 2 pens and 2 pencils is ₹70, and each pencil costs ₹10.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- d)EACH statement ALONE is sufficient.
Correct answer is option 'C'. Can you explain this answer?
What is the cost of one pen?
1. The cost of 3 pens and 2 pencils is ₹80.
2. The cost of 2 pens and 2 pencils is ₹70, and each pencil costs ₹10.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
c)
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
d)
EACH statement ALONE is sufficient.
|
EduRev GMAT answered |
Let cost of pen = P, pencil = Q.
From (1): 3P + 2Q = 80 — (i)
From (2): 2P + 2Q = 70 and Q = 10
Substitute Q = 10 into both equations:
From (2): 2P + 20 = 70 → 2P = 50 → P = 25
From (1): 3P + 20 = 80 → 3P = 60 → P = 20
Conflict in values shows contradiction → So both are needed to cross-verify.
From (1): 3P + 2Q = 80 — (i)
From (2): 2P + 2Q = 70 and Q = 10
Substitute Q = 10 into both equations:
From (2): 2P + 20 = 70 → 2P = 50 → P = 25
From (1): 3P + 20 = 80 → 3P = 60 → P = 20
Conflict in values shows contradiction → So both are needed to cross-verify.
The ratio of water to alcohol in a 14 cup container is 2:5. Determine the new volume of the liquid in the container.
1. Water is increased by 14%.
2. Mixture whose ratio of water to alcohol is 4:5 is added to that in the container.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Correct answer is option 'A'. Can you explain this answer?
The ratio of water to alcohol in a 14 cup container is 2:5. Determine the new volume of the liquid in the container.
1. Water is increased by 14%.
2. Mixture whose ratio of water to alcohol is 4:5 is added to that in the container.
1. Water is increased by 14%.
2. Mixture whose ratio of water to alcohol is 4:5 is added to that in the container.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
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Aditya Gupta answered |
Ratio water : alcohol = 2 : 5.
To imply that water = 2/7 × 14 = 4 cups
Alcohol = 14 - 4 = 10 cups.
If water is increased by 14%, we have
new capacity of water =114/100 × 4 = 4.56 cups.
The new volume of the liquid is 10 + 4.56 cups. Hence the statement is sufficient.
In statement 2, ratio of water : alcohol = 4 : 5 but we are not told the quantity of the liquid added or the quantity of water or alcohol added, hence, the statement is not sufficient.
To imply that water = 2/7 × 14 = 4 cups
Alcohol = 14 - 4 = 10 cups.
If water is increased by 14%, we have
new capacity of water =114/100 × 4 = 4.56 cups.
The new volume of the liquid is 10 + 4.56 cups. Hence the statement is sufficient.
In statement 2, ratio of water : alcohol = 4 : 5 but we are not told the quantity of the liquid added or the quantity of water or alcohol added, hence, the statement is not sufficient.
The average life expectancy for the United States population as a whole is 73.9 years, but
children born in Hawaii will live an average of 77 years, and those born in Louisiana, 71.7
years. If a newlywed couple from Louisiana were to begin their family in Hawaii, therefore, their
children would be expected to live longer than would be the case if the family remained in
Louisiana.
Which of the following, if true, would most seriously weaken the conclusion drawn in the
passage?- a)Insurance company statisticians do not believe that moving to Hawaii will significantlylengthen the average Louisianan's life.
- b)The governor of Louisiana has falsely alleged that statistics for his state are inaccurate.
- c)The longevity ascribed to Hawaii's current population is attributable mostly to geneticallydetermined factors.
- d)Thirty percent of all Louisianans can expect to live longer than 77 years.
- e)Most of the Hawaiian Islands have levels of air pollution well below the national average
for the United States.
Correct answer is option 'C'. Can you explain this answer?
The average life expectancy for the United States population as a whole is 73.9 years, but
children born in Hawaii will live an average of 77 years, and those born in Louisiana, 71.7
years. If a newlywed couple from Louisiana were to begin their family in Hawaii, therefore, their
children would be expected to live longer than would be the case if the family remained in
Louisiana.
Which of the following, if true, would most seriously weaken the conclusion drawn in the
passage?
children born in Hawaii will live an average of 77 years, and those born in Louisiana, 71.7
years. If a newlywed couple from Louisiana were to begin their family in Hawaii, therefore, their
children would be expected to live longer than would be the case if the family remained in
Louisiana.
Which of the following, if true, would most seriously weaken the conclusion drawn in the
passage?
a)
Insurance company statisticians do not believe that moving to Hawaii will significantlylengthen the average Louisianan's life.
b)
The governor of Louisiana has falsely alleged that statistics for his state are inaccurate.
c)
The longevity ascribed to Hawaii's current population is attributable mostly to geneticallydetermined factors.
d)
Thirty percent of all Louisianans can expect to live longer than 77 years.
e)
Most of the Hawaiian Islands have levels of air pollution well below the national average
for the United States.
for the United States.
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Sandeep Mehra answered |
Explanation:
Genetically determined factors
- The conclusion drawn in the passage is based on the assumption that moving from Louisiana to Hawaii would result in longer life expectancy for the children.
- Option C weakens this conclusion by suggesting that the longevity of Hawaiians is mostly due to genetically determined factors rather than environmental factors.
- This implies that simply moving to Hawaii may not necessarily result in longer life expectancy for the children of the newlywed couple from Louisiana.
- Therefore, if genetics play a significant role in the life expectancy of Hawaiians, the children of the newlywed couple may not live longer simply by virtue of being born in Hawaii.
By pointing out that the longevity in Hawaii is mostly due to genetic factors, option C weakens the argument that moving to Hawaii would lead to longer life expectancy for the children of the newlywed couple from Louisiana.
Genetically determined factors
- The conclusion drawn in the passage is based on the assumption that moving from Louisiana to Hawaii would result in longer life expectancy for the children.
- Option C weakens this conclusion by suggesting that the longevity of Hawaiians is mostly due to genetically determined factors rather than environmental factors.
- This implies that simply moving to Hawaii may not necessarily result in longer life expectancy for the children of the newlywed couple from Louisiana.
- Therefore, if genetics play a significant role in the life expectancy of Hawaiians, the children of the newlywed couple may not live longer simply by virtue of being born in Hawaii.
By pointing out that the longevity in Hawaii is mostly due to genetic factors, option C weakens the argument that moving to Hawaii would lead to longer life expectancy for the children of the newlywed couple from Louisiana.
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