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If –2<a<11 and 3<b<12, then which of the following is NOT true?
If we work with the two inequalities we subtract the max of 2nd from min
of 1st hence subtracting 11 from 3 gives us –8. Hence ineq. Should be –8<ba<14
a, b, and c are integers and a < b < c. S is the set of all integers from a to b, inclusive. Q is the set of all integers from b to c, inclusive. The median of set S is (3/4)b. The median of set Q is (7/8)c. If R is the set of all integers from a to c, inclusive, what fraction of c is the median of set R?
Since S contains only consecutive integers, its median is the average of the extreme
values a and b. We also know that the median of S is 3/4b. We can set up and simplify
the following equation:
Since set Q contains only consecutive integers, its median is also the average of the
extreme values, in this case b and c. We also know that the median of Q is 7/8c . We can
set up and simplify the following equation:
We can find the ratio of a to c as follows:
Taking the first equation
2a =b→8a = 4b
and the second equation, 4b = 3c
and setting them equal to each other, yields the following:
Since set R contains only consecutive integers, its median is the average of the extreme
values a and c: . We can use the ratio to substitute 3c/8 for a:
Thus the median of set R is 11/16c. The correct answer is C.
a, b, and c are positive integers. If a, b, and c are assembled into the sixdigit number abcabc, which one of the following must be a factor of abcabc?
This question looks daunting, but we can tackle it by thinking about the place values of the unknowns. If we had a threedigit number abc, we could express it as 100a + 10b + c
(think of an example, say 375: 100(3) + 10(7) + 5). Thus, each additional digit increases
the place value tenfold.
If we have abcabc, we can express it as follows:
100000a + 10000b + 1000c + 100a + 10b + c
If we combine like terms, we get the following:
100100a + 10010b + 1001c
At this point, we can spot a pattern in the terms: each term is a multiple of 1001. On the
GMAT, such patterns are not accidental. If we factor 1001 from each term, the
expression can be simplified as follows:
1001(100a + 10b + c) or 1001(abc).
Thus, abcabc is the product of 1001 and abc, and will have all the factors of both. Since
we don't know the value of abc, we cannot know what its factors are. But we can see
whether one of the answer choices is a factor of 1001, which would make it a factor of
abcabc.
1001 is not even, so 16 is not a factor. 1001 doesn't end in 0 or 5, so 5 is not a factor.
The sum of the digits in 1001 is not a multiple of 3, so 3 is not a factor. It's difficult to
know whether 13 is a factor without performing the division: 1001/13 = 77. Since 13
divides into 1001 without a remainder, it is a factor of 1001 and thus a factor of abcabc.
The correct answer is B.
We can simplify this problem by using variables instead of numbers.
x = 54,820
x + 2 = 54,822
The average of (54,820)^{2} and (54,822)^{2} =
Now, factor x^{2} + 2x +2. This equals x^{2} + 2x +1 + 1, which equals (x + 1)^{2} + 1.
Substitute our original number back in for x as follows:
(x + 1)^{2} + 1 = (54,820 + 1)^{2} + 1 = (54,821)^{2} + 1.
The correct answer is D.
A certain club has exactly 5 new members at the end of its first week. Every subsequent
week, each of the previous week's new members (and only these members) brings exactly x new
members into the club. If y is the number of new members brought into the club during the
twelfth week, which of the following could be y?
At the end of the first week, there are 5 members. During the second week, 5x new
members are brought in (x new members for every existing member). During the third
week, the previous week's new members (5x) each bring in x new members: (5x)x = 5x^{2}^{ }new members. If we continue this pattern to the twelfth week, we will see that 5x^{11 }new
members join the club that week. Since y is the number of new members joining during
week 12,y= 5x^{11.}
If y =5x^{11} , we can set each of the answer choices equal to 5x^{11} and see which one yields an integer value (since y is a specific number of people, it must be an integer value). The only choice to yield an integer value is (D):
Therefore x = 15.
Since choice (D) is the only one to yield an integer value, it is the correct answer.
Directions: The data sufficiency problem consists of a question and two statements, labeled (1)
and (2), in which certain data are given. You have to decide whether the data given in the
statements are sufficient for answering the question. Using the data given in the statements plus
your knowledge of mathematics and everyday facts (such as the number of days in July or the
meaning of counterclockwise), you must indicate whether
Q.
x is a positive number. If 9^{x} + 9^{x+1} + 9^{x+2} + 9^{x+3} + 9^{x+4} + 9^{x+5} = y, is y divisible by 5?
1) 5 is a factor of x.
2) x is an integer.
The key to this problem is to recognize that in order for any integer to be divisible by 5, it
must end in 0 or 5. Since we are adding a string of powers of 9, the question becomes
"Does the sum of these powers of 9 end in 0 or 5?" If we knew the units digits of each
power of nine, we'd be able to figure out the units digit of their sum.
9 raised to an even exponent will result in a number whose units digit is 1 (e.g., 9^{2} = 81,
9^{4} = 6561, etc.). If 9 raised to an even exponent always gives 1 as the units digit, then 9
raised to an odd exponent will therefore result in a number whose units digit is 9 (think
about this: 9^{2} = 81, so 9^{3} will be 81 x 9 and the units digit will be 1 x 9).
Since our exponents in this case are x, x+1, x+2, x+3, x+4, and x+5, we need to know
whether x is an integer in order to be sure the pattern holds. (NEVER assume that an
unknown is an integer unless expressly informed). If x is in fact an integer, we will have
6 consecutive integers, of which 3 will necessarily be even and 3 odd. The 3 even
exponents will result in 1's and the 3 odd exponents will result in 9's. Since the three 1's
can be paired with the three 9's (for a sum of 30), the units digit of y will be 0 and y
will thus be divisible by 5. But we don't know whether x is an integer. For that, we need
to check the statements.
Statement (1) tells us that 5 is a factor of x, which means that x must be an integer.
Sufficient.
Statement (2) tells us that x is an integer. Sufficient.
The correct answer is D: EACH statement ALONE is sufficient to answer the question.
If the range of the set of numbers {150, 90, 125, 110, 170, 155, x, 100, 140} is 95, which of thefollowing could be x?
They tell us the range of the set {150, 90, 125, 110, 170, 155, x, 100, 140} is 95. Since
the present range without is 80, x has to be either the highest or the lowest number in the
set. If x is the lowest number, it would be 17095=75, but that’s not an option. Therefore
x has to be the highest number. 90+95=185.
Frances can complete a job in 12 hours, and Joan can complete the same job in 8 hours.Frances starts the job at 9 a.m., and stops working at 3 p.m. If Joan starts working at 4 p.m. tocomplete the job, at what time is the job finished?
Plug in for number of tasks to be completed before the job is done; let the job involve making 24 widgets. Thus, Frances makes 2 per hour, and Joan makes 3 per hour. Frances works for 6 hours, so she makes 12 widgets. Joan needs 4 hours to make the other 12 widgets; if she starts at 4 p.m. she will finish at 8 p.m.
Directions: The data sufficiency problem consists of a question and two statements, labeled (1)
and (2), in which certain data are given. You have to decide whether the data given in the
statements are sufficient for answering the question. Using the data given in the statements plus
your knowledge of mathematics and everyday facts (such as the number of days in July or the
meaning of counterclockwise), you must indicate whether
Q.
A, B, C, D, and E are airline pilots with very busy travel schedules. Given that D is able to meet at
any time that B cannot meet, do the schedules of A, B, C, D, and E allow three of these five
individuals to meet together for two uninterrupted hours?
(1) Pilots A and C, who cannot meet together, are not able to end any meeting during the AM
hours of any weekday.
(2) Pilots B and E, who can never meet for longer than 2 uninterrupted hours, are only available
to meet for two straight hours starting at 10:30 PM on any weekday and not ending during the AM
hours of any weekend day.
This is a Yes/No data sufficiency question. The only way the statements will provide definitive information is if they lead to a definite YES answer or if they lead to a definite NO answer. (A "Maybe" answer means that the statements are not sufficient. Statement (1) alone only provides us information about when A and C cannot meet. It does not provide any information about when each of the pilots ARE able to meet. While we know that A and C cannot meet together, it is possible that some combination of three pilots would be able to meet together (such as ABD or CBE). Statement (1) alone therefore does not provide enough information to be able to definitively answer this question YES or NO. Statement (2) alone provides us with specific information about when B and E can meet. However we are not provided with information as to whether one of the other pilots A, C or D  will be able to join them for the meeting. Thus, statement (2) alone is not sufficient to answer this question
In analyzing statements (1) and (2) together, it is helpful to list the 10 possible ways that 3 of the pilots could meet: 1. ABC
2. ABD
3. ABE
4. ACD
5. ACE
6. ADE
7. BCD
8. BCE
9. BDE
10. CDE
Statements (1) and (2) taken together preclude pilots A or C from meeting with pilots B and E. This is due to the fact that pilots B and E can only meet for two straight hours from 10:30 PM to 12:30 AM starting on either Monday, Tuesday, Wednesday, or Thursday night while pilots A and C can never meet during the AM hours of any weekday (leaving the 12:00 AM to 12:30 AM slot impossible). This eliminates 8 of the 10 possibilities (1, 2, 3, 5, 6 because A can't meet with B or E and 7, 8, 10 because C can't meet with B or E.) In addition, since pilot A cannot meet with pilot C, possibility 4 is also eliminated. Thus, the only possibility that remains is #9: BDE. The question stem states that D is able to meet at any time that B cannot. It may be tempting to use this information to conclude that B and D are not able to meet together. However, while we know for sure that D is able to meet at any time that B cannot, this does not preclude the possibility that D is ALSO able to meet at times when B can meet. Given that we don't know whether or not D can meet at the same time that B and E can meet  we do not have enough information to evaluate whether pilots B, D, and E will be able to meet together.
Therefore, the correct answer is E: Statements (1) and (2) TOGETHER are NOT sufficient.
1/2^{12} + 2/2^{13} + 2^{2}/2^{14} + 2^{3}/2^{15} =
( answer to the nearest approximation)
If we express the numerators as powers of 2, then we would get 1/2^{12} + 2/2^{13} + 2^{2}/2^{14} + 2^{3}/2^{15} which is equal to 1/2^{12} + 1/2^{12} + 1/2^{12} + 1/2^{12} which equals 4/2^{12}. This can be further reduced to 2^{2}/2^{12} = ½^{10}.
1^{1}+2^{2}+3^{3}+...+10^{10} is divided by 5. What is the remainder?
When a whole number is divided by 5, the remainder depends on the units digit of that number.
Thus, we need to determine the units digit of the number 1^{1}+2^{2}+3^{3}+...+10^{10}. To do so, we need to first determine the units digit of each of the individual terms in the expression as follows:
To determine the units digit of the expression itself, we must find the sum of all the units digits of each of the individual terms:
1 + 4 + 7 + 6 + 5 + 6 + 3 + 6 + 9 = 47
Thus, 7 is the units digit of the number 1^{1}+2^{2}+3^{3}+...+10^{10}. When an integer that ends in 7 is divided by 5, the remainder is 2. (Test this out on any integer ending in 7.) Thus, the correct answer is C.
If n is an integer greater than 0, what is the remainder when 9^{12n+3} is divided by 10?
Look for the pattern: 9^{1}=9. 9^{2}=81. 9^{3}=729. Multiply that by another 9. You’ll get another no ending in 1. And so forth and so on. So the bottom line is that whenever 9 is raised to an odd power, the units digit is 9. When it’s raised to an even power, the units digit is 1. When you divide a number by 10, its remainder will always be its units digit. No matter what value you plug in for n, we’re always going to be raising 9 to an odd power, so the units digit and the remainder will both be 9.
Each of 435 bags contains at least one of the following three items: raisins, almonds, andpeanuts. The number of bags that contain only raisins is 10 times the number of bags that containonly peanuts. The number of bags that contain only almonds is 20 times the number of bags thatcontain only raisins and peanuts. The number of bags that contain only peanuts is onefifth thenumber of bags that contain only almonds. 210 bags contain almonds. How many bags containonly one kind of item?
This problem involves 3 overlapping sets. To visualize a 3 set problem, it is best to draw a Venn Diagram.
We can begin filling in our Venn Diagram utilizing the following 2 facts: (1) The number of bags that contain only raisins is 10 times the number of bags that contain only peanuts. (2) The number of bags that contain only almonds is 20 times the number of bags that contain only raisins and peanuts.
Next, we are told that the number of bags that contain only peanuts (which we have represented as x) is one fifth the number of bags that contain only almonds (which we have represented as 20y).
This yields the following equation: x = (1/5) 20y which simplifies to x = 4y. We can use this information to revise our Venn Diagram by substituting any x in our original diagram with 4y as in the figure.
Directions: The data sufficiency problem consists of a question and two statements, labeled (1)
and (2), in which certain data are given. You have to decide whether the data given in the
statements are sufficient for answering the question. Using the data given in the statements plus
your knowledge of mathematics and everyday facts (such as the number of days in July or the
meaning of counterclockwise), you must indicate whether
Q.
What is the probability that and are reciprocal fractions?
(1) v, w, y, and z are each randomly chosen from the first 100 positive integers.
(2) The product (u)(x) is the median of 100 consecutive integers.
In order for one number to be the reciprocal of another number, their product must equal 1. Thus, this question can be rephrased as follows:
What is the probability that
This can be simplified as follows:
What is the probability that
What is the probability that
Finally: What is the probability that ux = vywz ?
Statement (1) tells us that vywz is an integer, since it is the product of integers. However, this gives no information about u and x and is therefore not sufficient to answer the question.
Statement (2) tells us that ux is NOT an integer. This is because the median of an even number of consecutive integers is NOT an integer. (For example, the median of 4 consecut ive integers  9, 10, 11, 12  equals 10.5.) However, this gives us no information about vywz and is therefore not sufficient to answer the question.
Taking both statements together, we know that vywz IS an integer and that ux is NOT an integer. Therefore vywz CANNOT be equal to ux . The probability that the fractions are reciprocals is zero. The correct answer is C: Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.
If n is an integer greater than 5.3, then n! must be divisible by which of the following numbers?
If n is greater than 5.3 then the smallest n! can be 6!. Since 6! =6*5*4*3*2*1, it is definitely divisible by 12, because any n! bigger than 6 will include both a 6 and a 2, thus making it a multiple of 12.Also, n! does not have to be divisible by anything greater than 6, so 7,11 and 13 are eliminated as are any multiples of those numbers, like 14.
Directions: The data sufficiency problem consists of a question and two statements, labeled (1)
and (2), in which certain data are given. You have to decide whether the data given in the
statements are sufficient for answering the question. Using the data given in the statements plus
your knowledge of mathematics and everyday facts (such as the number of days in July or the
meaning of counterclockwise), you must indicate whether
Q.
what is population of the village
1. 7/11 of the village comprises of married people
2. 200 widows comprises 10% of the singles population
The question here is to find out the population of the village. Statement (1) tells us that 7/11 of the village comprises of married people. So if the population of the village is x, the no of married population is 7x/11. but this is absolutely not enough to get the total population. So we have BCE. Now statement (2) tells that 200 widows comprise 10% of the singles population. So the singles population is clearly 2000. so both the statements (1) and (2) ALONE are not sufficient to answer the question. So now we combine both of them. We get singles + widows + married = total population. Adding both statements we get 2000+200+7x/11=x which gives us the total population of 6050 people. Therefore the answer is (C)
Directions: The data sufficiency problem consists of a question and two statements, labeled (1)
and (2), in which certain data are given. You have to decide whether the data given in the
statements are sufficient for answering the question. Using the data given in the statements plus
your knowledge of mathematics and everyday facts (such as the number of days in July or the
meaning of counterclockwise), you must indicate whether
Q.
The sum of the ages of A, B and C is 137 years. What is C’s age
1. the sum of the ages of A and C is 91 years
2. the sum of the ages of B and C is 104 years
The question stem gives A+B+C=137. Now we look at the statement (1). It says A+C=91 which leads us to value of B=46. But it ALONE is not enough to get us the value of C. Looking at statement (2) we get B+C=104 which leads us to value of A=33. This also ALONE is not enough to get value of C. But both statements taken together will definitely lead us to get the value of C from the question stem as 58. Therefore answer is (C).
Directions: The data sufficiency problem consists of a question and two statements, labeled (1)
and (2), in which certain data are given. You have to decide whether the data given in the
statements are sufficient for answering the question. Using the data given in the statements plus
your knowledge of mathematics and everyday facts (such as the number of days in July or the
meaning of counterclockwise), you must indicate whether
Q.
Is the number x is divisible by 9.
1. The number x can be obtained by taking the difference between a number and another one obtained by reversing the digits.
2. The sum of the digits of x is divisible by 9.
We take the first statement and analyze it. Taking examples of 12 and 21 we get difference of 9 that is divisible by 9. Again 13 and 31 gives difference of 18 divisible by 9. And so and so forth. So statement (1) ALONE is enough to answer the stem question. So we have AD. Statement (2) gives us the divisibility rule of a number divisible by 9. So it clearly answers the question asked in stem. So both statements ALONE are enough to answer the question making (D) the right answer.
Directions: The data sufficiency problem consists of a question and two statements, labeled (1)
and (2), in which certain data are given. You have to decide whether the data given in the
statements are sufficient for answering the question. Using the data given in the statements plus
your knowledge of mathematics and everyday facts (such as the number of days in July or the
meaning of counterclockwise), you must indicate whether
Q.
In an election how many votes are cast.
1. the winning candidate gets 54% of the total votes
2. the winning candidate wins by 800
The statement (1) here tells us that the winning candidate gets 54% of the total votes. But this clearly is not enough to get the total vote count. So BDE. Statement (2) gives the margin of victory but that too is not enough to answer the question involved. Even when both the statements are taken together it leads us to nowhere. So some more data is required to solve this problem clearly making (E) the right choice.
Directions: The data sufficiency problem consists of a question and two statements, labeled (1)
and (2), in which certain data are given. You have to decide whether the data given in the
statements are sufficient for answering the question. Using the data given in the statements plus
your knowledge of mathematics and everyday facts (such as the number of days in July or the
meaning of counterclockwise), you must indicate whether
Q.
Is (y/x)*(1+x)^{2} > 2y
1. xy > 0
2. x + y > 5
If we expand the question stem we get
(y/x)*(x^{2} + 2x + 1),
which can be reduced as xy +2y +y/x. Now look at the statement (1). It tells that xy>0. If this is the case then surely the whole equation becomes greater than 2y, which answers the question. So AD. Now statement (2) gives us another equation that cannot help us solve the question asked in the stem. So answer is (A).
a,b are integers, Is b exactly divisible by 20?
Statement I: a / 20 + b / 20 is an integer
Statement II: a / 7 + b / 20 is an integer
Second statement to be integer definitely 'a' must be multiple of 7 let it be 140 then b must be multiple of 20 to give integer.
3, 5, 7, 11, 13, 17 is a prime number series. Hence next prime number in this series is 19
In a school, 35% girls and 19% boys participated in singing. Number of students in the school is 700. How many boys are there in the school?
Statement I: Number of boys are more than 200
Statement II: More than 190 students participated
Solution:
In a school, 35% girls and 19% boys participated in singing
Number of students in the school is 700
Let the number of boys in school be B
Let the number of girls in school be G
Then,
B + G = 700  eqn 1
From statement 1,
Number of boys are more than 200
B > 200
From statement 2,
More than 190 students participated
Therefore,
190 < 35 % of G + 19 % of B
Note that, B > 200
Then B = 300 only satisfies this condition
B + G = 700
300 + G = 700
G = 400
Then,
Thus, Statements I and II together are necessary to answer the question
A printer numbered consecutively the pages of a book, beginning with 1 on the first page. Innumbering the pages, he had to print a total of 187 digits. Find the number of pages inthe book.
The total number of digits is 187. The total number of single digit page numbers is 9(from 1 to 9). So subtracting this from 187 we get 178. After page number 9 we have 2 digit page numbers. So dividing this by 2 we get 89. So the total number of pages in the book are 89+9=98.
In a drawer of shirts, 8 r blue, 6 r green, and 4 r magenta. If Mason draws 2 shirts at random,what is the probability that at least one of the shirts he draws will be blue?
Remember that at least one is a clue, and when u see phrase, u need to find the probability of getting everything except what u want (in other words, the probability of getting any other color except blue), and then subtract that from 1. The formula for this would be 1(the probability of getting the other colors). 1(10/18 * 9/17)=15/17=12/17.
We don’t need to go about solving this question as per the REAL MATH way. We use our technique. Whenever we see variables in the answer choice we just plug in!! Plug in x=3, and the fraction becomes –7(target answer). Bingo!
Which of the following CANNOT yield an integer when divided by 10?
(i) Product of two prime numbers
(ii) An integer less than 10
(iii) Sum of three consecutive integers
(iv) An odd integer
This question requires deep thinking in the sense that you have to look for the examples to refute the statements. We will take one by one. If product of two prime numbers when divided by 10 gives us an integer we can remove all answers containing (i). So we take 5 and 2. When multiplied and then divided by 10 we get an integer 1. So (i) is true. Get rid of A. We move to (ii). Lets take 0. This when divided by 10 gives 0, which again is an integer. So (ii) is also true. So get rid of B and C. Now we just need to verify D as it is the obvious choice. Any odd integer when divided by 10 would always leave decimal and never an integer. So D cannot be true. Hence it is the answer.
A number, K, is a positive integer with the special property that 3 times its unit is equal to 2 timesits 10 digit. How many such numbers exist between 10 & 99?
Here’s another smart Question. It appears to be daunting but it’s not that tough. We start with 1 at units place. When multiplied 3 times and then divided by 2 we get 1.5. So it is ruled out. Next we try with 2. When we multiply by 3 we get 6 which when divided by 2 gives us 3.Bingo!! We get the first number 32. Similarly by trying out different numbers at unit place we get other 2 numbers as 64 and 96(which are also multiples of 32 for hint). So we get a total of 3 numbers between 10 and 99.
If two digit integer M and N are positive and have same digits, but in reverse order, which of thefollowing cannot be the sum of M and N.
Lets try this question by trial and error. Lets try to get all ans wers starting with smallest value 44. It can be sum of 22 and 22. So (E) is ruled out. Now move to 99. It could be sum of 54 and 45. So (D) goes. Next 121 could be written as 56 + 65. So even (C) goes. Now try out 165. It could be the sum of 87 and 78. So after POE rest four (A) becomes the answer, as it cannot be written as sum of desired combination.
Directions: The data sufficiency problem consists of a question and two statements, labeled (1)
and (2), in which certain data are given. You have to decide whether the data given in the
statements are sufficient for answering the question. Using the data given in the statements plus
your knowledge of mathematics and everyday facts (such as the number of days in July or the
meaning of counterclockwise), you must indicate whether
Q.
In the figure above, does x = 90?
(1) The length of AC is less than the length of BC.
(2) The length of AB is onefourth the circumference of the circle.
We need to see the fact statements. Statement (1) says that the length of AC is less than the length of BC. This clearly leads us to nowhere. So BCE. Now the fact statement (2) tells us that the length of AB is onefourth the circumference of the circle, which clearly leads us to know that it is not the diameter, it is just a chord. So the angle subtended is not equal to 90 deg. So the answer is (B).
In a group of 8 semifinalists, all but 2 will advance to the final round. If in the final round only thetop 3 will be awarded medals, then how many groups of medal winners are possible?
The entire discussion of rounds is a red herring. The question is asking for possible combinations of the final 3, and it is possible for any of the original 8 contestants to have advanced to the final round, thus we need to pick 3 out of 8, and order doesn’t matter. 8*7*6/3*2*1=56.
The marks scored by a student in three subjects are in the ratio of 4: 5: 6. If the candidate scoredan overall aggregate of 60% of the sum of the maximum marks and the maximum mark in allthree subjects is the same, in how many subjects did he score more than 60%?
Let the maximum in marks in each of the three subjects be 100.
Therefore, the candidate scored an aggregate of 60% of 3 * 100 = 60% of 300 marks = 180 marks.
Let the marks scored in the three subjects be 4x, 5x and 6x.
Then, 4x + 5x + 6x = 180 ? 15x = 180 or x = 12.
Therefore, marks scored by the candidate in the three subjects are 4*12, 5*12 and 6*12 = 48, 60 and 72. Hence, the candidate has score more than 60% in one subject.
There are 6 boxes numbered 1, 2,...6. Each box is to be filled up either with a red or a green ballin such a way that at least 1 box contains a green ball and the boxes containing green balls areconsecutively numbered. The total number of ways in which this can be done is
If only one of the boxes has a green ball, it can be any of the 6 boxes. So, this can be achieved in 6 ways.
If two of the boxes have green balls and then there are 5 consecutive sets of 2 boxes. 12, 23, 34, 45, 56.
Similarly, if 3 of the boxes have green balls, there will be 4 options.
If 4 boxes have green balls, there will be 3 options.
If 5 boxes have green balls, then there will be 2 options.
If all 6 boxes have green balls, then there will be just 1 option.
Total number of options = 6 + 5 + 4 + 3 + 2 + 1 = 21
vendor sells 60 percent of apples he had and throws away 15 percent of the remainder. Nextday he sells 50 percent of the remainder and throws away the rest. What percent of his applesdoes the vendor throw?
Let the number of apples be 100.
On the first day he sells 60% apples ie.,60 apples.Remaining apples =40.
He throws 15% of the remaining i.e., 15% of 40 = 6.Now he has 406 = 34 apples The next day he throws 50% of the remaining 34 apples i.e., 17.
Therefore in all he throws 6+17 =23 apples.
The product of two positive numbers is p. If each of the numbers is increased by 2, the newproduct is how much greater than twice the sum of the two original numbers?
Plug in p=10. This can be written as the product of 2 and 5. Their sum is 7. Twice of it is 14. Increasing the original numbers by 2 we get the two numbers as 4 and 7. The product of this is 7*4=28. So the difference between the product and the sum is 2814=14.This is our target answer. Plug in p=10 back in all the answer choices and look for the answer as 14. (D) is the answer.
If p and q are integers, such that p<0<q, which of the following must be true?
I. 2p<2q
II. p^{2}<q^{2}
III. p+q=0
Variables in the answer choices, plug in!! lets plug in p=2 and q=2. Now verify all the choices given. We get II false. So all the answers which contain II should go. So (B), (C) and (E) go. Since two answer choices remain we plug in once more. Put p=2 and q=3. Now we can see that III is false. So the answer is (A).
If is an integer, which of the following CANNOT be the value of p?
Factor out the numerator (4*3)(2*11)(5*7). Now this fraction when divided by p would get an integer only if p cancels out with some of the factors. So now lets try it with different answer choices. Except for the (E) all other choices can be cancelled out. So clearly (E) is the answer.
Who made a deposit? You can’t tell. They is the only pronoun that creates a clear reference and agreement.
Although the average Girl Scout joins the organization at age 14, they have already been Brownies for several years.
Use the 2/3 split. The pronoun refers to the average Girl Scout, so it should be she. Eliminate (A) and (B). One difference among the others is has vs. had. vs. was. The verb tense needs to be consistent with joins, so use has and choose (C).
In 1980, the Netherlands agreed to limit fishing in certain Atlantic Ocean beds, but in 1981, they terminated the agreement.
They Netherlands is an it (as is the United States) not a they. Eliminate (A) and (B). (D) terminates the Netherlands, always a bad idea. (E) is passive, so choose the active (C).
While brokers, as a rule, are not permitted to know executive access codes, in many instances they are widely known.
Step 1: The 2/3 split shown in italics (which doesn’t happen on the real test) is they vs. the codes. You want the codes because they is ambiguous; it could refer to brokers or codes. Step 2: Eliminate (A), (B), and (C). Step 3: The difference between (D) and (E) is able to be. Codes aren’t able (only people are), so choose (E).
Despite seeming tame and intelligent, the state troopers had no choice but to shoot the loose Gorilla.
(A) has a misplaced modifier because it suggests that the troopers were tame and intelligent. (B), (C), and (E) change the words around a little , but they still repeat this error.(D) fixes the misplaced modifier by turning the phrase into a clause. The pronoun it is okay because the only noun it could match is the loose gorilla.
Subject is The number, which is singular (a number is plural). Eliminate (A), (B), and (C). (D) is shorter and simpler than (E).
The commercial airliner flew too clos e to the military base, an act that the army saw as a violation of its air space.
The idiom is see/saw…as and only (A) gets it right.
For the past five years, US consumption of eggs has decreased. The National Egg Council plans to reverse this trend by launching an advertising campaign extolling the healthful benefits of eggs.
Which one of the following, if true, will provide the strongest support for the National Egg Council’s plan?
Support for the argument are the identifying words. C: Increase egg consumption with health ads. P: None worth mentioning. A: Health is an issue for potential eggeaters. (A) and (B) aren’t bad, but they require you to infer a connection between eggs, health, and consumers’ concerns rather than stating it outright. (C) clearly shows consumers are concerned with eggs’ health effects. (D) weakens the argument. (E) is out of scope.
In an effort to reduce the amount of fat and the number of calories that they consume, many citizens of the United States are making significant changes in their diets. For them staying in shape and looking fit now take precedence over eating foods that are filling and that taste good. It is likely that if they maintain these new priorities with consistent regard for other health issues, the length and quality of their lives will increase significantly.
Which one of the following is an assumption upon which the argument is based?
ID the question: Assumption is an obvious key word. Work the argument: C: If people maintain the new priorities (changes in diet), the length and quality of their lives will increase. P: People are making changes to their diets (a subsidiary conclusion) because they’d rather be fit than eat foods that are filling and taste good. Gap: better diet——longer life and changes to diet——filling, goodtasting foods. POE: (B) is irrelevant. If anything, this weakens by suggesting that changes in diet aren’t enough. (C) is irrelevant. This goes along with the general idea, but it’s not strictly necessary. In (D), the time of discovery is irrelevant. In (E), the goals of most citizens are irrelevant. You’re only interested in the people who are acting on their goals. (A) fills in the assumption needed to make the subsidiary conclusion true. If eating filling, goodtasting foods is inconsistent with staying in shape and looking fit, people who want to stay in shape and be fit are willing to give them up. They will maintain good habits and live longer, better lives.
Singing in the Rain Umbrella Corp. plans to institute a marketing campaign in which it sells umbrellas at the exits of subway stations during rainy weather. The umbrellas will be sold at a price that is slightly higher than normal. The company thinks the sales of these higher – priced umbrellas will be greater than normal sales of umbrellas, because the purchasers of these umbrellas will be forced to buy them if they do not want to get wet.
The author assumes which of the following about the purchasers of the umbrellas in predicting the sales of the umbrellas?
ID the question: Assume is an obvious key word. Work the argument: C: Sales of umbrellas at subway exits while it’s raining will be greater than normal sales. P: People will be forced to buy umbrellas if they don’t want to get wet. A: They don’t have umbrellas with them. They are unwilling to get wet. POE: In (B), profitability of normally priced umbrellas is irrelevant. In (C), sales of normally priced umbrellas are irrelevant. (D) doesn’t deal with the issue. (E) looks good, but it’s not right. Potential customers might have umbrellas, but the issue is whether they have an umbrella with them. (A) makes the link. If it’s raining and you don’t have an umbrella, you feel the pressure to make a purchase. On some assumption questions, you may have a lot of difficulty spotting the necessary assumption due to the way the answers are worded. This is particularly true with answer choices containing negative words such as not and never. One way to check whether an answer choice is a necessary assumption is to negate, or reverse, that answer. If the negation would weaken the argument, that answer is a necessary assumption.
A leading cement manufacture has been having problems processing manufacturing and delivery records since it expanded its operations. To solve this problem it plans to install a new platform on its central computing system which will run its tracking program five times faster than the current system does.
Which one of the following castes the most serious doubt on the manufacture’s plan?
ID the question: The keys words are casts the most doubt. Work the argument: C: The company will install the faster platform on its computer system. P: The company can’t process its records fast enough anymore. Gap: New platform——fixing current problems. A: (1) Speed won’t compromise accuracy; (2) the computer can run the program. (C) attacks assumption #2. (B) strengthens the argument; (A) is irrelevant (what if the platform the company has in mind can do the job?). (D) only addresses the company’s expansion, and (E) is irrelevant.
Critics insist that government regulation of business has made it more difficult for American businesses to operate profitably and has destroyed their ability to compete with foreign producers of consumer goods. This argument is not compelling. Government regulation of business was never as active in this nation as it was between the years 1975 and 1985, and in those years the average net worth of American family increased more than it had in any previous decade.
The author’s argument would be most seriously weakened if it were true that
ID the question: The key words are most seriously weakened. Work the argument: C: The idea that government regulation hinders profits is invalid. P: From 1975–1985, when government regulation was very active, the average net worth of American families rose. Gap: Business profits——families’ net worth. A: The profitability of businesses caused the average net worth of American families to rise. (D) provides an alternate reason why families were richer. (A) Is 80% better or worse than normal? Irrelevant. (B) Isn’t strong enough because it doesn’t list bankruptcies as a percentage of the whole. (C) Is out of the scope. If (E) were true, how would average net worth of families rise?
A recession is not caused by any economic force other than nation wide loss of confidence. If the economy is perceived as being unstable, banks are conservative in lending money, investors take fewer risks and hence economic growth is slowed.
Which of the following, if true, would most strengthen the argument above.
Identify the question: The key word is strengthen. Work the argument: C: A recession is caused only by a national loss of confidence. P: If people think the economy is sluggish, they won’t invest. (D) strengthens the link between investor confidence and economic growth by stating that greater investment strengthens the economy. (A) and (B) weaken the conclusion by offering other causes for a recession. (C) is backward; we don’t care what recessions cause; we care what causes a recession. In (E), economic stability is never mentioned.
In an effort to increase revenues, Sky Air recently partnered with several airlines to create a joint frequentflier program. In the new program, miles earned on all partner airlines can be combined for reward tickets valid on any airline in the partnership. Sky Air’s CEO cites a recent increase in the number of passengers on all the partner airlines as evidence that the new frequentflier program is having the desired effect. Industry analysts doubt the CEO’s claim.
Which of the following, if true, best supports the analysts’ positions?
Read the question carefully. It asks you to support the analyst’s position, not the CEO’s. The analysts argue that the CEO is wrong to say that increase in passengers on partner airlines is evidence that the program is working to increase revenues. P: The joint frequent flier program allows miles earned on partner airlines to be combined for reward tickets on any airline. There’s been an increase in the number of passengers on the partner airlines. You need to show that the frequent flier plan is NOT increasing revenues for Sky Air. POE: (A) is irrelevant. (B) is irrelevant. (C) goes along the CEO’s position, not that of the analysts. (E) supports the CEO’s position. Only (D) supports the analysts’ position.
Neither my mother nor my father, both of whom are English professors, agree with my contention that James Joyce’s novel Ulysses is overrated.
Another common subjectverb agreement issue arises when a sentence has a compound subject. The split is agree/agrees. With neither...nor, the verb agrees with the subject closest to it, so father is the subject. Eliminate choices with plural verbs. (A), (C), and (D) are out. Choice (E) contains awkward, unidiomatic wording (English professors the both of them). (B) is the answer.
A number of military personnel who served in Operation Desert Storm has encountered a series of unexplainable symptoms that were attributed to Gulf War syndrome.
The number/a number is an ETS favorite. A number is plural; eliminate (A) and (B). The next split is attribute...as/attribute...to. The idiom is attribute to, so (C) and (E) are out. (D) is the answer.
Although Smith once championed the charity, he changed his mind after journalist linked its origin to a corrupt individual.
The tense shifts in the answer choices. Two events happened in the past, and one happened earlier than the other did (Smith championed the charity, and then he changed his mind). The past perfect tense is best to convey this meaning. (A), (C), (D), and (E) don’t use the correct tense. Choose (B).
A swarm of desert honeybees, a phenomenon seen by few of the select scientists and entomologists, occur when a portion of the colony leave the current nest to find a new home.
This example has modifier problems because only moves around in the answer choices and because of the select/selected split. Only should emphasize a select few scientists. However, it’s probably easier to work the subjectverb error first. Start with the leave/leaves or occur/occurs split. The subject, swarm, is singular. Eliminate (A) and (C) because occurs is plural. Eliminate (B) because portions does not agree with leaves.
The choice between (D) and (E) comes down to meaning. Selected means a group chosen by someone, while select means a special group. (E) is better at conveying the meaning of a small group of scientists who have been lucky enough to witness the swarm.
During the State of the Union address every February the president announced the amount of the new programs the administration planned to create and the amounts of money it invested in each one.
The errors are tense (announce/announces/had announced) and quantity words (amount/number). Programs are countable and should be modified by number. Eliminate (A), (B), and (D). Since the action occurs every February, it’s ongoing, and present tense is best. Eliminate (E).
Of the numerous decisions facing the Supreme Court this term, the question of an individual’s right to die is for certain the more perplexing.
There’s a comparative vs. superlative split (more/most). The sentence compares more than two things (Numerous decisions), so choose most. Eliminate (A), (B), and (E). (D) is unidiomatic and unnecessarily wordy, so (C) is the best answer.
In response to losing a significant part of its market share to a competitor, the soft drink company has cut costs by withholding executive bonuses, changed their advertising agency, and have redesigned the company logo.
This one is tricky because withholding is a red herring. The three verbs are cut, changed, and redesigned. (A) and (B) have pronoun trouble because company is singular; therefore, the proper pronoun is it. (C) and (D) aren’t parallel. (E) is the answer.
Now even directors of off Broadway productions, desperate for actors who are talented, charismatic, and aspiring more to a solid career in the theater than to the lucrative rewards and stardom proffered by movie moguls and studios, are turning to independent casting directors for guidance in assembling their casts.
Ideally, you want the list to have three adjectives. However, there’s no form of aspiring that fits in the sentence. You’re left looking for the answer that sucks the least. You can keep the two adjectives and refer to aspire separately. (A), (B), and (D) are not parallel, and the two and’s in (C) are redundant. For parallel construction in lists, use the “apples to apples, oranges to oranges” mnemonic.
The Supreme Court can effectively rule on a case in two ways, either by deciding to hear the case and handling down its judgment, or rather to simplify refuse to hear the case at all.
The either/or option of deciding or refusing needs parallel construction. (A), (C), and (E) are not parallel. (E) uses the gerund form the refusing, which is not parallel to the verb deciding. (D) does not make the options clear. (B) keeps by deciding and by refusing parallel.
The establishment of land trusts in New England has been praised not because of its restricting overdevelopment but because it allows the inheritance by future generations of the property.
This example serves as a leadin to idiom errors. Not only...but also demands parallel construction. (B) and (C) don’t have the correct idiom. (A) and (D) are not parallel. (E) keeps restricts and allows parallel.
Some students of literary criticism consider the theories of Blaine to be a huge advance in modern critical thinking and question the need to study the discounted theories of Rauthe and Wilson.
The idiom is consider…(nothing), so eliminate everything but (D). The changing prepositions at the beginning of each answer are the giveaway.
One of the possible results of the further depletion of the ozone in the atmosphere would be a sharp increase in the demand for sunscreens. Many of the ingredients in sunscreens are natural, and the demand for these products will require strict conservation laws. This will represent the victory for those who desire greater protection for the environment.
Which one of the following best states the conclusion in the passage above?
THE Results aren’t all bad because they will require stricter conversation laws. Use POE to eliminate the other answers. (A) The author never encourages ozone depletion. Also, should is extreme. (B) Level of government is never mentioned. Also, should is extreme. (C) Synthetics aren’t mentioned and should is extreme. (E) The relative positive/ negative balance is not mentioned and far outweighed is extreme.
The American division of the Acme running shoe company should begin marketing running shoes with doublethick soles. Acme’s Swedish division is selling a large number of these items, and is enjoying its most profitable quarter ever.
Which of the following is an assumption made by the author of the argument above?
Conclusion: The American division should sell the thick soled shoes. Premise: The thick soled shoes are selling like crazy in Sweden. Assumption: Americans and Swedes have comparable tastes in shoes.
Currently about 70 percent of all urban households recycle some portion of their garbage, 25 percent more than did ten years ago. This increase can be attributed , in part , to the fact that a larger portion of the population is now under the age of 47.
Of the following, which can be most properly inferred from the passage above?
The second sentence connects the propensity to recycle to age. So,( c)is true. (A) We don’t know anything about the potential amount of recycling . (B) Waste disposal is too general; we only know about recycling. (D) We don’t know about overall population, only the age distribution within the population . (E) We don’t know about these people in the past.
State colleges have lower tuitions than do private colleges because many of their operating costs are covered by federal and state funds.
Which of the following inferences is best supported by the statement made above?
State colleges can lower their tuition costs because the federal and state funds cover some of the colleges’ costs. The two must therefore be related. (A) fits with the real world, but the argument never mentions it. (B) never mentioned. (D) never mentioned , and always is extreme.( E) might seem to make sense , but we don’t know private colleges raise their funds. If they were to lower tuition, they could make up for it firing teachers or making other cutbacks.
Many people feel that hard work deserves a reward. However, this is not true. Hard work should be its own reward, because such work intrinsically gives the worker satisfaction when it is performed satisfactorily.
The author of the argument draws his or her conclusion by
The author’s impression of a reward is different from the more widely held belief. In the author’s estimation, a job well done is the reward. Extrinsic to the task means that the work isn’t enough. You need to get a prize.
If we reduce the salaries of our employees, then profits will increase by 35 percent. Because we must increase our profits, it is clear that employee salaries must be reduced.
Which of the following most closely parallels the reasoning used in the argument above?
C: Employee salaries must be reduced. P: We want to increase profits. If we reduce salaries, profits will increase. In its general form the argument says, “If A, then B. Want B, so do A.” (A), (B), and (C) don’t match. (D) might look attractive because it mentions salaries. However, don’t be drawn to answer choices that use words or topics similar to those in the question. In fact, they’re usually wrong. (E) matches. C: The number of commercials should be increased. P: The number of television watchers should be reduced. If there were more commercials, the number of television watchers would decline.
As we traveled the back roads of Arkansas, each of us were equipped with a canteen, a knife, and a compass.
Each is a singular pronoun, so each…. were doesn’t agree;(A) dies. (C) has the same problem, because every is also singular.( B) and (E) create sentence fragments without a main subject/ verb arrangement.
The best labor negotiators are the ones that have the ability of settling even the most irreconcilable stalemates.
Get rid of (A) right away, because the ones is awkward. The idiom is ability to, not ability of. Use the 2/3 split and get rid of (A) and (E) .When you refer to people, it’s proper to use who, not that; eliminate (B) and (D). (D) also has a split infinitive (which we’ll also talk about later.
Many small companies expand their client bases not so much by aggressive marketing as by networking and word of mouth.
The idiom is not so much_____ as ______, and (A) is parallel; not so much by…as by.
The questions in this group are based on the content of a passage. After reading the passage, choose the best answer to each question. Answer all questions following the passage on the basis of what is stated or implied in the passage.
Until recently corporate ideology in the United States has held that bigger is better. This traditional view of the primacy of big, centralized companies is now being challenged as some of the giants of American business
5. are being out formed by a new generation of smaller, streamlined business. If it was the industrial revolutions that spawned the area of massive industrialize companies, then perhaps it is the information revolutions of the 1990s that is spawning the area of the small company.
10. For most of this century, big companies dominated an American business scene that that seemed to thrive on its own Grandness of scale. The expansion westward, the growth of railroad and steel industries, an almost limitless supply of cheap raw materials, plus a populations boom
15.That provided an ever increasing demand for new products(although not cheap source of labor) all coincided to encourage the growth of large companies.
But rapid developments in the market place have begun to change the accepted rules of business and have underscored
20. the need for fast reaction times. Small companies without huge overhead and inventory, can respond quickly to a technologically advanced age in which new products and technologies can become outmoded within a year of their being brought to market.
25. Of course, successful emerging small companies face a potential dilemma in that their very success will tend to turn them into copies of the large corporate dinosaurs they are now supplanting. To avoid this trap, small companies may look to the example of several CEOs of large corporations who
30. have broken down their sprawling organizations into small semiindependent divisions capable of making their way into the twenty first century.
1. The primary purpose of the passage is to
Make a map of the passage. There are no contradictions that are being talked about, so A is out. The passage is not testing any model hence C is out. D is a trap answer it talks about “traditional ideology” while the passage is about “corporate ideology” and traditional views. Option E is out as no conflicting explanation for a phenomenon has been discussed in the passage.
2. The author’s attitude toward emerging small companies is one of the
Option (E) is out as too extreme. The author’s attitude is not critical or negative hence options (A) and (D) are out. (C) is a trap answer as it uses language from the passage – dilemma .
3. Which of the following best describes the organization of the first paragraph of the passage?
Option (B) is out as the author is not asserting himself. Option C is not correct as there are no evaluations being made. (D) is a trap answer as it talks about historical overview . A student would be attracted to this answer as the first paragraph talks about traditional view, gives dates and events etc. ( E ) is again not the correct option as no new theory is being described.
Passage 2
One recent example of industrial hyper growth has taken place in the recycling industry, led by the rapid expansion of the recycled paper market.
Though many laws were enacted in the late 1980s to encourage (and in some cases require) the collection of waste paper for recycling, there were not, at that time, companies with sufficient capacity to recycle it all. Consequently the collected paper accumulated in storage, usually at the expense of the recycling companies, thereby adding to their overhead and squeezing their already thin profit margins.
Today a different situation exists. Fiftyseven new paper mills have been built since 1991, and of these, at least twentynine use recycled fiber.
This surge in capacity has resulted in a concurrent rise in profits. The price per Ton of waste paper has quadrupled in the past year, as have the prices of corrugated cardboard and used newsprint. Trash haulers have benefited from these conditions by combining their trash hauling and recycling operations.
Recycling centers are connected both to the clients to whom they sell endproducts and to those from whom they collect refuse; thus, the company gets paid twice for the same trash, once for hauling the waste and once for selling the usable material. Industry profits have increased more than tenfold during this period. As the industry has become more competitive, some haulers have chosen to rebate a portion of this money to their clients in the hopes of ensuring their loyalty.
1. According to the passage, which of the following is a reason for the increase in profits in the trash hauling business?
Look for the cause of increased profits for trash haulers. This is discussed in lines 1622. (A) paraphrases the idea that the companies haul the trash (services) and sell the recycled paper (products). (B) is a trap because preferred customers is a recognizable phrase from a different part of the passage. (C), (D), and (E) are all out of scope.
2. It can be inferred from the passage that the price of waste paper
Look for the price of waste paper. It’s discussed in lines 1416. In step 3, students will answer that prices have increased a lot. (A) and (B) come close to that, but they make predictions rather than describing the past. (C) and (D) are out of scope. (E) is true (price per ton), even though it may seem trivial.
3. The author of the passage would most likely agree with which of the following?
(A) says the opposite of the passage: they cooperate more than they compete. (B), (D), and (E) are all out of scope. (C) isn’t great, but it’s probably true (you gotta love may) and consistent with the author’s description.
4. According to the passage, all of the following are results of the increase in the number of new mills using recycled finer except
With EXCEPT questions, find each of the wrong answers in the passage before you cross them off. The remaining, correct answer may either contradict the passage or just be out of scope. (A) is supported by lines 1416. (B) is supported by lines 2023. (C) is supported by lines 2223. (D) is supported by lines 1516. (E) contradicts the idea of cooperation between trash haulers and recyclers.
The graph is a scatter plot with 35 points, each representing the population of a city and the number of auto thefts in that city, per person, per year. All 35 measurements were made in the year 2010, counting the number of auto thefts during the year and the number of residents in each city as of January 1, 2010. The dashed line runs through points (0,0) and (35,1200).
Q. The percentage of cities that had at least 20 auto thefts per 1,000 is closest to?
The given information notes that there are 35 cities plotted. Counting the data points to the right of the 20theftsper1000people line, you'll find that there are 12 such cities. To quickly estimate the percentage, note that 12/36 would be exactly 1/3, or 33%, and 33% is the only answer choice that falls anywhere near the anticipated justabove1/3 figure, so it must be correct in this "is closest to which figure" question.
The graph is a scatter plot with 35 points, each representing the population of a city and the number of auto thefts in that city, per person, per year. All 35 measurements were made in the year 2010, counting the number of auto thefts during the year and the number of residents in each city as of January 1, 2010. The dashed line runs through points (0,0) and (35,1200).
Q. Every city with a population of no more than 600,000 had no more than _____ auto thefts per 1,000 people.
Looking below the 600,000 population line on the graph, you'll find that the highest theftsperthousand data point is between the 25 and 30 gridlines, meaning that every city in that under 600,000 group fell below the 30 theftsperthousand mark.
The graph is a scatter plot with 35 points, each representing the population of a city and the number of auto thefts in that city, per person, per year. All 35 measurements were made in the year 2010, counting the number of auto thefts during the year and the number of residents in each city as of January 1, 2010. The dashed line runs through points (0,0) and (35,1200).
Q. There is a __________ relationship between a city's population and its number of auto thefts per 1,000 people.
Viewing the regression line, you can note that it slopes upward and to the right  a positive slope. That slope indicates a positive relationship between population and average thefts: as the population increases, so does the rate.
Article 1:
News article in a popular business publication
June 7  If current trends continue, farmed seafood will overtake ocean fishing as the world's largest source of seafood by 2025. Aggressive overfishing of the world's oceans and the inability of world governments to agree on fishing limits mean that farming will become critical to the industry's ability to meet worldwide seafood demand. Additionally, recent concerns about mercury levels in wildcaught fish have led many consumers to prefer farmed fish, further creating increased demand for this relatively new source of seafood.
Article 2:
Interview with a well known scientist in a technology journal
July 2  Dr. Jason Dempster, one of the world's most outspoken critics of the seafood industry's unwillingness to curb its output in order to protect the fish population, suggests that more than two dozen popular species may become virtually extinct in the next several decades.
"I understand that consumers keep buying the seafood, and fishermen are naturally going to meet demand wherever they can find it. However, if something isn't done to meet the demand another way, by the middle of this century even something as common as tuna may become a delicacy only the world's wealthiest families can afford."
Article 3:
Article from a weekly news magazine
July 20  Demand for tilapia, one of the world's most popular species of fish, has grown 1000% over the last decade as people around the world have discovered it as a lowcost fish that goes well with a variety of foods. This increased demand has encouraged countless tilapia farms to open in China, and American officials have expressed concern that not all tilapia imported from China meets U.S. safety standards. Some experts in the U.S. have called for creating more stringent standards for all seafood imports, but Chinese authorities warn that this may dramatically increase the cost of seafood imported into the United States.
Consider each of the following statement. Does the information in the three articles support the inference as stated?
Statement : The world's governments usually do not agree with one another on how to deal with matters related to fishing and seafood farming.
While the first article notes that the world governments have been unable to agree on fishing limits, that does not necessarily mean that such disagreements are usually the case. Because this current situation could potentially be a unique occurrence, the statement in question is not necessarily true, and therefore not a valid conclusion just based on the information provided.
Article 1:
News article in a popular business publication
June 7  If current trends continue, farmed seafood will overtake ocean fishing as the world's largest source of seafood by 2025. Aggressive overfishing of the world's oceans and the inability of world governments to agree on fishing limits mean that farming will become critical to the industry's ability to meet worldwide seafood demand. Additionally, recent concerns about mercury levels in wildcaught fish have led many consumers to prefer farmed fish, further creating increased demand for this relatively new source of seafood.
Article 2:
Interview with a well known scientist in a technology journal
July 2  Dr. Jason Dempster, one of the world's most outspoken critics of the seafood industry's unwillingness to curb its output in order to protect the fish population, suggests that more than two dozen popular species may become virtually extinct in the next several decades.
"I understand that consumers keep buying the seafood, and fishermen are naturally going to meet demand wherever they can find it. However, if something isn't done to meet the demand another way, by the middle of this century even something as common as tuna may become a delicacy only the world's wealthiest families can afford."
Article 3:
Article from a weekly news magazine
July 20  Demand for tilapia, one of the world's most popular species of fish, has grown 1000% over the last decade as people around the world have discovered it as a lowcost fish that goes well with a variety of foods. This increased demand has encouraged countless tilapia farms to open in China, and American officials have expressed concern that not all tilapia imported from China meets U.S. safety standards. Some experts in the U.S. have called for creating more stringent standards for all seafood imports, but Chinese authorities warn that this may dramatically increase the cost of seafood imported into the United States.
Consider each of the following statement. Does the information in the three articles support the inference as stated?
Statement : An increase in worldwide demand for tilapia has driven the world's ocean fish population to dangerously low levels.
Article 3 discusses the large increase in demand for tilapia, but it does not indicate whether the ocean tilapia population has been threatened; in fact, the article only mentions farmed tilapia as a consumer product, so we cannot conclude anything about the ocean population.
Article 1:
News article in a popular business publication
June 7  If current trends continue, farmed seafood will overtake ocean fishing as the world's largest source of seafood by 2025. Aggressive overfishing of the world's oceans and the inability of world governments to agree on fishing limits mean that farming will become critical to the industry's ability to meet worldwide seafood demand. Additionally, recent concerns about mercury levels in wildcaught fish have led many consumers to prefer farmed fish, further creating increased demand for this relatively new source of seafood.
Article 2:
Interview with a well known scientist in a technology journal
July 2  Dr. Jason Dempster, one of the world's most outspoken critics of the seafood industry's unwillingness to curb its output in order to protect the fish population, suggests that more than two dozen popular species may become virtually extinct in the next several decades.
"I understand that consumers keep buying the seafood, and fishermen are naturally going to meet demand wherever they can find it. However, if something isn't done to meet the demand another way, by the middle of this century even something as common as tuna may become a delicacy only the world's wealthiest families can afford."
Article 3:
Article from a weekly news magazine
July 20  Demand for tilapia, one of the world's most popular species of fish, has grown 1000% over the last decade as people around the world have discovered it as a lowcost fish that goes well with a variety of foods. This increased demand has encouraged countless tilapia farms to open in China, and American officials have expressed concern that not all tilapia imported from China meets U.S. safety standards. Some experts in the U.S. have called for creating more stringent standards for all seafood imports, but Chinese authorities warn that this may dramatically increase the cost of seafood imported into the United States.
Consider each of the following statement. Does the information in the three articles support the inference as stated?
Statement : Dr. Dempster supports an increase in fish farming.
In article 2 Dr. Dempster is quoted as opposing the current fishing output, in order to "to protect the fish population". This does not necessarily mean that he favors farming, however; his comments are specific to fishing and not to farming, so we cannot make any inferences as to his opinions on farming.
Work crews Alpha and Zeta are repaving a section of freeway in Los Angeles. Work crew Alpha started its work one week (40 working hours) earlier than work crew Zeta, and started on the north end of the freeway, working its way south at a rate of 12 meters per hour since starting the job. Now, work crew Zeta has started at the south end, working its way north at a rate of 10 meters per hour. The section of freeway that needs to be repaved is 1.5 kilometers long, including the section that has already been paved.
Given that each crew will not necessarily work the same number of hours, which of the following answer choices represents an hourly workload for each crew that will finish the project? Please make only one selection in each column.
To solve this problem, you must create a model that generates the potential solutions. The total distance paved by Crew Alpha is 12*A, and the total distance paved by Crew Zeta is 10*Z, where A and Z are the hours worked by the respective crews. Thus, the answer will be a solution to:
12A + 10Z = Distance To Be Paved
Note that 480 meters of highway have already been paved (12 meters/hour * 40 hours), so there are only 1020 meters remaining. This gives you:
12A + 10Z = 1020
By plugging in values from one column, you will be able to compare the result with values from the second column, and you will find that A = 60, Z = 30 gives you the correct answer.
12(60) + 10Z = 1020
10Z = 300
Z = 30
Two companies are competing with one another for a contract to provide work uniforms to a customer, which is a large global manufacturing business. Company A sells its uniforms for $25 per uniform, and Company B's price is $30 per uniform. Both companies sell their uniforms in lots of 5,000 each. The customer has considered ordering some uniforms from both companies, in order to test them out before committing to one company on an ongoing basis. The company wants to spend exactly $1,000,000 on the test purchase.
In the table below, identify the number of uniforms that the customer should buy from Company A and from Company B so that the customer spends exactly $1,000,000. Make only one selection in each column.
This problem, like other 2part reasoning problems, asks you to find the one solution (out of many potential solutions) that is present in the table. We must first create an algebraic model for the situation at hand. We have shirts from Company A that cost $25 each, and shirts from Company B that cost $30 each, and that we want to spend exactly $1,000,000. This gives us the following model:
25A + 30B = 1,000,000
We also know that each must be purchased in bundles of 5,000 shirts (that is, A and B must both be multiples of 5,000), but the answer choices already take this into account for us. By testing values from one column, you will find that the correct answer is A = 10,000, B = 25,000.
25(10,000) + 30B = 1,000,00
30B = 750,000
B = 25,000
Blindly testing values can be timeconsuming, however, so it is often to your advantage to look for ways to simplify your search. For example, you could subtract 25A from the lefthand side, and divide all terms by 5 to rewrite the equation above as:
6B = 200,000  5A
Framing the equation in this manner should help you quickly eliminate some of the larger values from Column A, encouraging you to spend your time checking the smaller values instead  and finding the correct answer in the process.
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