At a furniture maker, the cost of manufacturing a type of chair varies between $100 and $150, depending on the current prices of raw materials. The selling price of the chair varies between $300 and $400, depending on the availability of seasonal discounts. The profit percentage earned by the furniture maker on the sale of a chair of this type must be between:
Given
To Find: The maximum and minimum percentage profit
Approach:
Working out :
Looking at the answer choices, we see that the correct answer is Option B
In a country X, length is measured in the units of sycras. If 1 sycra is equal to 3.24 inches and there are 0.083 feet in 1 inch, which of the following best approximates the height of a 5 feet 3 inches tall woman in sycras?
Given:
To Find: The approximate value of H in sycras
Approach:
Working out:
S is the sum of the reciprocals of the squares of the prime numbers between 19 and 41, exclusive. Which of the following is closest to
the value of S?
Given
Prime numbers between 19 and 41, exclusive = {23, 29, 31, 37}
To Find: The option that is closest to the value of S
Approach:
Working out
Looking at the answer choices, we see that the only option that satisfies this range is Option B
Nick appeared in a test of quantitative ability that consisted of 100 questions. Nick was awarded 4 marks for each correct answer and 1 mark was deducted for each wrong answer. If the number of questions attempted by Nick was between 70 and 80, inclusive, and his accuracy range was 60%  75%, inclusive, in what range did Nick’s score lie?
Given:
To Find: Range of Nick’s score?
Approach
Working out:
a. Maximum number of questions that Nick could attempt = 80
b. Highest accuracy rate = 75%
c. Number of questions that Nick got correct = 75% of 80 = 60
d. Number of questions that Nick got incorrect = 25% of 80 = 20
e. Total marks = 60 * 4 – 20 * 1 = 220
2. Calculating the Minimum Possible Score
a. Minimum number of questions that Nick could attempt = 70
b. Lowest accuracy rate = 60%
c. Number of questions that Nick got correct = 60% of 70 = 42
d. Number of questions that Nick got incorrect = 40% of 70 = 28
e. Total marks = 42 * 4 – 28 * 1 = 140
3. So, Nick’s scores would range between 140 – 220, inclusive
Answer C
If , where A is a positive integer lesser than or equal to 20, B is a nonzero integer between 10 and 10, inclusive, and m and n are nonnegative singledigit numbers, which of the following expressions is true?
Given:
To Find: Out of the given options on the range of P, which is correct?
Approach:
Working out:
Looking at the answer choices, we see that the correct answer is Option C
The sum is between
Given:
The sum
To Find: The value of this sum lies between which of the 5 ranges given in the answer choices
Approach:
Working out:
Therefore,√30 will almost lie midway between 5 and 6
Looking at the answer choices, we see that the correct answer is Option B
If R and S are threedigit positive integers, what is the quotient when the sum of R and S is divided by 1000?
(1) The hundreds digit of the sum of R and S is less than the sum of the hundreds digits of R and S.
(2) When R, rounded to the nearest hundreds, is added to S, rounded to the nearest hundreds, the result is 1000.
Step 1 & 2: Understand Question and Draw Inference
To find: The quotient when R + S is divided by 1000
Step 3 : Analyze Statement 1 independent
The hundreds digit of the sum of R and S is less than the sum of the hundreds digits of R and S.
There are 4 possible cases for the hundreds digit of R+S:
Case A: There is no carryover into the hundreds digit and there is no carryover at the hundreds digit
Example: 1 2 3
+ 2 3 4
In this example, R + S = 357
So, (hundreds digit of R+S) = 3
And (hundreds digit of R) + (hundreds digit of S) = 1 + 2 = 3
In this case, (hundreds digit of R+S) = (hundreds digit of R) + (hundreds digit of S)
Case B: There is no carryover into the hundreds digit but there is carryover happening AT the hundreds digit
Example: 9 2 3
+ 1 3 4
In this example, R + S = 1057
So, (hundreds digit of R+S) = 0
But (hundreds digit of R) + (hundreds digit of S) = 9 + 1 = 10
So, here, (hundreds digit of R+S) < (hundreds digit of R) + (hundreds digit of S)
Case C: There is carryover into the hundreds digit and there is no carryover AT the hundreds digit
Example: 7 9 4
+ 1 2 2
In this example, R + S = 916
So, (hundreds digit of R + S) = 9
Whereas, (hundreds digit of R) + (hundreds digit of S) = 7 + 1 = 8
In this case, (hundreds digit of R+S) > (hundreds digit of R) + (hundreds digit of S)
Case D: There is carryover into the hundreds digit and there is carryover happening AT the hundreds digit
Example 1: 6 9 4
+ 3 2 1
In this example, R + S = 1015
So, (hundreds digit of R + S) = 0
Whereas, (hundreds digit of R) + (hundreds digit of S) = 6 + 3 = 9
Here, (hundreds digit of R+S) < (hundreds digit of R) + (hundreds digit of S)
Example 2: 8 9 4
+ 7 2 1
In this example, R + S = 1615
So, (hundreds digit of R + S) = 6
Whereas, (hundreds digit of R) + (hundreds digit of S) = 15
Here too, (hundreds digit of R+S) < (hundreds digit of R) + (hundreds digit of S)
Therefore, we notice that in all the cases where Statement 1 is satisfied, that is the cases where (hundreds digit of R+S) < (hundreds digit of R) + (hundreds digit of S), there is carryover is happening at the hundreds digit. Therefore, we can be sure that Case 2 discussed in ‘Steps 1 and 2’ is applicable. So, the quotient when R + S is divided by 1000 is 1.
Since we get a unique answer from this Statement, Statement 1 is sufficient to answer the question.
Step 4 : Analyze Statement 2 independent
When the R, rounded to the nearest hundreds, is added to S, rounded to the nearest hundreds, the result is 1000.
Thus, we’ve seen that from Statement 2, the value of the quotient may be 0 or 1.
So, Statement 2 is not sufficient to get a unique value of the quotient.
Step 5: Analyze Both Statements Together (if needed)
Since we’ve got a unique answer in Step 3, this step is not required
Answer: Option A
T = 2.z hours
If z denotes the tenths digit in the decimal representation of the time T that a car takes to cover 258 miles, what is the value of z?
(1) The speed of the car is 1 mile per minute, rounded to the nearest integer
(2) When T is rounded to the nearest 100 minutes, the result is 200.
Step 1 & 2: Understand Question and Draw Inference
Given:
Step 3 : Analyze Statement 1 independent
Step 4 : Analyze Statement 2 independent
Thus, from Statement 2, we get 5 possible values of z: {5, 6, 7, 8, 9}
So, Statement 2 is not sufficient to arrive at a unique answer.
Step 5: Analyze Both Statements Together (if needed)
We’ve already arrived at a unique answer in Step 3, so this step is not required Answer: Option A
For every x celestial objects of the Sunny Way galaxy that can be seen from the Earth, there are x – (x) celestial objects of the galaxy that cannot be seen from the Earth. In the years of research done on the Sunny Way galaxy, scientists have been able to see only 93 planets in the galaxy. These planets were seen to have an average of 7 satellites per planet. It is also known that the ratio of the number of stars in the galaxy that are seen from the Earth to the number of satellites in the galaxy that are seen from the Earth is 2600:1 Assuming the same ratios are followed for the invisible celestial objects, which of the following is closest to the number of celestial objects in the Sunny Way galaxy?
Given:
To Find: Number of objects in the galaxy?
Approach:
Working out
Answer C
In a recurring manufacture – to sale cycle, a toy manufacturer sells a type of toys to a retailer at a profit that varies between 50% and 60%, depending on the size of the retailer’s order (the retailer gets a proportional discount for bulk purchase of toys). The retailer marks up the price of these toys by 20% to 40% depending on the location of his different shops. The retailer then offers a discount, across all shops, of either 10% or $15 on the purchase of a toy to the customer. If the manufacturer incurs a cost of $100 to manufacture a toy, the profit earned by the retailer per toy must be between:
Given:
To Find: Range of profit earned by the retailer
Approach:
ii.
iii. Selling price of the retailer will be maximum when the marked price is maximum and the discount offered is minimum
iv. Selling price of the retailer will be minimum when the marked price is minimum and the discount offered is maximum
6. So, we see here that the maximum selling price of the manufacturer depends on the maximum markup price of the retailer, which is further dependent on the maximum cost price of the retailer.
Working out
i. Maximum profit% = 60%
ii. So, maximum selling price = 100 + 60% of 100 = 160
iii. So, maximum cost price of retailer = 160 …………..(1)
i. Minimum profit% = 50%
ii. So, minimum selling price = 100 +50% of 100 = 150
iii. So, minimum cost price of retailer = 150……………(2)
3. Hence, the profit ranges from $12 $49
Answer: C
A plot is in the shape of a rightangled triangle whose shorter sides measure 78.8 meters and 62.4 meters respectively. If an insect takes 1.79 minutes to cover a distance of 100 inches, what is the approximate time that it will take to return to its starting point after covering the entire perimeter of the plot in one direction? (1 meter is approximately 39.37 inches)
Given:
To Find: Time taken by the insect to cover the perimeter of the plot
Approach:
2. Also note the huge difference in the magnitude of different answer choices. This means, we can afford to use the principle of estimation and rounding aggressively to ease our calculations
Working out
Looking at the answer choices, we see that the correct answer is Option D
The length and breadth of a rectangle are 2.4 units and 3.6 units respectively. If A is the area obtained by first multiplying the dimensions and then rounding the product to the nearest integer, and A* is the area obtained by first rounding each dimension to the nearest integer and then multiplying them, by what percentage is A* lesser or greater than A?
Given:
To Find: By what percentage is A* less or greater than A?
Approach:
d. So, to find the value of p, we need to find the value of A^{*}/A
e. (Note: if upon calculation, the value of p comes to be negative, this will mean that A* is less than A by p percentage)
2. To find the value of A^{*}/A, we’ll calculate the values of A* and A.
Working out :
Looking at the answer choices, we see that the correct answer is Option D
If x is a positive integer, what is the tens digit of x?
Step 1 & 2: Understand Question and Draw Inference
To Find: tens digit of x?
Step 3 : Analyze Statement 1 independent
As we do not have a unique value of tens digit of x, the statement is insufficient to answer.
Step 4 : Analyze Statement 2 independent
2. When the product of 3 and (x+1) is rounded to the nearest tens, the result is 70
As we have a unique value of tens digit of x, this statement is sufficient to answer.
Step 5: Analyze Both Statements Together (if needed)
As we have a unique answer from step 4, this step is not required.
Answer: B
is closest to which of the following
Given:
To Find: Approximate value of the expression
Approach:
Working out:
Answer C
x = ab.cd, where a, b, c and d are the tens, units, tenths and hundredths digits respectively in the decimal representation of x. If the number obtained when x is rounded to the nearest integer is subtracted from the number 10a + b + 1, what is the result?
Step 1 & 2: Understand Question and Draw Inference
When x is rounded off to the nearest integer, the results can be:
I. 10a + b+ 1, if c ≥ 5
II. 10a + b , if c < 5
So, when the number obtained by rounding off x to the nearest integer is subtracted from 10a + b+ 1, we get:
Thus, we need to find if c ≥ 5 in order to find the required answer.
Step 3 : Analyze Statement 1 independent
1. 10a + b and 10c + d are prime numbers less than 50
As 10c + d < 50, c < 5.
Sufficient to answer the question
Step 4 : Analyze Statement 2 independent
2. When the number is rounded to the nearest integer, the result is 10b +a +1
It tells us that d ≥ 5, however it does not tell us anything about c.
Step 5: Analyze Both Statements Together (if needed)
Since, we have a unique answer from step 4, this step is not required.
Answer: C
In the third century BC, Greek mathematician and astronomer Eratosthenes calculated the circumference of the Earth to be 252,000 stadia. The stadion (plural: stadia) was a unit of length used in ancient Greece and the value of 1 stadion in terms of later units of length has been the subject of much debate. One belief is that 1 stadion is equivalent to 157.5 metres while another is that 1 stadion equals 185 metres. If the circumference of the Earth is now known to be 24,902 miles (where 1 mile is approximately 1.61 kilometres), depending upon the chosen equivalent measure of a stadion, the error in Erastothenes’ calculation is the closest to
Given:
To Find: % error in Erastothenes’ calculation
Approach:
Working out:
The Actual circumference of Earth = 24,902 miles = 24,900 miles approx.
(Looking at the answer choices, we’ll already know that the answer will be Option A, but still for the sake of completeness of the solution, we’ll also show below the calculation of % Error for the other possible value of 1 stadion)
Looking at the answer choices, we see that the correct answer is Option A
A company offers an allowance of $500 perday to its employees for an official outstation visit. Pristine went on a two day official trip to Singapore. She made all triprelated expenses out of the allowance offered by the company and fully exhausted the allowance by the end of her trip. During the trip, she spent not less than $350 and not more than $400 each day on expenses other than food. If she had only 2 meals each day and paid a 15% tax and 5% tip on the price of each meal, the average price of her meal, excluding the tax and the tip, must be between:
Given:
Approach:
Working out:
3. Minimum amount spend on nonfood items = $350 *2 = $700
a. So, maximum amount available to spend on food = $1000  $700 = $300
d. Hence, the range of her average cost of meal was between $41 and $63
Answer C
z = 56.x43
In the decimal representation of z above, x denotes the tenths digit of z. Can x be equal to 2?
(1) When the product of 10 and z is rounded to the nearest integer, the result is 564
(2) When the product of 100 and z is rounded to the nearest integer, the result is 5644
Step 1 & 2: Understand Question and Draw Inference
Given: Number z = 56.x43
To find: Can x be equal to 2? _______________
Step 3 : Analyze Statement 1 independent
Statement 1 says that ‘When the product of 10 and z is rounded to the nearest integer, the result is 564’
Statement 1 alone is sufficient to answer the question
Step 4 : Analyze Statement 2 independent
Statement 2 says that ‘When the product of 100 and z is rounded to the nearest integer, the result is 5644’
Statement 2 alone is sufficient to answer the question
Step 5: Analyze Both Statements Together (if needed)
Since we get a unique answer in each of Steps 3 and 4, this step is not required
Answer: Option D
If a, b, c and d denote the hundreds, tens, units and tenths digits respectively in the decimal representation of z above, is the number that results when z is rounded to the nearest integer divisible by 3?
(1) When z100 is rounded to the nearest hundredths, the result is 1.85
(2) When z +2 is rounded to the nearest tens, the result is 190
Step 1 & 2: Understand Question and Draw Inference
Given:
To find: When z is rounded to the nearest integer, is the result divisible by 3?
Step 3 : Analyze Statement 1 independent
So, Statement 1 is sufficient to find a unique answer to the question.
Step 4 : Analyze Statement 2 independent
So, Statement 2 alone is not sufficient to answer the question
Step 5: Analyze Both Statements Together (if needed)
Since we’ve already arrived at a unique answer in Step 3, this step is not required
Answer: Option A
n = 92.abc, where a, b and c denote the tenths, hundredths and thousandths digits respectively in the decimal representation of n.
When n is rounded to the nearest integer, the result is 92. If c is the average of two consecutive prime numbers such that c > b > a,
what is the difference between the maximum and minimum possible sum of a, b and c?
Given:
Approach:
Working out:
a. Maximum value of a = 4
b. Minimum value of a = 0
2. Since c is an integer ≤ 9 and c is the average of two consecutive prime numbers, possible values of c can be:
3. Now, b is a digit from 0 to 9, however keeping in mind the constraint that b > a, b ≠ 0, because in that case b will not be greater than a.
a. So, Minimum value of b = 1 …….(3)
b. Also, since b < c, b ≠ 9, because in that case b will not be less than c.
c. So, maximum value of b = 8…….(4)
4. Combining (1), (2), (3) and (4), we have
5. Hence, Max (a + b + c) – Min (a+ b + c) = 21 – 5 = 16
Answer B
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