GRE Quantitative Comparison (QC) Practice Questions

Written Explanation

s = 17k + 9
t = 13k + 5
k is a positive integer.
We need to determine the relationship between the ones digit of s – t and 9.

Quantity A: 
s – t = (17k + 9) – (13k + 5) = 4k + 4
Since 4k + 4 will always be an even number for any positive integer k, the ones digit of s – t must be an even number.
Therefore, the ones digit of s – t will always be less than 9.

Quantity B: 
9

Hence, Quantity B is greater.

B is the correct answer.    

Written Explanation

The number of Radom Skincare products containing aloe vera = 29.
The number of Radom Skincare products containing vitamin K = 18.
The number of Radom Skincare products containing both aloe vera and vitamin K = 7.
We need to determine the relationship between the number of Radom Skincare products containing aloe vera or vitamin K but not both and 40.

Quantity A:
The number of Radom Skincare products containing aloe vera but not vitamin K
= (The number of Radom Skincare products containing aloe vera) – (The number of Radom Skincare products containing both aloe vera and vitamin K)
= 29 – 7
= 22

The number of Radom Skincare products containing only vitamin K but not aloe vera
= (The number of Radom Skincare products containing vitamin K) – (The number of Radom Skincare products containing both aloe vera and vitamin K)
= 18 – 7
= 11

The number of Radom Skincare products containing aloe vera or vitamin K but not both
= (The number of Radom Skincare products containing aloe vera but not vitamin K) + (The number of Radom Skincare products containing vitamin K but not aloe vera)
= 22 + 11
= 33 

Quantity B:
40

Hence, Quantity B is greater.

B is the correct answer. 

Written Explanation

f (x – 5 / 3)= x² – 8x + 4
We need to determine the relationship between f(2) and 30.   

Quantity A:
Since we need to calculate f(2) and f is expressed in terms of x, we first need to calculate the corresponding value of x.
(x – 5) / 3 = 2
x – 5 = 6
x = 11

Therefore, f(2) = x² – 8x + 4
= (11)² – 8(11) + 4
= 121 – 88 + 4
= 37

Quantity B:
30

Hence, Quantity A is greater.

A is the correct answer.   

Written Explanation

The above figure is a right-angled triangle.
We need to determine the relationship between x and 50.

Quantity A:
Since the sum of the angles of a triangle is 180°,
x° + y° + 90° = 180°
x° + y° = 90°
y° = 90° – x°          (Equation I)

The side opposite to angle y = y + 10 = (90 – x) + 10 = 100 – x.
Since the side opposite to angle x is also (100 – x), the above figure is an isosceles triangle.
Therefore, y° = x°.

Substituting the value of y in Equation I,
x° = 90° – x°
2x° = 90°
x° = 45° 

Quantity B:
50°           

Hence, Quantity B is greater.

B is the correct answer.   

Written Explanation

Daily late fee for a book = ( f / 100 ) × (Weekly rental fee for a book)
We need to determine the relationship between the total late fee for a book rented for 12 days, for which the total charge, including the late fee, was $12 and $5.

Since the daily late fee for a book that costs $5 to rent for a week is calculated at $0.5;
$5 × ( f / 100 ) = $0.5
f = ($0.5 × 100) / $5
f = 10

Quantity A:
Let the weekly rental fee for the book be w.
The book was rented for 12 days. This implies that the total charge includes 12 – 7 = 5 days of daily late fee.
Since the daily late fee is 10 percent of the book’s weekly rental fee, the daily late fee for 1 day = 0.1w.
Thus, the total late fee for 5 days = 5 × 0.1w = 0.5w.

The total charge for a book rented for 12 days, including the late fee, was $12.
(Weekly rental fee) + (Total late fees) = $12
w + 0.5w = $12
1.5w = $12
w = $8

The total late fee for 5 days 
= 0.5w
= 0.5 × $8
= $4

Quantity B:
$5

Hence, Quantity B is greater.

B is the correct answer.   

Written Explanation

Let the length of each side of square R be x.
Since the length of each side of a square S is 4 times the length of each side of square R, the length of each side of square S = 4x.
We need to determine the relationship between the ratio of the area of square S to the perimeter of square S and the ratio of the area of square R to the perimeter of square R.

Quantity A:
The area of square S = (Length of each side of a square S)² = (4x)² = 16x².
The perimeter of square S = 4(Length of each side of a square S) = 4(4x) = 16x.
The ratio of the area of square S to the perimeter of square S = (16x²) / (16x) = x.

Quantity B:
The area of square R = (Length of each side of a square R)² = x².
The perimeter of square R = 4(Length of each side of a square R) = 4(x) = 4x.
The ratio of the area of square R to the perimeter of square R = (x²) / (4x) = x / 4 .

Since the side length cannot be negative, it follows that x > ( x / 4 ).

Hence, Quantity A is greater.

A is the correct answer.   

Written Explanation

D = 80⁸⁰ – 80
When D is divided by 27, the remainder is k.
We need to determine the relationship between k and 3.   

Quantity A:
When 80 is divided by 27, we get the remainder of 26.
To simplify calculations, we can use the equivalent negative remainder –1 (since 26 – 27 = –1).
(Note: Using the remainder 26 instead of –1 would also result in the same answer, however, we choose to use –1 as it is easier to calculate powers of –1)
Therefore, when 80⁸⁰ is divided by 27, we get the remainder of (–1)⁸⁰.

Remainder when (80⁸⁰ – 80) divided by 27 
= Remainder when (–1⁸⁰ – 80) divided by 27
= Remainder when (1 – 80) divided by 27
= Remainder when –79 divided by 27
= 2 

Quantity B:
3

Hence, Quantity B is greater.

B is the correct answer. 

Written Explanation

–2 < m + n < 6          (Inequality I)
1 < m < 3
We need to determine the relationship between n and –5.

Quantity A:
1 < m < 3
Multiplying by –1,
–1 > –m > –3
Rearranging the terms,
–3 < –m < –1          (Inequality II)

Adding Inequality I and II,
–2 + (–3) < m + n + (–m) < 6 + (–1)
–5 < n < 5
Thus, all values of n are greater than –5.

Quantity B:
–5

Hence, Quantity A is greater.

A is the correct answer.   

Written Explanation

|–x| = x
We need to determine the relationship between x and –1.

Since |–x| is always non-negative and |–x| = x, x must be non-negative which implies that x must be 0 or positive.
Thus, x ≥ 0.

Hence, Quantity A is greater.

A is the correct answer.   

Written Explanation

We need to determine the relationship between p + q and a + b.

The line shown in the graph passes through the origin (0, 0) and the point (4, –4).
Thus, the equation of the line shown in the graph is y = –x.

For any point above the y = –x line, the y coordinate will be greater than the negative of the x coordinate. Therefore, q > –p.
Similarly, for any point below the y = –x line, the y coordinate will be less than the negative of the x coordinate. Therefore, –a > b.

Since q > –p and –a > b;
q – a > –p + b
p + q > a + b

Hence, Quantity A is greater.

A is the correct answer.