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GRE GRE Test Exam
Graduate Record Examination Test: Verbal, Quantitative, Analytical Writing (Page 5 )

Updated On: 7-Feb-2026
Page 5 of 119
PDF with 793 Questions

x is the units digit of the number 1114 - 1.

Quantity A
x

Quantity B
1

  1. Quantity A is greater.
  2. Quantity B is greater.
  3. The two quantities are equal.
  4. The relationship cannot be determined from the information given.

Answer(s): B

Explanation:

The units digit of powers of 11 repeats in a cycle. Let's examine the first few powers of 11:
111 = 11, so the units digit is 1.

112 = 121, so the units digit is 1.

113 = 1331, so the units digit is 1.

114 = 14641, so the units digit is 1.

We observe that the units digit of 11n for any positive integer n is always 1.
Since the units digit of 1114 is 1, the units digit of 1114 - 1 is:
1 - 1 = 0
Quantity A: The units digit of 1114 - 1, which is 0.

Quantity B: 1.

Since 0 < 1, Quantity B is greater.



In a study of the size of frogs, group I consists of five frogs whose average (arithmetic mean) length is 4.7 centimeters. Group II consists of five frogs whose lengths are 4.3, 4.6, 4.7, 4.8, and 5.1 centimeters.

Quantity A
The standard deviation of the lengths of the five frogs in group I

Quantity B
The standard deviation of the lengths of the five frogs in group II

  1. Quantity A is greater.
  2. Quantity B is greater.
  3. The two quantities are equal.
  4. The relationship cannot be determined from the information given.

Answer(s): B

Explanation:

The standard deviation measures how spread out the values are from the mean. A higher spread results in a larger standard deviation.
Group I - All Frogs Have the Same Length:
· The average length in Group I is 4.7 cm.
· Since no specific lengths are given, we assume all five frogs have the same length of 4.7 cm.
· Since all values are equal to the mean (4.7), the deviations from the mean are all zero. Thus, the standard deviation of Group I is 0.
Group II - Variability Exists:
· The given lengths are 4.3, 4.6, 4.7, 4.8, and 5.1.
· These values are not all the same, meaning there is some spread.
· Since the values deviate from the mean, their standard deviation is greater than 0.





Quantity A
x + y

Quantity B
240

  1. Quantity A is greater.
  2. Quantity B is greater.
  3. The two quantities are equal.
  4. The relationship cannot be determined from the information given.

Answer(s): B

Explanation:

The shape resembles a rectangle with two diagonals forming a triangular flap at the top.
At the intersection of the two diagonals, we have three angles labeled x°, x°, and y°.
Since these three angles form a straight line at the vertex where they meet, they must sum to 180°:
x + x + y = 180
2x + y = 180
However, without an additional equation to find x, we cannot directly determine the exact value of x + y.
We only know that x + y < 180 (since x is a positive angle).
Since Quantity B is 240, and we determined that x + y < 180, it is clear that 240 is greater.



The area of circular region X is four times the area of a circular region with a radius of 3.

Quantity A
The radius of circular region X

Quantity B
6

  1. Quantity A is greater.
  2. Quantity B is greater.
  3. The two quantities are equal.
  4. The relationship cannot be determined from the information given.

Answer(s): C

Explanation:

The area of a circle is
A = r2
A = (32) = 9
Calculate the Area of Circular Region X:
Area of X = 4 × 9 = 36
Let r be the radius of circular region X. Using the area formula, we set up the equation:
r2 = 36
r2 = 36
r = 6



Integer m is a multiple of 15.

Quantity A
The remainder when 14m is divided by 6

Quantity B
0

  1. Quantity A is greater.
  2. Quantity B is greater.
  3. The two quantities are equal.
  4. The relationship cannot be determined from the information given.

Answer(s): C

Explanation:

m = 15k for some integer k.
14m = 14 × (15k) = 210k
First, simplify 210 mod 6:
210 ÷ 6 = 35 (exact division, remainder is 0)
Since 210k is always a multiple of 6 for any integer k, the remainder when 210k is divided by 6 is always 0.






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