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Free practice questions/GRE General Test

GRE General Test — Arithmetic

30 free practice questions with full explanations.

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Question 1

A number increased by 50% and then decreased by 20% results in 96. What was the original number?

  • A) 72
  • B) 76
  • C) 80
  • D) 84
  • E) 90
Show answer & explanation

Correct answer: C) 80

Let x be the original number. x x 1.5 x 0.8 = 1.2x = 96. x = 96/1.2 = 80.

Question 2

What is 5/8 expressed as a percent?

  • A) 58%
  • B) 60%
  • C) 62.5%
  • D) 65%
  • E) 80%
Show answer & explanation

Correct answer: C) 62.5%

5/8 = 0.625 = 62.5%.

Question 3

What is the value of 2^6 + 2^5?

  • A) 96
  • B) 100
  • C) 112
  • D) 128
  • E) 160
Show answer & explanation

Correct answer: A) 96

2^6 = 64 and 2^5 = 32. 64 + 32 = 96.

Question 4

What is the greatest common divisor of 60 and 90?

  • A) 10
  • B) 15
  • C) 20
  • D) 30
  • E) 45
Show answer & explanation

Correct answer: D) 30

60 = 2^2 x 3 x 5. 90 = 2 x 3^2 x 5. Common factors: 2 x 3 x 5 = 30.

Question 5

What is the value of |4 - 11| + |6 - 2|?

  • A) 17
  • B) 9
  • C) 11
  • D) 3
  • E) -3
Show answer & explanation

Correct answer: C) 11

|4-11|=7. |6-2|=4. 7+4=11.

Question 6

What is the value of 6^2 + 8^2?

  • A) 100
  • B) 112
  • C) 48
  • D) 96
  • E) 64
Show answer & explanation

Correct answer: A) 100

6^2=36. 8^2=64. 36+64=100.

Question 7

What is 3/8 expressed as a percent?

  • A) 38%
  • B) 35%
  • C) 40%
  • D) 32.5%
  • E) 37.5%
Show answer & explanation

Correct answer: E) 37.5%

3 divided by 8 = 0.375 = 37.5%.

Question 8

What is the least common multiple of 6, 8, and 12?

  • A) 12
  • B) 36
  • C) 96
  • D) 24
  • E) 48
Show answer & explanation

Correct answer: D) 24

6=2x3, 8=2^3, 12=2^2x3. LCM=2^3x3=24.

Question 9

A number x is decreased by 40% and then the result is increased by 50%. The final value is what percent of x?

  • A) 60%
  • B) 75%
  • C) 90%
  • D) 100%
  • E) 110%
Show answer & explanation

Correct answer: C) 90%

Decreasing by 40% gives 0.60x. Increasing that by 50% gives 0.60x x 1.5 = 0.90x, which is 90% of x.

Question 10

What is the remainder when 7^100 is divided by 5?

  • A) 0
  • B) 1
  • C) 2
  • D) 3
  • E) 4
Show answer & explanation

Correct answer: B) 1

The units digits of powers of 7 cycle: 7, 9, 3, 1, 7, 9, 3, 1... with period 4. Since 100 is divisible by 4, 7^100 ends in 1, and dividing a number ending in 1 by 5 leaves remainder 1.

Question 11

Which of the following is equivalent to |{-8}| + |{5} - {9}|?

  • A) 4
  • B) 8
  • C) 12
  • D) 13
  • E) 17
Show answer & explanation

Correct answer: C) 12

|-8| = 8. |5 - 9| = |-4| = 4. 8 + 4 = 12.

Question 12

What is the value of 3^4 - 2^5?

  • A) 49
  • B) 45
  • C) 51
  • D) 65
  • E) 17
Show answer & explanation

Correct answer: A) 49

3^4 = 81 and 2^5 = 32. 81 - 32 = 49.

Question 13

If a number is increased by 25% and the result is 60, what was the original number?

  • A) 45
  • B) 48
  • C) 50
  • D) 52
  • E) 75
Show answer & explanation

Correct answer: B) 48

Let x be the original number. x(1.25) = 60, so x = 60/1.25 = 48.

Question 14

What is the greatest common divisor of 84 and 126?

  • A) 6
  • B) 12
  • C) 21
  • D) 42
  • E) 63
Show answer & explanation

Correct answer: D) 42

84 = 2^2 x 3 x 7. 126 = 2 x 3^2 x 7. The common factors are 2 x 3 x 7 = 42.

Question 15

If x is 40% of y and y is 60 more than x, what is the value of x?

  • A) 20
  • B) 30
  • C) 40
  • D) 50
  • E) 60
Show answer & explanation

Correct answer: C) 40

x = 0.40y and y = x + 60. Substituting: x = 0.40(x+60) = 0.40x + 24. 0.60x = 24. x = 40.

Question 16

What is the value of 5^3 - 4^3?

  • A) 39
  • B) 61
  • C) 64
  • D) 89
  • E) 125
Show answer & explanation

Correct answer: B) 61

5^3 = 125, 4^3 = 64. 125 - 64 = 61.

Question 17

A number decreased by 30% equals 84. What is the original number?

  • A) 100
  • B) 105
  • C) 110
  • D) 114
  • E) 120
Show answer & explanation

Correct answer: E) 120

Let x be the original number. 0.70x = 84. x = 84/0.70 = 120.

Question 18

What is the least common multiple of 9 and 15?

  • A) 30
  • B) 45
  • C) 60
  • D) 90
  • E) 135
Show answer & explanation

Correct answer: B) 45

9 = 3^2, 15 = 3 x 5. LCM = 3^2 x 5 = 45.

Question 19

What is the value of 6^2 + 3^3?

  • A) 45
  • B) 54
  • C) 63
  • D) 72
  • E) 81
Show answer & explanation

Correct answer: C) 63

6^2 = 36 and 3^3 = 27. 36 + 27 = 63.

Question 20

A number increased by 20% equals 96. What is the original number?

  • A) 72
  • B) 76
  • C) 78
  • D) 80
  • E) 84
Show answer & explanation

Correct answer: D) 80

Let x be the original number. 1.20x = 96. x = 96/1.20 = 80.

Question 21

What is the least common multiple of 8 and 12?

  • A) 16
  • B) 24
  • C) 36
  • D) 48
  • E) 96
Show answer & explanation

Correct answer: B) 24

8 = 2^3, 12 = 2^2 x 3. LCM = 2^3 x 3 = 24.

Question 22

If x is 30% of y and y is 80% of z, what percent of z is x?

  • A) 12%
  • B) 18%
  • C) 24%
  • D) 26.7%
  • E) 30%
Show answer & explanation

Correct answer: C) 24%

x = 0.30y and y = 0.80z, so x = 0.30 x 0.80z = 0.24z, meaning x is 24% of z.

Question 23

What is the least common multiple of 18 and 30?

  • A) 540
  • B) 60
  • C) 45
  • D) 90
  • E) 180
Show answer & explanation

Correct answer: D) 90

18 = 2 x 3^2. 30 = 2 x 3 x 5. LCM takes the highest power of each prime: 2 x 3^2 x 5 = 90.

Question 24

A number when divided by 7 leaves a remainder of 4. What is the remainder when 3 times that number is divided by 7?

  • A) 4
  • B) 3
  • C) 6
  • D) 0
  • E) 5
Show answer & explanation

Correct answer: E) 5

If n = 7k + 4, then 3n = 21k + 12 = 7(3k+1) + 5. Remainder is 5.

Question 25

If 0.4 liters of a solution is mixed with 0.6 liters of pure water, what percent of the resulting mixture is the original solution?

  • A) 40%
  • B) 60%
  • C) 50%
  • D) 36%
  • E) 44%
Show answer & explanation

Correct answer: A) 40%

Total mixture = 0.4 + 0.6 = 1.0 liters. Original solution fraction = 0.4/1.0 = 40%.

Question 26

A store marks up the wholesale price of an item by 40% to set the retail price, then later offers a 25% discount off that retail price during a sale. The sale price, as a percentage of the original wholesale price, is closest to:

  • A) 95%
  • B) 115%
  • C) 105%
  • D) 75%
  • E) 140%
Show answer & explanation

Correct answer: C) 105%

Retail = wholesale x 1.40. Sale price = retail x 0.75 = wholesale x 1.40 x 0.75 = wholesale x 1.05, i.e., 105% of wholesale.

Question 27

What is the value of 7^2 - 5^2?

  • A) 12
  • B) 24
  • C) 35
  • D) 49
  • E) 74
Show answer & explanation

Correct answer: B) 24

7^2=49. 5^2=25. 49-25=24.

Question 28

A car travels 224 miles using 8 gallons of gas. At this rate, how many miles can it travel on 11 gallons?

  • A) 300
  • B) 320
  • C) 296
  • D) 308
  • E) 288
Show answer & explanation

Correct answer: D) 308

Rate = 224/8 = 28 miles/gallon. 28 x 11 = 308.

Question 29

What is the least common multiple of 10, 15, and 25?

  • A) 50
  • B) 75
  • C) 100
  • D) 300
  • E) 150
Show answer & explanation

Correct answer: E) 150

10=2x5, 15=3x5, 25=5^2. LCM=2x3x5^2=150.

Question 30

What is 5/16 expressed as a percent?

  • A) 31.25%
  • B) 30%
  • C) 32.5%
  • D) 35%
  • E) 28%
Show answer & explanation

Correct answer: A) 31.25%

5 divided by 16 = 0.3125 = 31.25%.

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