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Arithmetic Questions for GRE Quantitative Reasoning
Question 1: A number ( n ) is 20% less than another number ( m ). If ( m = 50 ), what is ( n )?
A) 35
B) 40
C) 42
D) 45
E) 48
Answer: B) 40.
Explanation: ( n = m - 0.2m = 50 - 10 = 40 )
Question 2: If ( a ) and ( b ) are positive integers such that ( a \times b = 36 ), and ( a ) is 3 less than twice ( b ), what is the value of ( a + b )?
A) 11
B) 13
C) 15
D) 17
E) 19
Answer: C) 15.
Explanation: Let ( a = 2b - 3 ). Then, ( (2b - 3)b = 36 ). Solving, ( b = 6, a = 9 ). So, ( a + b = 15 ).
Question 3: A bakery sells cupcakes in packs of 6 and packs of 9. If ( p ) packs of 6 and ( q ) packs of 9 are bought, and the total number of cupcakes is 90, what is the smallest possible value of ( p + q )?
A) 7
B) 8
C) 9
D) 10
E) 11
Answer: B) 8.
Explanation: Solve ( 6p + 9q = 90 ). Simplifying, ( 2p + 3q = 30 ). Smallest ( p + q ) occurs when ( p = 3, q = 5 ). Thus, ( p + q = 8 ).
Question 4: If ( x ) is an even integer and ( y = 3x + 5 ), which of the following must be odd?
A) ( x )
B) ( y )
C) ( 2x + y )
D) ( x + y )
E) ( 2y )
Answer: B) ( y ).
Explanation: Since ( x ) is even, ( 3x ) is even, and ( 3x + 5 ) is odd.
Question 5: If a number ( n ) leaves a remainder of 3 when divided by 5, what is the remainder when ( 2n ) is divided by 5?
A) 1
B) 2
C) 3
D) 4
E) 0
Answer: D) 4.
Explanation: If ( n = 5k + 3 ), then ( 2n = 10k + 6 = 5(2k) + 6 ). So, the remainder is 4
Algebra Questions for GRE Quantitative Reasoning
Question 6: If
A) 4
B) 5
C) 6
D) 7
E) 8
Answer: A) 4.
Explanation: Substitute ( x = 4 ) into
( x^2 - 6x + 9 ) : ( 16 - 24 + 9 = 4 ).
Question 7: Solve for ( x ) if
A) 4
B) 5
C) 6
D) 7
E) 8
Answer: A) 4.
Explanation: Simplify: ( x - 3 = 2(x + 2) ). Solving, ( x - 3 = 2x + 4 ). Thus, ( x = -7 ).
Question 8: If ( f(x) = 2x^2 - 3x + 4 ), what is ( f(2) - f(-2) )?
A) 20
B) 22
C) 24
D) 26
E) 28
Answer: C)24.
Explanation: ( f(2) = 2(4) - 3(2) + 4 = 6 ). ( f(-2) = 2(4) + 6 + 4 = 14 ). So, ( f(2) - f(-2) = -8 ).
Question 9: If ( 3x + 2y = 6 ) and ( 2x - y = 4 ), what is ( x + y )?
A) 0
B) 1
C) 2
D) 3
E) 4
Answer: B) 1.
Explanation: Solve the system: ( x = 2, y = -1 ). So, ( x + y = 1 )
Question 10: If
A) -4
B) -2
C) 0
D) 2
E) 4
Answer: E) 4.
Explanation: Factor:
( (x - 2)^2 = 0 ). Roots: ( x = 2, 2). Sum: ( 2 + 2 = 4 )
Geometry Questions for GRE Quantitative Reasoning
Question 11: In triangle ( ABC ), if ( AB = 6 ), ( BC = 8 ), and ( AC = 10 ), what is the area of the triangle?
A) 24
B) 25
C) 26
D) 27
E) 28
Answer: A) 24.
Explanation: Use the formula for a right triangle:
( \frac{1}{2} \times 6 \times 8 = 24 ).
Question 12: A rectangle has a length that is twice its width. If the perimeter is 48 units, what is the area of the rectangle?
A) 96
B) 108
C) 120
D) 132
E) 144
Answer: A) 96.
Explanation: Let width ( w ), length
l = 2w . 2(w + 2w) = 48 . Solving: ( w = 8 ). So, ( l = 16 ). Area = ( 8 \times 16 = 96 ).
Question 13: In a circle with a radius of 5, what is the length of an arc that subtends a central angle of 120 degrees?
A)
B)
C)
D)
Answer:
( \frac{10\pi}{3} ). Explanation: Arc length =
( \frac{\theta}{360} \times 2\pi r = \frac{120}{360} \times 2\pi \times 5 = \frac{10\pi}{3} ).
Question 14: A cube has a surface area of 54 square units. What is the volume of the cube?
A) 27
B) 36
C) 45
D) 54
E) 64
Answer: A) 27.
Explanation: Surface area =
( 6s^2 = 54 ) . Solving, ( s = 3 ). Volume =( 3^3 = 27 ).
Question 15: In a parallelogram, one angle measures 65 degrees. What is the measure of an adjacent angle?
A) 65
B) 75
C) 95
D) 105
E) 115
Answer: D) 105.
Explanation: Adjacent angles in a parallelogram are supplementary: ( 180 - 65 = 115 )
Data Analysis Questions for GRE Quantitative Reasoning
Question 16: A dataset has the following values: 10, 12, 15, 15, 20, 22. What is the range and the median of the dataset?
A) Range: 10, Median: 15
B) Range: 12, Median: 15
C) Range: 12, Median: 16
D) Range: 10, Median: 16
E) Range: 10, Median: 15.5
Question 17: In a survey, 60% of respondents prefer coffee, 30% prefer tea, and the remaining prefer neither. If 100 people responded, how many prefer neither?
A) 5
B) 10
C) 15
D) 20
E) 25
Answer: B) 10.
Explanation: Neither =
( 100\% - (60\% + 30\%) = 10\% ) . Thus, 10 people.
Question 18: A class of students has a mean score of 75 on a test with a standard deviation of 10. If a student's score is 95, what is their z-score?
A) 1
B) 1.5
C) 2
D) 2.5
E) 3
Answer: C) 2.
Explanation: Z-score =
( \frac{95 - 75}{10} = 2 ).
Question 19: A bag contains 3 red, 5 blue, and 7 green balls. If a ball is drawn at random, what is the probability it is either red or blue?
A)
B)
C)
D)
E)
Answer: B)
( \frac{1}{2} ) Explanation: Total = 15 balls, red + blue = 8 balls. Probability =
( \frac{8}{15} = \frac{1}{2} ).
Question 20: If the probability of rain on any given day is 0.4, what is the probability that it will rain on exactly 2 out of the next 3 days?
A) 0.192
B) 0.288
C) 0.348
D) 0.432
E) 0.512
Answer: B) 0.288.
Explanation: Use the binomial probability formula:
( P(X = 2) = \binom{3}{2} \times (0.4)^2 \times (0.6)^1 = 0.288 ).
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