Multiple choice questions select one answer type question format on GRE quant contributes to roughly 40% of all questions on the GRE quantitative reasoning section. Therefore, full coverage and thorough practice on this question format is a must in a GRE preparation course. On this page, we present a set of GRE MCQ select one practice questions spanning a wide range of GRE topics and concepts. Use this exercise carefully and review the explanations closely, especially for questions where you were wrong or slow. Carry the learnings into your further GRE practice across GRE quizzes, GRE sectional simulations, and GRE full-length simulations.
Practice Question 1 | MCQ – Select One
If x is an integer, which of the following must be an odd integer?
A. x3 + 4x2 – 11
B. 3x3 – 4x2 + 6x – 10
C. 4x3 + 5x2 – 7x + 3
D. x2 + 3x – 6
E. 8x2 – 5x + 10
Written Explanation
x is an integer.
We need to determine which of the following answer choices must be an odd integer.
A. x3 + 4x2 – 11
4x2 will always be even for all values of x.
If x is odd, then x3 will be odd, and x3 + 4x2 – 11 will be even.
Hence, this answer choice is incorrect.
B. 3x3 – 4x2 + 6x – 10
– 4x2 + 6x will always be even for all values of x.
If x is even, then 3x3 will be even, and 3x3 – 4x2 + 6x – 10 will also be even.
Hence, this answer choice is incorrect.
C. 4x3 + 5x2 – 7x + 3
4x3 will always be even for all values of x.
Possibility 1: If x is even, then 5x2 – 7x will be even, and 4x3 + 5x2 – 7x + 3 will be odd.
Possibility 2: If x is odd, then 5x2 – 7x will be even, and 4x3 + 5x2 – 7x + 3 will be odd.
Thus, 4x3 + 5x2 – 7x + 3 must be an odd integer.
Hence, this is the correct answer choice.
D. x2 + 3x – 6
If x is odd, then x2 + 3x will be even, and x2 + 3x – 6 will also be even.
Hence, this answer choice is incorrect.
E. 8x2 – 5x + 10
8x2 will always be even for all values of x.
If x is even, then –5x will be even, and 8x2 – 5x + 10 will also be even.
Hence, this answer choice is incorrect.
C is the correct answer choice.
Practice Question 2 | MCQ – Select One
Which of the following functions g(x), defined for all elements x of a finite set of integers, results in a set of numbers with the least standard deviation?
A. g(x) = –4x + 2
B. g(x) = –2x – 2
C. g(x) = –2x + 2
D. g(x) = x + 4
E. g(x) = 2x – 2
Written Explanation
Adding or subtracting any constant n from a set of numbers does not change the standard deviation of that set of numbers.
Multiplying any constant n to a set of numbers increases the standard deviation of that set of numbers by a factor of |n|.
A. g(x) = –4x + 2
Since x is multiplied by –4, the standard deviation of the set formed from g(x) = |–4| times the standard deviation of S = 4 times the standard deviation of S.
B. g(x) = –2x – 2
Since x is multiplied by –2, the standard deviation of the set formed from g(x) = |–2| times the standard deviation of S = 2 times the standard deviation of S.
C. g(x) = –2x + 2
Since x is multiplied by –2, the standard deviation of the set formed from g(x) = |–2| times the standard deviation of S = 2 times the standard deviation of S.
D. g(x) = x + 4
Since x is multiplied by 1, the standard deviation of the set formed from g(x) = |1| times the standard deviation of S = standard deviation of S.
E. g(x) = 2x – 2
Since x is multiplied by 2, the standard deviation of the set formed from g(x) = |2| times the standard deviation of S = 2 times the standard deviation of S.
Hence, the function g(x) = x + 4 results in a set of numbers with the least standard deviation.
D is the correct answer choice.
Practice Question 3 | MCQ – Select One
Over 24 hours, Dave drank, on average, 5 ounces of water per hour. Additionally, 25 percent of his solid food consumption, by weight, counted toward his water intake. If Dave consumed 60 ounces of solid food over the 24 hours, what percentage of his water intake was from solid food?
A. 11.11%
B. 12.00%
C. 12.50%
D. 14.29%
E. 14.81%
Written Explanation
Dave drank 5 ounces of water per hour over 24 hours.
Therefore, the total amount of water Dave drank = 5 × 24 = 120 ounces.
Dave consumed 60 ounces of solid food over the 24 hours and 25 percent of his solid food consumption counted toward his water intake.
Therefore, water intake was from solid food = 25% of 60 = 15 ounces.
Required percentage = (Water intake from solid food) / (Total water intake) = (15) / (120 + 15) = 11.11%
A is the correct answer choice.
Practice Question 4 | MCQ – Select One
Out of 50 dogs bred by a dog breeder, 60 percent are purebred huskies, meaning both their mother and father are huskies. If x is the number of dogs in this group whose mother is a husky, and y is the number of dogs in this group whose father is a husky, which of the following represents the number of dogs in the group for which neither parent is a husky?
A. 20 – x – y
B. 80 – x – y
C. x + y – 20
D. x + y – 80
E. x + y + 20
Written Explanation
The total number of dogs = 50.
Since 60 percent of dogs are purebred huskies, the number of dogs for which both parents are huskies = 60% of 50 = 30.
The number of dogs whose mother is a husky = x.
The number of dogs whose mother but not father is a husky
= The number of dogs whose mother is a husky – The number of dogs for which both parents are huskies
= x – 30
The number of dogs whose father is a husky = y.
The number of dogs whose father but not mother is a husky
= The number of dogs whose father is a husky – The number of dogs for which both parents are huskies
= y – 30
The number of dogs for which neither parent is a husky + The number of dogs for which both parents are huskies + The number of dogs whose mother but not father is a husky + The number of dogs whose father but not mother is a husky = The total number of dogs
The number of dogs for which neither parent is a husky + 30 + (x – 30) + (y – 30) = 50
The number of dogs for which neither parent is a husky + x + y – 30 = 50
The number of dogs for which neither parent is a husky = 50 + 30 – x – y
The number of dogs for which neither parent is a husky = 80 – x – y
B is the correct answer choice.
Practice Question 5 | MCQ – Select One
Out of 7 available streets, 2 have already been assigned to a mailman’s route. The mailman needs to be assigned a total of 4 out of the 7 streets. How many different combinations of the remaining streets can be added to his route?
A. 5
B. 10
C. 20
D. 21
E. 60
Written Explanation
Out of 7 available streets, 2 have already been assigned to a mailman’s route.
Since the mailman needs to be assigned a total of 4 streets, we need to select 2 more streets out of the remaining 5 streets.
The number of ways to choose 2 streets out of 5 streets, where order does not matter, is given by 5C2 = (5!) / [(2!)(3!)] = 10.
Hence, there are 10 different combinations of the remaining streets that can be added to the mailman’s route.
B is the correct answer choice.
Practice Question 6 | MCQ – Select One
The total sales for a restaurant in 2018 were x dollars. In 2019, a new menu was introduced, and the restaurant’s sales increased by 25 percent. In 2020, due to a decrease in tourism, sales decreased by 20 percent. What were the restaurant’s sales in 2020, in terms of x?
A. 0.25x
B. 0.75x
C. x
D. 1.05x
E. 1.2x
Written Explanation
The total sales for the restaurant in 2018 = x.
The total sales increased by 25 percent in 2019 after introducing a new menu.
Therefore, the total sales in 2019 = 1.25x.
The total sales decreased by 20 percent in 2020 due to a decrease in tourism.
Therefore, the total sales in 2020 = (0.8)1.25x = x.
C is the correct answer choice.
Practice Question 7 | MCQ – Select One
S(x) denotes the sum of the first x multiples of 11, where x is a positive integer.
For example, S(20) = 11 + 22 + 33 + … + 220 = 2,310. What is the value of S(40)?
A. 4,620
B. 5,115
C. 9,020
D. 11,385
E. 14,025
Written Explanation
Shortcut:
Sn = n(a1 + an) / 2 where Sn is the sum of n terms in an arithmetic progression (AP), n is the number of terms, a1 is the first term of the AP and an is the last term of the AP.
Sn = 40(11 + 440) / 2
Sn = 9,020
Detailed Explanation:
S(x) denotes the sum of the first x multiples of 11, where x is a positive integer.
S(20) = 11 + 22 + 33 + … + 220 = 2,310
We need to determine the value of S(40).
S(40) = (11 + 22 + 33 + … + 220) + (231 + 242 + … + 440)
S(40) = S(20) + (220 + 11) + (220 + 22) + … + (220 + 220)
S(40) = S(20) + (220 × 20) + (11 + 22 + 33 + … + 220)
S(40) = S(20) + (220 × 20) + S(20)
S(40) = 2S(20) + (220 × 20)
S(40) = (2 × 2,310) + (220 × 20)
S(40) = 9,020
C is the correct answer choice.
Practice Question 8 | MCQ – Select One
Hillcrest is a school that is attended by students in the middle school (5th – 8th grades) and high school (9th – 12th grades) brackets. If 36 percent of the students are in the middle school bracket, what is the ratio of the number of high school students to the number of middle school students?
A. 25 to 9
B. 16 to 25
C. 16 to 9
D. 9 to 25
E. 9 to 16
Written Explanation
The percentage of middle school students = 36 percent.
Thus, the percentage of high school students = 100 – 36 = 64 percent.
The ratio of the number of high school students to the number of middle school students
= (The percentage of high school students) / (The percentage of middle school students)
= 64 / 36
= 16 / 9
C is the correct answer choice.
Practice Question 9 | MCQ – Select One
The figure shows rhombus ABCD in the xy-plane. If the coordinates of point A are (4, 8), the coordinates of point C are (6, 4), and the slope of side BC is 1, what are the coordinates of point B?
A. (8, 9)
B. (11, 9)
C. (12, 9)
D. (12, 10)
E. (13, 11)
Written Explanation
ABCD is a rhombus.
The coordinates of point A are (4, 8), the coordinates of point B are (6, 4), and the slope of side BC is 1.
Let (x, y) be the coordinates of point B.
We need to determine the coordinates of point B.
Since all sides of a rhombus are equal, the length of side AB must be equal to the length of side BC.
AB = BC
√(x – 4)2 + (y – 8)2 = √(x – 6)2 + (y – 4)2
Squaring both sides,
(x – 4)2 + (y – 8)2 = (x – 6)2 + (y – 4)2
(x2 – 8x + 16) + (y2 – 16y + 64) = (x2 – 12x + 36) + (y2 – 8y + 16)
Cancelling x2 + y2 from both sides,
–8x + 16 – 16y + 64 = –12x + 36 – 8y + 16
–8x – 16y + 80 = –12x – 8y + 52
Rearranging the terms,
(12x – 8x) + (–16y + 8y) = –28
4x – 8y = –28
Dividing both sides by 4,
x – 2y = –7 (Equation I)
Additionally, the slope of side BC = 1.
(y – 4) / (x – 6) = 1
y – 4 = x – 6
Rearranging the terms,
x – y = –4 + 6
x – y = 2 (Equation II)
Subtracting Equation II from Equation I,
x – y – (x – 2y) = 2 – (–7)
y = 9
Substituting the value of y in Equation II,
x – y = 2
x – 9 = 2
x = 2 + 9
x = 11
Hence, the coordinates of point B are (11, 9).
B is the correct answer choice.
Practice Question 10 | MCQ – Select One
There are 900 vehicles on a particular highway, of which 600 are cars and the remainder are two-wheeled vehicles. Out of all these vehicles, 2 / 3 of the cars and 4 / 5 of the two-wheeled vehicles are traveling at less than 60 miles per hour. If a random vehicle pulls over, what is the probability that the vehicle was traveling at less than 60 miles per hour?
A. 22 / 45
B. 32 / 45
C. 34 / 45
D. 37 / 45
E. 44 / 45
Written Explanation
The total number of vehicles = 900.
The number of cars = 600.
Since the rest of the vehicles are two-wheeled vehicles, the number of two-wheeled vehicles = 900 – 600 = 300.
We need to determine the probability that any randomly selected vehicle was traveling at less than 60 miles per hour.
(2 / 3) of the cars are traveling at less than 60 miles per hour.
Thus, the number of cars traveling at less than 60 miles per hour = (2 / 3) × 600 = 400.
(4 / 5) of the two-wheeled vehicles are traveling at less than 60 miles per hour.
Thus, the number of two-wheeled vehicles traveling at less than 60 miles per hour = (4 / 5) × 300 = 240.
The probability that any randomly selected vehicle was traveling at less than 60 miles per hour
= (The number of vehicles traveling at less than 60 miles per hour) / (The total number of vehicles)
= (400 + 240) / 900
= 640 / 900
= 32 / 45
B is the correct answer choice.
Additional GRE-style MCQ – Select One Questions with Explanations
Please find a set of GRE-style Quant questions (all types) with explanations on: Free GRE Quant Practice Questions with Solutions
Please find a set of assorted GRE-style questions (all sections and types) with explanations on: Free GRE Practice Questions with Solutions
For Further GRE Prep and Practice…
Complete GRE preparation course with 7-day free trial
15 GRE full length mock tests
60 GRE section mock tests
Free full length GRE diagnostic test
5-week GRE crash course
