GRE multiple choice questions, select one or more answer appear around four times out of the 27 questions across the two GRE quantitative reasoning sections put together, so thorough coverage of this question type is essential in a comprehensive GRE course. These questions present background information and a question stem, followed by three or more answer choices, out of which one or more is correct. You must select all the correct answer choices, and you receive credit only when all your responses are correct, with no partial credits. On this page, we present a rich set of GRE Quant MCQ – Select One or More practice questions with detailed explanations. Use this resource carefully and apply the learnings in further practice across GRE drills, GRE sectional practice tests and GRE full-length practice tests.
Practice Question 1 | MCQ – Select One or More
The mean of the distribution of the number of books borrowed per patron at Larang Library is 8 and the standard deviation is 2. Which of the following values are within 2 standard deviations of the mean of the distribution of the number of books borrowed per patron?
Indicate all such values.
A. 3
B. 6
C. 9
D. 11
E. 14
F. 15
Written Explanation
The mean of the distribution of the number of books borrowed per patron (µ) = 8.
The standard deviation of the distribution of the number of books borrowed per patron (σ) = 2.
We need to determine which of the given values are within 2 standard deviations of the mean of the distribution of the number of books borrowed per patron.
The number of books corresponding to 2 standard deviations below the mean of the distribution = µ – 2σ = (8) – 2(2) = 4.
The number of books corresponding to 2 standard deviations above the mean of the distribution = µ + 2σ = (8) + 2(2) = 12.
Hence, all values between 4 and 12 are within 2 standard deviations of the mean of the distribution of the number of books borrowed per patron.
B, C, and D are the correct answer choices.
Practice Question 2 | MCQ – Select One or More
Which of the following could be the unit digit of 24k – 15k, where k is a positive integer?
Indicate all such digits.
A. 0
B. 1
C. 2
D. 4
E. 5
F. 6
G. 8
H. 9
Written Explanation
The units digit of 24k – 15k is the same as the units digit of 4k – 5k.
The units digit of powers of 4 follows a repeating pattern of 4 and 6.
The units digit of powers of 5 is always 5.
Possibility 1: If the units digit of 4k is 4, then the units digit of 4k – 5k = units digit of (4 – 5) = units digit of (10 + 4 – 5) = 9.
Possibility 2: If the units digit of 4k is 6, then the units digit of 4k – 5k = units digit of (6 – 5) = 1.
Hence, 1 and 9 are the only possible units digit of 24k – 15k.
B and H are the correct answer choices.
Practice Question 3 | MCQ – Select One or More
The function f is defined for all numbers p by f(p) = 2p2 – 3p. If m is a number such that f(4m) = 20, which of the following could be the possible values of f(8m)?
Indicate all such numbers.
A. 35
B. 40
C. 65
D. 80
E. 104
Written Explanation
f(p) = 2p2 – 3p (Equation I)
f(4m) = 20 (Equation II)
We need to determine which of the given answer choices could be the possible values of f(8m).
Substituting p = 4m in Equation I,
f(p) = 2p2 – 3p
f(4m) = 2(4m)2 – 3(4m)
f(4m) = 32m2 – 12m
Substituting f(4m) = 20 from Equation II,
20 = 32m2 – 12m
Rearranging the terms, we get;
32m2 – 12m – 20 = 0
Dividing by 4, we get;
8m2 – 3m – 5 = 0
8m2 – 8m + 5m – 5 = 0
8m(m – 1) + 5(m – 1) = 0
(8m + 5)(m – 1) = 0
Thus, either m = – 5 / 8 or m = 1.
Possibility 1: If m = – 5 / 8 , then substituting p = 8m in the Equation I, f(8m) = 2(8m)2 – 3(8m) = 128m2 – 24m = 128(– 5 / 8 )2 – 24(– 5 / 8 ) = 65.
Possibility 2: If m = 1, then substituting p = 8m in the Equation I, f(8m) = 2(8m)2 – 3(8m) = 128m2 – 24m = 128(1)2 – 24(1) = 104.
C and E are the correct answer choices.
Practice Question 4 | MCQ – Select One or More
Research indicates that the biggest weekly expenses for most households are rent, childcare, and transportation. Among 1,800 households studied, transportation was found to be the biggest expense for t percent of households. Rounded to the nearest integer, the value of t is 12. Which of the following could be the number of households whose biggest expense was found to be transportation?
Indicate all such numbers.
A. 185
B. 200
C. 205
D. 210
E. 220
F. 230
G. 250
Written Explanation
The total number of households studied = 1,800.
If t rounded to the nearest integer is 12, then the range of values for t must be 11.5 ≤ t < 12.5.
t percent of households reported transportation as their biggest expense.
Thus, the number of households whose biggest expense was transportation = t% of 1,800.
Since 11.5 ≤ t < 12.5, it follows that;
11.5% of 1,800 ≤ Required number of households < 12.5% of 1,800
207 ≤ Required number of households < 225
Hence, the number of households whose biggest expense was found to be transportation could be any value from 207 to 224.
D and E are the correct answer choices.
Practice Question 5 | MCQ – Select One or More
A playlist consists of 15 songs of various lengths, as shown in the table. If 5 songs from this list are played at random, which of the following could be the total length of music played, in seconds?
Indicate all such lengths.
A. 700
B. 740
C. 750
D. 780
Written Explanation
5 of the 15 songs of various lengths listed in the table are played at random.
We need to determine which of the given answer choices could be the total length of music played.
A. 700 seconds
700 seconds = 100 seconds + 120 seconds + 120 seconds + 180 seconds + 180 seconds
Hence, the total length of music played can be 700 seconds.
B. 740 seconds
740 seconds = 100 seconds + 100 seconds + 180 seconds + 180 seconds + 180 seconds
Hence, the total length of music played can be 740 seconds.
C. 750 seconds
No combination of the lengths of any 5 songs listed in the table results in a sum of 750 seconds.
Hence, the total length of music played cannot be 750 seconds.
D. 780 seconds
780 seconds = 120 seconds + 120 seconds + 180 seconds + 180 seconds + 180 seconds
Hence, the total length of music played can be 780 seconds.
A, B, and D are the correct answer choices.
Practice Question 6 | MCQ – Select One or More
PQ is a diameter of the circle and has length 15. Points R and S are on the circle such that PR = QS = 9. What is the area of the shaded region?
A. 54
B. 81
C. 108
D. 135
E. 246
Written Explanation
PQ is a diameter of the circle and has length 15.
PR = QS = 9
We need to determine the area of the shaded region.
The diameter of a circle subtends a right angle at any point on the circumference of the circle.
Therefore, ∠QRP = 90° and triangle QRP is a right triangle.
Using Pythagoras Theorem,
PR2 + QR2 = PQ2
92 + QR2 = 152
QR2 = 152 – 92
QR2 = 144
Taking square roots on both sides,
QR = 12
The area of triangle QRP = ( 1 / 2 )(QR)(PR) = ( 1 / 2 )(12)(9) = 54.
Similarly, we can show that, the area of triangle PSQ = 54.
The area of the shaded region = The area of triangle QRP + The area of triangle PSQ = 54 + 54 = 108.
C is the correct answer choice.
Practice Question 7 | MCQ – Select One or More
If m / n represents a fraction, which of the following are equivalent to the value of m / n?
Indicate all such fractions.
A. m + 1/n + 1
B. m – 1/n – 1
C. 3m / 3n
D. m2 / n2
E. √m / √n
F. m / 3 / n / 3
Written Explanation
A.
If m = 2 and n = 1, then m / n= 2 and (m + 1) / (n + 1) = 3 / 2 .
Thus, m / n ≠ (m + 1) / (n + 1) for all values of m and n.
B.
If m = 3 and n = 2, then m / n = 3 / 2 and (m – 1) / (n – 1) = 2.
Thus, m / n ≠ (m – 1) / (n – 1) for all values of m and n.
C.
Dividing the numerator and the denominator of 3m / 3n by 3, we get m / n .
Thus, m / n = 3m / 3n for all values of m and n.
D.
If m = 2 and n = 1, then m / n= 2 and m2/ n2= 4.
Thus, m / n ≠ m2/ n2 for all values of m and n.
E.
If m = 4 and n = 1, then m / n= 4 and √m / √n= 2.
Thus, m / n ≠ √m / √n for all values of m and n.
F.
Multiplying the numerator and the denominator of (m/ 3 ) / (n/ 3 ) by 3, we get m / n.
Thus, m / n = (m / 3 ) / (n/ 3 ) for all values of m and n.
C and F are the correct answer choices.
Practice Question 8 | MCQ – Select One or More
On the number line, the given points are equally spaced. Which of the following statements about the numbers p, q, r, and s must be true?
Indicate all such statements.
A. pr > |qs|
B. p2 < q2 + r2 + s2
C. p + r = 4(q + s)
Written Explanation
The given points p, q, r, 0, and s are equally spaced.
Let the distance between the points 0 and s be D.
Thus, the coordinate of point s = D.
Since points r, 0, and s are equally spaced, the coordinate of point r = –D.
Since points q, r, and 0 are equally spaced, the coordinate of point q = –2D.
Since points p, q, and r are equally spaced, the coordinate of point p = –3D.
We need to determine which of the given statements must be true.
A.
pr = (–3D)(–D) = 3D2
|qs| = |(–2D)(D)| = |–2D2| = 2D2
Since D is always positive, it follows that 3D2 > 2D2.
Hence, this statement is true.
B.
p2 = (–3D)2 = 9D2
p2 + r2 + s2 = (–2D)2 + (–D)2 + (D)2 = 6D2
Since D is always positive, it follows that 9D2 > 6D2.
Hence, this statement is not true.
C.
p + r = (–3D) + (–D) = –4D
4(q + s) = 4(–2D + D) = 4(–D) = –4D
Hence, this statement is true.
A and C are the correct answer choices.
Practice Question 9 | MCQ – Select One or More
The probability that event X will occur is 3 / 10 and the probability that event X ∪ Y (that is, the event X or Y, or both) will occur is 3 / 4 . Which of the following values could be the probability that the event Y will occur?
Indicate all such values.
A. 0.35
B. 0.55
C. 0.70
D. 0.80
Written Explanation
The probability that event X will occur is 3 / 10 . Thus, P(X) = 3 / 10.
The probability that event X ∪ Y will occur is 3 / 4 . Thus, P(X ∪ Y) = 3 / 4.
We need to determine which of the given values could be the probability of the event Y.
The probability of event Y will be minimum when the events X and Y are mutually exclusive.
In this case, P(Y) = P(X ∪ Y) – P(X) = 3 / 4 – 3 / 10 = 0.45.
The probability of event Y will be maximum when event X is a subset of event Y.
In this case, P(Y) = P(X ∪ Y) = 3 / 4 = 0.75.
Hence, the probability of the event X ∪ Y can be any value from 0.45 to 0.75.
B and C are the correct answer choices.
Practice Question 10 | MCQ – Select One or More
4,800 hectares of farmland owned by Crates Farms have been devoted to growing alfalfa, wheat, and millets. m percent of this land has been devoted to growing millets. If rounded to the nearest integer, m is 28. Which of the following could be the number of hectares Crates Farms has devoted to growing millets?
Indicate all such numbers.
A. 1,300
B. 1,310
C. 1,315
D. 1,325
E. 1,350
F. 1,365
G. 1,375
Written Explanation
The total farmland owned by Crates Farms = 4,800 hectares.
If m rounded to the nearest integer is 28, then the range of values for m must be 27.5 ≤ m < 28.5.
m percent of the land has been devoted to growing millets.
Thus, the number of hectares devoted to growing millets = m% of 4,800.
Since 27.5 ≤ m < 28.5, it follows that;
27.5% of 4,800 ≤ Required number of hectares < 28.5% of 4,800
1,320 ≤ Required number of hectares < 1,368
Hence, the number of hectares Crates Farms has devoted to growing millets could be any value from 1,320 to 1,367.
D, E, and F are the correct answer choices.
Additional Free GRE-style MCQ – Select One or More Questions with Explanations:
Please find a set of GRE-style Quant MCQ – Select One or More questions with explanations on: Free GRE Quant MCQ – Select One or More Practice Questions Prep
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
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