GRE MCQ Select One or More questions form an important question format within GRE Quantitative Reasoning and deserve focused attention in your GRE preparation course. This format does not test new concepts but checks how well you apply familiar quantitative ideas with care and precision. These questions differ because more than one option can be correct, and you must identify every valid choice to earn credit.
Overview and Approach for GRE MCQ Select One or More questions
The following video explains the question format clearly and shows how to approach it effectively for your GRE drills, GRE sectional mocks, and GRE full length mocks.
How an MCQ – Select 1 or More Question Appears on the GRE
Correct Answer: C,D,E
GRE-Style Practice Questions | MCQ – Select 1 or More
Work through the exercise below, a set of GRE style MCQ – Select 1 or More questions with clear explanations. Solve carefully without focusing on speed at this stage and target full accuracy. After you finish, study every explanation, review your incorrect and slow attempts, and extract maximum learning from the exercise.
All the best!
Practice Question 1 | GRE MCQ – Select 1 or More
If x is a positive integer and x2 is a multiple of 270, which of the following must be a factor of x?
Indicate all such integers.
A. 2
B. 4
C. 6
D. 9
E. 27
F. 45
Show Explanation
Written Explanation
x is a positive integer and x2 is a multiple of 270.
We need to determine which of the given integers must be a factor of x.
x2 is a multiple of 270. x2 = 270k, where k is any positive integer. x2 = (2 × 33 × 5)k
Since x is a positive integer, the exponents of 2, 3, and 5 in x2 must be even.
Thus, the minimum possible value of x2 = 22 × 34 × 52.
Therefore, the minimum possible value of x = 2 × 32 × 5.
Note that we are considering the minimum possible value of x because if any specific number n is a factor of the minimum value of x, then n will also be a factor of all multiples of x.
A. 2
2 is a factor of (2 × 32 × 5).
Thus, 2 is a factor of x.
B. 4
22 is a not factor of (2 × 32 × 5).
Thus, 4 is not a factor of x.
C. 6
(2 × 3) is a factor of (2 × 32 × 5).
Thus, 6 is a factor of x.
D. 9
32 is a factor of (2 × 32 × 5).
Thus, 9 is a factor of x.
E. 27
33 is not a factor of (2 × 32 × 5).
Thus, 27 is not a factor of x.
F. 45
(32 × 5) is a factor of (2 × 32 × 5).
Thus, 45 is a factor of x.
Hence, 2, 6, 9, and 45 must be factors of x.
A, C, D, and F are the correct answer choices.
Practice Question 2 | GRE MCQ – Select 1 or More
The table shows the length, in miles, of the 18 railway tracks maintained by Tara Industries. Which of the following lengths could be the median of the lengths of these tracks?
Indicate all such lengths.
A. 16
B. 24
C. 29
D. 33
E. 36
F. 42
Show Explanation
Written Explanation
The table shows the lengths, in miles, of the 18 railway tracks maintained by Tara Industries. We need to determine which of the given lengths could be the median of the tracks’ length.
The median of an ordered set of an even number of integers is the average of the middle two numbers.
Since there are 18 tracks, the median of the tracks’ length is the average of the length of the 9th and 10th tracks, when all tracks are ordered according to their lengths.
From the table, we see that;
There are 2 tracks (1st to 2nd) that have a length under 10 miles.
There are 4 tracks (3rd to 6th) that have a length between 11 miles and 20 miles.
There are 6 tracks (7th to 12th) that have a length between 21 miles and 30 miles.
Since both the 9th and 10th tracks have a length between 21 miles and 30 miles, the average length of the 9th and 10th tracks must also be some value between 21 miles and 30 miles.
Hence, the median of the tracks’ lengths could be any value from 21 to 30 miles.
B and C are the correct answer choices.
Practice Question 3 | GRE MCQ – Select 1 or More
The Progress Party’s candidate for mayor received only 8,250 votes, entirely from Districts 11, 36, and 38, of the city. p percent of these votes came from District 11. If p is rounded to the nearest integer, its value is 42. Which of the following could be the number of votes the Progress Party’s candidate received from District 11?
Indicate all such numbers.
A. 3,293
B. 3,424
C. 3,450
D. 3,482
E. 3,506
f. 3,521
G. 3,546
Show Explanation
Written Explanation
The total number of votes received by the Progress Party’s candidate = 8,250.
If p rounded to the nearest integer is 42, then the range of values for p must be 41.5 ≤ p < 42.5. p percent of the votes came from District 11.
Thus, the number of votes received from District 11 = p% of 8,250.
Since 41.5 ≤ p < 42.5, it follows that;
41.5% of 8,250 ≤ Required number of votes < 42.5% of 8,250 3,423.75 ≤ Required number of votes < 3,506.25
Hence, the number of votes the Progress Party’s candidate received from District 11 could be any value from 3,424 to 3,506.
B, C, D, and E are the correct answer choices.
Practice Question 4 | GRE MCQ – Select 1 or More
In the xy-plane, a rectangle has one side described by the equation y = 2x + 3. Which of the following equations could represent one of the other three sides of the rectangle?
Indicate all such equations.
A. y = –2x + 3
B. y = –1/2 x + 1
C. y = 1/2x – 3
D. y = x – 1/3
E. y = 2x – 1
Show Explanation
Written Explanation
The rectangle has one side described by the equation y = 2x + 3.
Comparing with the slope-intercept form y = mx + c, where m is the slope and c is the y-intercept, the slope of line y = 2x + 3 is 2.
The opposite sides of a rectangle are parallel to each other.
If two lines are parallel, then their slopes must be equal.
Thus, a line with a slope of 2 could represent the opposite side of the rectangle.
The adjacent sides of a rectangle are perpendicular to each other.
If two lines are perpendicular, then the product of their slopes must be –1.
Therefore, since the slope of the line y = 2x + 3 is 2, the slope of the line perpendicular to y = 2x + 3 must be –1/2.
Thus, a line with a slope of –1/2 could represent one of the adjacent sides of the rectangle.
We need to determine which of the given lines have a slope of either 2 or –1/2 .
A. y = –2x + 3
The slope of this line = –2.
Thus, this answer choice is incorrect.
B. y = –1/2 x + 1
The slope of this line = –1/2 .
This could be the slope of one of the adjacent sides of the rectangle.
Thus, this is a correct answer choice.
C. y = 1/2x – 3
The slope of this line = 1/2 .
Thus, this answer choice is incorrect.
D. y = x – 1/3
The slope of this line = 1.
Thus, this answer choice is incorrect.
E. y = 2x – 1
The slope of this line = 2.
This could be the slope of the opposite side of the rectangle.
Thus, this is a correct answer choice.
B and E are the correct answer choices.
Practice Question 5 | GRE MCQ – Select 1 or More
A truck with a maximum carrying capacity of y pounds was at half capacity at 2:00 PM. By 3:00 PM, the truck had offloaded 20 percent of its cargo, and half an hour later, it picked up another 250 pounds of cargo. Which of the following expressions represents the weight, in pounds, of the cargo on the truck at 3:30 PM?
Indicate all such expressions.
A. 0.2y/2 + 250
B. y/10 + 250
C. y – 3y/5 + 250
D. 2y + 1,000/5
E. 2y/5 + 250
Show Explanation
Written Explanation
The maximum carrying capacity of the truck = y pounds.
Since the truck was at half capacity at 2:00 PM, the weight of the cargo on the truck at 2:00 PM = y/2 pounds.
Since the truck had offloaded 20 percent of its cargo by 3:00 PM, the weight of the cargo on the truck at 3:00 PM = 0.8 y/2 pounds.
Since the truck picked up another 250 pounds of cargo half an hour later, the weight of the cargo on the truck at 3:30 PM = 0.8y/2 + 250 = 0.4y + 250 pounds. We need to determine which of the given expressions is equal to 0.4y + 250.
A. 0.2y/2 + 250
This expression is not equal to the expression calculated above.
Hence, this answer choice is incorrect.
B. y/10 + 250
This expression is not equal to the expression calculated above.
Hence, this answer choice is incorrect.
C. y – 3y /5 + 250 = 5y/5 – 3y/5 + 250 = 2y/5 + 250 = 0.4y + 250
This expression is the same as the expression calculated above. Hence, this is a correct answer choice.
D. (2y + 1,000) /5 = 2y/5 + 1,000 /5 = 0.4y + 200
This expression is not equal to the expression calculated above.
Hence, this answer choice is incorrect.
E. 2y/5 + 250 = 0.4y + 250
This expression is the same as the expression calculated above. Hence, this is a correct answer choice.
C and E are the correct answer choices.
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