Quantitative Comparisons
Quantitative Comparison questions on the GRE require you to choose one of the two quantities to determine which value is greater.
Here are the four answer choices:
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
A "quant comp" question may look like this:
Which is greater where x is a positive number
Quantity A Quantity B
x + 12 x + 20
You have to look at the two quantities and determine their relationship (which is any one of the four choices):
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Here, of course, the answer is (B).
Some of the best strategies on these questions is to plug in the values under the quantities into the question stem (the question stem is the phrase about the two quantity choices-- which sometimes isn't even there).
Other times, you need to plug in numbers for variables if they are used in Quantity A or B. Plugging in numbers is the most common strategy on these questions. When plugging in numbers, remember that positive and negative numbers can product different results, so test the variables for both positive and negative number. Fractions may also be necessary for testing if the question doesn't specify that the variables must be integers.
See the 15 examples below to get a good idea for these questions.
Question 1 (easy)
2x = y
Quantity A: Quantity B:
perimeter of an equilateral triangle, perimeter of a square,
side = y side = x
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Answer explanation:
(A) We need to first calculate the perimeters of the two polygons, and then compare them. For the triangle, we are told that it is equilateral, meaning that all sides are the same length. Therefore, the perimeter is y + y + y, or 3y. For the square, the side is of length x. Therefore, the perimeter is x + x + x + x, or 4 x. Now we need to compare 3y and 4x. We are told that 2x = y. If we multiply this by 2, we see that 4x, or the perimeter of the square, is equal to 2y. Now we just need to compare 2y and 3y, and we can see that 3y is greater. (Keep in mind that these are distances, so we know that the values for x and y are positive numbers.)
Question 2 (easy).
Quantity A: Quantity B:
3/7 + 3/5 1
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Answer explanation:
(A) In order to compare quantities A and B, we first need to calculate a value for the expression in quantity A. To do this, we convert the fractions to have the least common denominator, in this case 35. For the first term, we multiply through by 5, converting 3/7 to 15/35. For the second term, we multiply through by 7, converting 3/5 to 21/35. Now we have 15/35 + 21/35, or 36/35. This can be simplified to 1 1/35, which is greater than 1, so we must choose choice A.
Question 3 (easy).
The average (arithmetic mean) of 12, 17, 43, 11, 16, and 27 is y.
Quantity A: Quantity B:
y 21
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Answer explanation:
(B) In order to solve this problem, we must calculate the average (arithmetic mean) of these numbers. To do that, we add the numbers, and then divide by the number of terms, in this case 6. The numbers sum to 126. When we divide by 6, we get 21, which is also the value in quantity B. Therefore, choice C is correct.
Question 4 (easy).
p and q are positive integers, q > 1
Quantity A: Quantity B:
p + q (p + q)
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Answer explanation:
(B) We are told that p and q are both positive integers (1, 2, 3…), and q is greater than 1. To solve this, it is best to compare the two expressions by substituting in a few values. Let's start with p = 1, q = 2. If we substitute into the expression in quantity A, we get p + q = 12 + 22 = 1 + 4 = 5. Substituting these same values into the second equation, we get (p + q)2= (1 + 2)2 = (3) 2 = 9. If we try more values, we see that the relationship holds. Substitution of any values into the expression in quantity B always gives a greater value than the one in quantity A.
Question 6 (easy).
21w = 28z
Quantity A: Quantity B:
3w 4z
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Answer explanation:
C) In order to compare the two values, we need to first simplify the original expression. If we divide both sides of the equation by 7, we get 3w = 4z. These are the same values we are being asked to compare! Since we are told that they are equal, we must choose choice C.
Question 7 (easy).
2/5 < t/15
Quantity A: Quantity B:
6 t
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Answer explanation:
(B) We are given a proportion with the variable t. In order to more easily look at the value of t, it is best to convert the fraction on the left to have the same denominator as that of the fraction on the right. (Note: if 5 were not a factor of 15, we would have to figure out what the least common denominator was for the two fractions.) If we convert the fraction on the left by multiplying both the top and the bottom of the fraction by 3, we get 6/15 < t/15. Therefore, 6 < t. Now if we look at the values in quantity A and B, we are comparing 6 and t. Since we know that 6 < t, t is greater, choice B is correct.
MEDIUM
Question 1 (medium).
x = 16
Quantity A: Quantity B:
x 4
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Answer explanation:
(D) We are told that x2 = 16. What number, when multiplied by itself equals 16? Yes, 4 is a correct answer, 4 x 4 = 16. However, -4 when multiplied by itself also equals 16, -4 x -4 = 16. Therefore, x could be either 4 or -4, we don't know. Therefore the correct answer is choice D. Be careful with problems like these, do not make assumptions beyond the information that is given to you.
Question 2 (medium).
k is an even integer
Quantity A: Quantity B:
2k k
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Answer explanation:
(D). We are told that k is an even integer. To determine whether how the expressions in quantity A and B compare, let's try to substitute in a few different values. We can start with 2. For quantity A, we would have 4, for B, we would have 2. In this case, the value of quantity A is greater. Let's try another even integer to substitute for k, -4. In this case, we get -8 for A, and -4 for B, so quantity B would be greater. Whenever you can get two different results (one substitution resulting in quantity A being greater, the other in B being greater), you should know that you must choose D, answer cannot be determined.
Question 3 (medium).
x = 3, y = -4
Quantity A: Quantity B:
(x + y) 2 (x - y) 2
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Answer explanation:
(B). If we substitute in the values for x and y for the expression in quantity A, we get (x + y) 2 = (3 + -4) 2 = (-1) 2 =-2. When we substitute into the expression in quantity B, we get (x - y) 2 = (3 - -4) 2 = (3 + 4) 2 = (7) 2 = 14. Therefore the value in quantity B, 14, is greater than the value in quantity A, -2.
Question 4 (medium).
b is a positive integer
Quantity A: Quantity B:
b/6 0.17 b
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Answer explanation:
(B). We are told that b is a positive integer. To solve this problem, we can try to substitute in a value for b and test whether the expressions in A or B are greater. However, we might not need to do this. The expression in A can be thought of as multiplying b by 1/6, and the expression in B is multiplying b by 0.17. Since we already know that b is a positive integer, we don't need to worry about negative numbers or fractions, o, what we really want to know is which is greater, 1/6 or 0.17. If you try to divide 1 by 6, in order to convert it to decimal form, you get 0.16666….with 6 repeating. Is this greater than or less than 0.17? Less than, therefore choice B is correct.
Question 5 (medium).
1/P > 0
Quantity A: Quantity B:
P 0
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Answer explanation:
(A). Because we know that 1/p is greater than 0, we know that p must be a positive, not a negative number. (If p were -5, then the value of 1/p would be -1/5, which would not satisfy the condition that 1/p be greater than 0.) Since p is positive, it is by definition greater than 0.
Question 6 (medium).
x + 2y = 7
3x - 3y = -15
Quantity A: Quantity B:
y - x 5
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Answer explanation:
(C) This is a simultaneous equation problem. First, simplify the equations by multiplying through both sides of one equation in order to have one of the variable containing terms being equal to one of the terms in the second equation. For example, we see that there is a 3x in the second equation. If we multiply the first equation by 3, we get 3 (x + 2y) = 3 (7) or 3x + 6y = 21. Now, multiply this same equation by -1, giving -3x -6y = -21. Now we can add the two equations: -3x +3x +-6y -3y = -21 + -15. Simplifying, the x terms drop out, and we get -9y = -36. Dividing through by -9, we get y = 4. Now is we substitute this value of y back into either of the equations, we can solve for x. If x + 2y = 7, and we know that y = 4, we can see that x +2 (4) =7, or x + 8 =7, therefore x = -1. Now that we have values for x and y, we can compare the terms in quantities A and B. Quantity A is y - x. When we substitute for x and y, we get 4 - (-1), or 4 + 1, which equals 5. Therefore the values in A and B are the same, choice C.
Question 7 (medium)
A marble is drawn at random from a box containing 5 purple marbles and 3 yellow marbles.
Quantity A: Quantity B:
probability of a yellow marble 3/5
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Answer explanation:
(B) The probability that the marble is yellow is given by the number of yellow marbles (3) divided by the total number of marbles (purple plus yellow, 5 + 3, or 8). Therefore the probability is 3/8, which is smaller than 3/5.
Question 1 (hard)
For any non-negative number y, let y* = 1/y
Quantity A: Quantity B:
15*/3* (15/3)*
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Answer explanation:
(C) Made-up functions are common questions on the GRE. To solve these, it is usually best to just solve each expression. For A, we get 15*/3* = (15) -1/15/ 1/3 = (1/15)/(1/3) = (1/15)(3) = 3/15 or 1/5. For B, we get (15/3)* = (5)* =(5) - 1 = 1/5. Therefore they are equivalent.
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