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Home Test Prep GRE Section 2 Quantitative

Test Prep GRE Section 2 Quantitative Exam Practice Questions (P. 4)

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Question #31
In a group of 18 students taking Spanish and German, 12 are taking Spanish, and 4 are taking both Spanish and German.


  1. A
    The quantity in Column A is greater;
  2. B
    The quantity in Column B is greater;
  3. C
    The quantities are equal;
  4. D
    The relationship cannot be determined from the information given.

Correct Answer:
B
Of the 12 students taking Spanish, 4 are taking both languages, leaving 8 taking only Spanish. Since 12 of the 18 are taking Spanish, just 6 are taking only
German. Thus, the quantity in Column B is greater.

Question #32
If n is the first of two consecutive odd integers, and if the difference of their squares is 120, which of the following equations can be used to find their values?


  1. A
    Option A
  2. B
    Option B
  3. C
    Option C
  4. D
    Option D
  5. E
    Option E

Correct Answer:
E
The other integer is n+ 2. The difference between n and (n+ 2) must be positive (it is given as 120), so the term (n+ 2) must appear first in the equation.

Question #33


  1. A
    The quantity in Column A is greater;
  2. B
    The quantity in Column B is greater;
  3. C
    The quantities are equal;
  4. D
    The relationship cannot be determined from the information given.

Correct Answer:
A
The least common multiple of 4, 6, and 8 is 24. The greatest common factor of 44, 66, and 88 is 22.

Question #34
Ps age is twice Qs age. One year ago, Rs age was exactly half of Ps age at that time.


  1. A
    The quantity in Column A is greater;
  2. B
    The quantity in Column B is greater;
  3. C
    The quantities are equal;
  4. D
    The relationship cannot be determined from the information given.

Correct Answer:
B
You can approach this problem intuitively, without a written system of equations. If Ps age were twice what Rs age is now, then Qs age would equal Rs age, and the correct answer would be choice (C). Rs current age must be greater than half of Ps (because one year ago Rs age was exactly half of Ps). Given that Qs age is exactly half of Ps age, R must be older than Q.

Question #35


  1. A
    The quantity in Column A is greater;
  2. B
    The quantity in Column B is greater;
  3. C
    The quantities are equal;
  4. D
    The relationship cannot be determined from the information given. D

Correct Answer:
Explanation
The inequality ab< 0 tells you that either a or b, but not both, is negative. Since a<b, a must be negative and b must be positive. But you cannot make the
comparison between Quantity A and Quantity B. Which is greater depends on the absolute values of the two variables. For example, if a= -1 and b= 2, then

On the other hand, if a= -2 and b= 1, then

Question #36


  1. A
    The quantity in Column A is greater;
  2. B
    The quantity in Column B is greater;
  3. C
    The quantities are equal;
  4. D
    The relationship cannot be determined from the information given.

Correct Answer:
D
In the distribution described in Column B, if the third term is the precise average (arithmetic mean) of the other two terms, then Quantity A would equal Quantity B
(for example, if the two distributions are {2,4} and {2,3,4}). Otherwise, Quantity B would be greater, since its middle term deviates from the mean of the other two terms.

Question #37


  1. A
    The quantity in Column A is greater;
  2. B
    The quantity in Column B is greater;
  3. C
    The quantities are equal;
  4. D
    The relationship cannot be determined from the information given.

Correct Answer:
B
The two number series have in common integers 21 through 50. So you can subtract (or cancel) all of these integers from both sides of the comparison. That leaves you to compare (19 + 20) to 51. You can now see clearly that Quantity B is greater.

Question #38


  1. A
    The quantity in Column A is greater;
  2. B
    The quantity in Column B is greater;
  3. C
    The quantities are equal;
  4. D
    The relationship cannot be determined from the information given.

Correct Answer:
A
First, Quantity A:x is the average of 2 and 4; that is, x= 3. Next, Quantity B:y is the average of 3 and 1; that is,y= 2.

Question #39


  1. A
    The quantity in Column A is greater;
  2. B
    The quantity in Column B is greater;
  3. C
    The quantities are equal;
  4. D
    The relationship cannot be determined from the information given.

Correct Answer:
C
To make the comparison, set up two proportions. Quantity A is x in the equation

and Quantity B is y in the equation
You can easily see that x= 2.5 and that y= 2.5.

Question #40


  1. A
    The quantity in Column A is greater;
  2. B
    The quantity in Column B is greater;
  3. C
    The quantities are equal;
  4. D
    The relationship cannot be determined from the information given.

Correct Answer:
A
Wheel Bs radius, and therefore its circumference as well, is 50 times greater than Wheel As (3:150 = 1:50). In order to travel as far each minute as Wheel A travels per hour, Wheel Bs circumference would need to be 60 times greater (since there are 60 minutes per hour), but its not that big. Thus, Wheel A travels further in one minute than Wheel B does in one hour. (The number of revolutions per minute is not relevant, since the rotation rate is the same for both wheels.)

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