GRE Test Exam Questions and Answers

QUESTION: 49

Let Q, R, and S be positive integers such that S is a factor of Q and R. Let

Which of the following is equal to ?

|q - r|2
|(q - r)(S)|2
|q2 - r2|
|(q2 - r2)(S)|
|(q2 - r2)(S2)|

Answer(s): D

Explanation:

We are given that S is a factor of both Q and R, meaning that we can express Q and R in terms of S as:
Q = qS

R = rS

where q and r are integers.
We need to simplify the given expression:

Since Q = qS and R = rS,

S(q2 - r2), or |(q2 - r2)(S)|

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QUESTION: 50

The integer p is a prime number greater than 5, and 5 is a factor of p +p2.
What is the remainder when p is divided by 5?

0
1
2
3
4

Answer(s): E

Explanation:

We can express p + p2 as:
p + p2 = p(1 + p)
The problem states that 5 is a factor of p + p2, which means:
p(1 + p) 0 (mod 5)
This implies that p(1 + p) is divisible by 5. Since p is a prime number greater than 5, p is not divisible by 5.
Therefore, the factor of 5 must come from 1 + p.
We know that 1 + p must be divisible by 5. Thus, we have:
1 + p 0 (mod 5)
p -1 (mod 5)
Since -1 4 (mod 5), we conclude that:
p 4 (mod 5)

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QUESTION: 51

If n is an odd integer, which of the following must be an even integer?

n + 2
n2 + 3
n2 + 2n

Answer(s): D

Explanation:

· Since n is odd, n - 1 is even. Dividing an even number by 2 results in an integer, but it could be odd or even depending on n.
· Since n is odd, n + 1 is even. Dividing an even number by 2 results in an integer, but it could be odd or even depending on n.
· Since n is odd, adding 2 results in an odd number.
· Since n is odd, squaring it keeps it odd, meaning n2 is odd. Adding 3 to an odd number results in an even number. This must be even.
· Since n is odd, n2 is odd. Since n is odd, multiplying it by 2 results in an even number. Adding an odd number (n2) and an even number (2n) results in an odd number.

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QUESTION: 52

If 0 < r < t and r = 50 - t, what is the greatest possible value of the median of r, t, and 28?

23
24
26
28
29

Answer(s): D

Explanation:

Since r = 50 - t, we substitute it into the inequality 0 < r < t:
1. 0 < 50 - t, which simplifies to t < 50.
2. 50 - t < t, which simplifies to
50 < 2t
25 < t
So, the range of t is 25 < t < 50.
The median is the middle number when r, t, and 28 are arranged in increasing order.
Since r = 50 - t, we note that r decreases as t increases.
Case 1: If t < 28
r = 50 - t would be greater than 28 because t is small.

The numbers in order are t, 28, r.

The median is 28.

Case 2: If t > 28
r = 50 - t would be less than 28 because t is large.

The numbers in order are r, 28, t.

The median is still 28.

From both cases, the median is always 28, regardless of the values of t and r.
The greatest possible value of the median is 28.

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QUESTION: 53

It costs d dollars to buy n nails. At this rate, what is the cost of n + 1,850 nails, in dollars?

Answer(s): E

Explanation:

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QUESTION: 54

Based on the information given, which of the following pairs of energy sources accounted for more than one- half of the world primary energy supply? (Choose all that apply.)

Coal and oil
Natural gas and oil
Natural gas and nuclear power
Natural gas and renewable sources

Answer(s): A,B

Explanation:

We sum the percentages for each pair:
· Coal and Oil: 24.4 + 34.4 = 58.8% More than 50%
· Natural Gas and Oil: 21.2 + 34.4 = 55.6% More than 50%
· Natural Gas and Nuclear Power: 21.2 + 6.5 = 27.7% Less than 50% · Natural Gas and Renewable Sources: 21.2 + 13.5 = 34.7% Less than 50%

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