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If p and q are integers, such that p < 0 < q, and s is

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by BTGModeratorVI » Sat May 16, 2020 7:25 am

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B

C

D

E

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Difficulty—

If p and q are integers, such that p < 0 < q, and s is a nonnegative integer, which of the following must be true?

A. p^2 < q^2
B. p + q = 0
C. sp < sq
D. sp ≠ sq
E. p/q < s

Answer: E
Source: Princeton Review
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Re: If p and q are integers, such that p < 0 < q, and s is

by Brent@GMATPrepNow » Tue May 19, 2020 5:23 am
BTGModeratorVI wrote: ↑
Sat May 16, 2020 7:25 am
 If p and q are integers, such that p < 0 < q, and s is a nonnegative integer, which of the following must be true?

A. p^2 < q^2
B. p + q = 0
C. sp < sq
D. sp ≠ sq
E. p/q < s

Answer: E
Source: Princeton Review
Approach #1
If p < 0 < q, then p is NEGATIVE and q is POSITIVE

So, p/q = NEGATIVE/POSITIVE, which means p/q is NEGATIVE

If s is a non-negative integer, then we can be certain that p/q < s

Answer: E

Approach #2
The question asks, "Which of the following must be true?"
So, if we can find a counterexample that shows an answer choice can be false, then we can eliminate that answer choice.

A. p² < q²
If p = -2 and q = 1, we get: (-2)² < 1²
Simplify to get: 4 < 1, which is not true.
Eliminate A

B. p + q = 0
If p = -2 and q = 1, we get: (-2) + 1 = 0, which is not true.
Eliminate B

C. sp < sq
p = -2, q = 1, and s = 0, we get: (0)(-2) < (0)(1)
Simplify to get: 0 < 0, which is not true.
Eliminate C

D. sp ≠ sq
p = -2, q = 1, and s = 0, we get: (0)(-2) ≠ (0)(1)
Simplify to get: 0 ≠ 0, which is not true.
Eliminate D

By the process of elimination, the correct answer must be E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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Re: If p and q are integers, such that p < 0 < q, and s is

by Scott@TargetTestPrep » Sun May 24, 2020 6:15 am
BTGModeratorVI wrote: ↑
Sat May 16, 2020 7:25 am
 If p and q are integers, such that p < 0 < q, and s is a nonnegative integer, which of the following must be true?

A. p^2 < q^2
B. p + q = 0
C. sp < sq
D. sp ≠ sq
E. p/q < s

Answer: E
Since p < q, p ≠ q. We also know that p is negative and q is positive. This means that p/q is negative. Since s is a nonnegative integer, then p/q < s.

Answer: E

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