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If p and q are integers, such that p < 0 < q, and s is a non
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01 Apr 2020, 09:10
01 Apr 2020, 09:10
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51% (01:12) wrong based on 117 sessions
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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. \(\frac{p}{q} < s\)
Kudos for the right answer and explanation
A. \(p^2 < q^2\)
B. \(p + q = 0\)
C. \(sp < sq\)
D. \(sp ≠ sq\)
E. \(\frac{p}{q} < s\)
Kudos for the right answer and explanation
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If p and q are integers, such that p < 0 < q, and s is a non
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01 Apr 2020, 09:27
01 Apr 2020, 09:27
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Carcass wrote:
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. \(\frac{p}{q} < s\)
Kudos for the right answer and explanation
A. \(p^2 < q^2\)
B. \(p + q = 0\)
C. \(sp < sq\)
D. \(sp ≠ sq\)
E. \(\frac{p}{q} < s\)
Kudos for the right answer and explanation
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
General Discussion
Re: If p and q are integers, such that p < 0 < q, and s is a non
[#permalink]
29 Jun 2023, 13:22
29 Jun 2023, 13:22
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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