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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
If x and y are both negative and xy < y^2, which of the following must
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28 Dec 2022, 09:47
28 Dec 2022, 09:47
Expert Reply
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Question Stats:
42% (01:21) correct
57% (01:13) wrong based on 7 sessions
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If x and y are both negative and \(xy < y^2\), which of the following must be true?
A. \(x < y < x^2 < y^2\)
B. \(x < y < y^2 < x^2\)
C. \(y < x < x^2 < y^2\)
D. \(x^2 < y^2 < y < x\)
E. \(y^2 < x^2 < y < x\)
A. \(x < y < x^2 < y^2\)
B. \(x < y < y^2 < x^2\)
C. \(y < x < x^2 < y^2\)
D. \(x^2 < y^2 < y < x\)
E. \(y^2 < x^2 < y < x\)
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
Re: If x and y are both negative and xy < y^2, which of the following must
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30 Dec 2022, 23:26
30 Dec 2022, 23:26
Expert Reply
Since \(y\) is negative then after reducing \(xy < y^2\) by \(y\) we get: \(x > y\) which is the same as \(y<x\). Both x^2 and y^2 will be greater than either x or y. Only C fits.
Answer: C.
Answer: C.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If x and y are both negative and xy < y^2, which of the following must
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02 Jan 2023, 12:55
02 Jan 2023, 12:55
1
GeminiHeat wrote:
If x and y are both negative and \(xy < y^2\), which of the following must be true?
A. \(x < y < x^2 < y^2\)
B. \(x < y < y^2 < x^2\)
C. \(y < x < x^2 < y^2\)
D. \(x^2 < y^2 < y < x\)
E. \(y^2 < x^2 < y < x\)
A. \(x < y < x^2 < y^2\)
B. \(x < y < y^2 < x^2\)
C. \(y < x < x^2 < y^2\)
D. \(x^2 < y^2 < y < x\)
E. \(y^2 < x^2 < y < x\)
We have xy < y²
If we divide both sides by y we must REVERSE the inequality sign (because we are dividing by a NEGATIVE value).
So, we get: x > y
This allows us to ELIMINATE answer choices A and B (since they suggest that x < y)
From here, let's PLUG IN values for x and y such that they are both negative AND x > y
Let's try x = -1 and y = -2
This means x² = 1 and y² = 4
When we arrange the four values in ascending order we get: y < x < x² < y²
Answer: C
