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# QOTD # 13 If –1 < x < y < 0, which of the following shows th

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QOTD # 13 If –1 < x < y < 0, which of the following shows th [#permalink]  13 Sep 2016, 07:04
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Question Stats:

55% (01:05) correct 44% (01:28) wrong based on 122 sessions
If $$-1 < x < y < 0$$, which of the following shows the expresions $$xy$$, $$x^2y$$, and $$xy^2$$ listed in order from least to greatest?

A) $$xy, x^2 y, xy^2$$

B) $$xy, xy^2 , x^2 y$$

C) $$xy^2 , xy, x^2 y$$

D) $$xy^2 , x^2 y, xy$$

E) $$x^2 y, xy^2 , xy$$

Practice Questions
Question: 13
Page: 205
[Reveal] Spoiler: OA

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Founder
Joined: 18 Apr 2015
Posts: 13892
GRE 1: Q160 V160
Followers: 313

Kudos [?]: 3676 [0], given: 12919

Re: QOTD # 13 If –1 < x < y < 0, which of the following shows th [#permalink]  13 Sep 2016, 07:06
Expert's post
Explanation

You are given that –1 < x < f < 0. Since x and f are both negative numbers, it follows that xy is positive and both $$x^2 y$$ and $$xy^2$$ are negative. So xy is greater than both $$x^2 y$$ and $$xy^2$$ . Now you need to determine which is greater, $$x^2 y$$ or $$xy^2$$ . You can do this by multiplying the inequality x < y by the positive number xy to get $$x^2 y$$ < $$xy^2$$ . Thus $$x^2 y$$ < $$xy^2$$ < $$xy$$, and the correct answer is Choice E.
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Re: QOTD # 13 If –1 < x < y < 0, which of the following shows th [#permalink]  20 Sep 2016, 14:25
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Expert's post
Carcass wrote:
If –1 < x < y < 0, which of the following shows the expressions xy, x²y, and xy² listed in order from least to greatest?

A) $$xy, x^2 y, xy^2$$

B) $$xy, xy^2 , x^2 y$$

C) $$xy^2 , xy, x^2 y$$

D) $$xy^2 , x^2 y, xy$$

E) $$x^2 y, xy^2 , xy$$

Another approach is to plug in some values.
Given: –1 < x < y < 0
So, let x = -0.5 and let y = -0.1

xy = (-0.5)(-0.1) = 0.05
x²y = (-0.5)(-0.5)(-0.1) = -0.025
xy² = (-0.5)(-0.1)(-0.1) = -0.005

-0.025 < -0.005 < 0.05, which means x²y < xy² < xy

[Reveal] Spoiler:
E

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Re: QOTD # 13 If –1 < x < y < 0, which of the following shows th   [#permalink] 20 Sep 2016, 14:25
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