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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] New post 13 Sep 2016, 07:04
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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) \(x^2 y, xy^2 , xy\)

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

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Re: QOTD # 13 If –1 < x < y < 0, which of the following shows th [#permalink] New post 13 Sep 2016, 07:06
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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] New post 20 Sep 2016, 14:25
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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

Answer:
[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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