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# If -1 < x < y < 0 which of the following shows the expressions xy, x^

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Math Expert
Joined: 02 Sep 2009
Posts: 51301
If -1 < x < y < 0 which of the following shows the expressions xy, x^  [#permalink]

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29 Jun 2018, 01:33
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Difficulty:

55% (hard)

Question Stats:

64% (01:42) correct 36% (01:42) wrong based on 99 sessions

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If $$-1 < x < y < 0$$, which of the following shows the expressions $$xy$$, $$x^2y$$, 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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Joined: 07 Dec 2017
Posts: 842
Re: If -1 < x < y < 0 which of the following shows the expressions xy, x^  [#permalink]

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29 Jun 2018, 01:46
Bunuel wrote:
If $$-1 < x < y < 0$$, which of the following shows the expressions $$xy$$, $$x^2y$$, 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. $$x^2 y, xy^2 , xy$$

As all we're given are variables, we'll pick simple numbers.
This is an Alternative approach.

Say x = -1/2 and y = -1/3
Then xy = 1/6, x^2y = -1/12 and xy^2 = -1/18
So the correct order is x^2y < xy^2 < xy

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Director
Joined: 31 Oct 2013
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Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: If -1 < x < y < 0 which of the following shows the expressions xy, x^  [#permalink]

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29 Jun 2018, 08:03
Bunuel wrote:
If $$-1 < x < y < 0$$, which of the following shows the expressions $$xy$$, $$x^2y$$, 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. $$x^2 y, xy^2 , xy$$

Note:

Both x and y are negative fractions. xy will be positive. So, it is greatest.

let assume the value of x and y .

x = - 0.5
y = - 0.25

1. $$x^2$$ y =$$(-0.5)^2$$ (-0.25) = 0.25*(-0.25) = -0.0625
2. x $$y^2$$ = (-0.5) *$$(-0.25)^2$$ =-0.5 * 0.0625

In one result is -0.0625 where in 2 result is the 50% of 0.0625. So, surely 2 will be the second largest.

Thus E is the best answer.
Intern
Joined: 08 Oct 2017
Posts: 24
Re: If -1 < x < y < 0 which of the following shows the expressions xy, x^  [#permalink]

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29 Jun 2018, 08:23
-1<x<y<0 ; Number picking approach - x = -0.5 y = -0.1
xy = 0.05
x^2*y = 0.25*(-0.1) = -0.025
x*y^2 = -0.5*(0.01)=-0.005
So order will be x*y^2, x^2y, xy. Answer is E.
Re: If -1 < x < y < 0 which of the following shows the expressions xy, x^ &nbs [#permalink] 29 Jun 2018, 08:23
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