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# If x < 0 and 0 < y < 1, which of the following has the greatest value?

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Math Expert
Joined: 02 Sep 2009
Posts: 52971
If x < 0 and 0 < y < 1, which of the following has the greatest value?  [#permalink]

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28 Jul 2015, 06:19
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Difficulty:

15% (low)

Question Stats:

74% (01:21) correct 26% (01:15) wrong based on 128 sessions

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If x < 0 and 0 < y < 1, which of the following has the greatest value?

A. $$x^2$$

B. $$(xy)^2$$

C. $$(\frac{x}{y})^2$$

D. $$\frac{x^2}{y}$$

E. $$x^2*y$$

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Re: If x < 0 and 0 < y < 1, which of the following has the greatest value?  [#permalink]

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28 Jul 2015, 06:29
Bunuel wrote:
If x < 0 and 0 < y < 1, which of the following has the greatest value?

A. x^2
B. (xy)^2
C. (x/y)^2
D. x^2/y
E. x^2*y

Plug in the values, x = -1, y =0.5

A: 1
B: 0.25
C: 4
D: 2
E: 0.5

Thus, C is the correct answer.
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Re: If x < 0 and 0 < y < 1, which of the following has the greatest value?  [#permalink]

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28 Jul 2015, 06:56
Bunuel wrote:
If x < 0 and 0 < y < 1, which of the following has the greatest value?

A. x^2
B. (xy)^2
C. (x/y)^2
D. x^2/y
E. x^2*y

Given, x < 0 and 0 < y < 1

Let, x = -2 and y = 1/2

A. x^2 = (-2)^2 = 4
B. (xy)^2 = (-2*1/2)^2 = 1
C. (x/y)^2 = {-2/(1/2)}^2 = (-4)^2 = 16
D. x^2/y = (-2)^2 / (1/2) = 4*2 = 8
E. x^2*y = (-2)^2*(1/2) = 2

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Re: If x < 0 and 0 < y < 1, which of the following has the greatest value?  [#permalink]

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28 Jul 2015, 07:19
1
Bunuel wrote:
If x < 0 and 0 < y < 1, which of the following has the greatest value?

A. x^2
B. (xy)^2
C. (x/y)^2
D. x^2/y
E. x^2*y

Hi,
all choices have x^2 in it , so we just require to know that it is a positive value...
now y is a value between 0 and 1 so its value will become lesser as we square it...
so the greatest value will be when we divide anything with the highest value of y..
C stands out ..ans C
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Re: If x < 0 and 0 < y < 1, which of the following has the greatest value?  [#permalink]

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30 Jul 2015, 00:35
It doesn't specify that x < -1; x can be a value between 0 and -1 hence changes the whole question. IMO E.
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Re: If x < 0 and 0 < y < 1, which of the following has the greatest value?  [#permalink]

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Updated on: 30 Jul 2015, 02:49
1
chetan2u wrote:
Bunuel wrote:
If x < 0 and 0 < y < 1, which of the following has the greatest value?

A. x^2
B. (xy)^2
C. (x/y)^2
D. x^2/y
E. x^2*y

Hi,
all choices have x^2 in it , so we just require to know that it is a positive value...
now y is a value between 0 and 1 so its value will become lesser as we square it...
so the greatest value will be when we divide anything with the highest value of y..
C stands out ..ans C

As chetan2u rightly said, x^2 appears in all options, so it does not matter what is its value. Hence, we effectively need to compare 1, y^2, y^(-2), y^(-1) and y^1. For any number between 0 and 1, as its power increases value decreases. Thus Option (C) is the greatest value.
Also chetan2u, please note that the value in denominator need to be smallest.

Originally posted by SKMishra on 30 Jul 2015, 02:11.
Last edited by SKMishra on 30 Jul 2015, 02:49, edited 1 time in total.
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Joined: 05 Nov 2014
Posts: 41
Re: If x < 0 and 0 < y < 1, which of the following has the greatest value?  [#permalink]

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30 Jul 2015, 02:12
GMATinsight wrote:
Bunuel wrote:
If x < 0 and 0 < y < 1, which of the following has the greatest value?

A. x^2
B. (xy)^2
C. (x/y)^2
D. x^2/y
E. x^2*y

Given, x < 0 and 0 < y < 1

Let, x = -2 and y = 1/2

A. x^2 = (-2)^2 = 4
B. (xy)^2 = (-2*1/2)^2 = 1
C. (x/y)^2 = {-2/(1/2)}^2 = (-4)^2 = 16
D. x^2/y = (-2)^2 / (1/2) = 4*2 = 8
E. x^2*y = (-2)^2*(1/2) = 2

Perfect! I did exactly this.. the best way to solve these problems is to Plug In.
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Re: If x < 0 and 0 < y < 1, which of the following has the greatest value?  [#permalink]

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30 Jul 2015, 08:22
roopika2990 wrote:
It doesn't specify that x < -1; x can be a value between 0 and -1 hence changes the whole question. IMO E.

Hi roopika2990,

I'm not sure how the whole equation changes when $$x^{2}$$ is in each of the solutions. Could you help elaborate?
Thank you.
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Re: If x < 0 and 0 < y < 1, which of the following has the greatest value?  [#permalink]

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11 Apr 2018, 21:04
+1 for option C. We need a positive value in the numerator ; denominator requires to be as small as possible. B/W C and D - we see that in C the value is multiplied by one more factor of y. Hence option C.
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Re: If x < 0 and 0 < y < 1, which of the following has the greatest value?   [#permalink] 11 Apr 2018, 21:04
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