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Bunuel
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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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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chetan2u
Bunuel
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.
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Bunuel
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

Answer: option C

Perfect! I did exactly this.. the best way to solve these problems is to Plug In.
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roopika2990
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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+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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A. \(x^2\)

B. \((xy)^2\) = \(x^2 * y^2\)

E. \(x^2*y\)

x^2 is multiplied by a fractional value with powers so the value decreases with each multiplication

A>E>B


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

D. \(\frac{x^2}{y}\)

x^2 is divided by a fractional value with powers so the value increases with each division

C>D

and C>A (as C is being divided by a number less than 1 and will result in a number more than x^2

Bunuel
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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