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Is xy < x^2*y^2? (1) xy > 0 (2) x + y = 1

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Intern
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Joined: 28 May 2018
Posts: 48
Location: India
Schools: Tuck '21, ISB '20, NTU '20
GMAT 1: 640 Q45 V35
GMAT 2: 670 Q45 V37
Is xy < x^2*y^2? (1) xy > 0 (2) x + y = 1  [#permalink]

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New post 19 Oct 2018, 08:42
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A
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C
D
E

Difficulty:

  45% (medium)

Question Stats:

59% (01:40) correct 41% (01:28) wrong based on 40 sessions

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Is \(xy < x^2y^2\)?

(1) xy > 0
(2) x + y = 1

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Director
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Re: Is xy < x^2*y^2? (1) xy > 0 (2) x + y = 1  [#permalink]

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New post 19 Oct 2018, 13:19
PriyankaPalit7 wrote:
Is \(xy < x^2y^2\)?

1) xy>0
2) x+y=1


X and Y are of the same sign.

If x = 2 and y = 2

Then 4 < 16 yes

If x = 1/2 and y = 1/2

1/4 < 1/16 no.

Insufficient.

Eliminate A/D

Statement 2)

If x = -1

Y= 1
Then the statement -1 < 1 yes

If x = 1/2 and y = 1/2

Then the answer is xy < x^2 y^2 is no

Combined it is sufficient.

1/4 < 1/16 no.

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Re: Is xy < x^2*y^2? (1) xy > 0 (2) x + y = 1  [#permalink]

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New post 19 Oct 2018, 22:16
Hi,

Slightly tricky question.

We can solve this using either Plugging in values for x and y OR we can do the mathematical approach.

Let’s see the mathematical approach.

Question:

Is x * y < x^2 * y^ 2 ?

Let’s simplify the question a bit.

Is 0 < x^2 * y^ 2 - x * y?

Is 0 < x * y (x * y - 1)?

If M = x * y, then

Is 0 < M * (M - 1)?

Answer to the question would be YES if M < 0 or M > 1 i.e., “x” and “y” have alternate signs OR “x” and “y” both positive or both negative and their product greater than 1.

Answer to the question would be NO if 0 < M < 1 i.e., “x” and “y” both positive or both negative and their product less then 1.

Statement I is insufficient:

x*y >0

i.e., M > 0

Answer to the question, would be YES or NO.

If M = 1/4

i.e., let’s say X = ½ and Y = ½, then answer to the question would be NO.

If M = 2

i.e., let’s say X = 2 and Y = 1, then answer to the question would be YES.

So not sufficient.

Statement II is insufficient:

x+y=1

If M = 1/4

let’s say X = ½ and Y = ½, then answer to the question would be NO.

If M = -2

i.e., let’s say X = 2 and Y = -1, then answer to the question would be YES.

So not sufficient.

Together it is sufficient.

x*y > 0

and x+y = 1

Only way we could achieve this is,

x and y has to lie between 0 and 1.

i.e., M has to be between 0 and 1. So answer to the question would be NO.

So together it is sufficient.

Answer is C.

Hope it is clear.
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Re: Is xy < x^2*y^2? (1) xy > 0 (2) x + y = 1   [#permalink] 19 Oct 2018, 22:16
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