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# If x and y are positive integers, what is the value of xy?

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Senior Manager
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If x and y are positive integers, what is the value of xy?  [#permalink]

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06 Apr 2019, 05:48
00:00

Difficulty:

55% (hard)

Question Stats:

67% (02:12) correct 33% (01:32) wrong based on 48 sessions

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If x and y are positive integers, what is the value of xy?

I. 2^(x^2+y^2)=256
II. (2^x+y)^x−y=1
Senior Manager
Joined: 25 Feb 2019
Posts: 288
Re: If x and y are positive integers, what is the value of xy?  [#permalink]

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06 Apr 2019, 06:31
IMO 4

from 1 statement

256 = 2^8

so x^2+y^2 = 8

from statement 2 we get

2^(x^2 -y^2) = 2^0

x^2 - y^2 = 0

so it means x-y = 0 becauae x and y are positive integers

so put x= y in first statememt we get x = 2

so y = x = 2

so xy = 4

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Senior Manager
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GMAT 1: 460 Q42 V13
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Re: If x and y are positive integers, what is the value of xy?  [#permalink]

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06 Apr 2019, 06:34
m1033512 wrote:
IMO 4

from 1 statement

256 = 2^8

so x^2+y^2 = 8

from statement 2 we get

2^(x^2 -y^2) = 2^0

x^2 - y^2 = 0

so it means x-y = 0 becauae x and y are positive integers

so put x= y in first statememt we get x = 2

so y = x = 2

so xy = 4

Posted from my mobile device

I thought the same, but OA is A
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Re: If x and y are positive integers, what is the value of xy?  [#permalink]

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06 Apr 2019, 06:51
ohkay ,

x and y are positive integers

By hit and trial, we see that only x = 2 and Y = 2

satisfy the given equation

2^2+2^2 = 8

Thanks for quick response !!!

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Joined: 17 Feb 2019
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Re: If x and y are positive integers, what is the value of xy?  [#permalink]

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09 Apr 2019, 09:26
Could Somebody please explain why answer is A? How alone using statement 1, we are able to deduce value of XY?
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Re: If x and y are positive integers, what is the value of xy?  [#permalink]

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09 Apr 2019, 09:33
2
brassmonkey wrote:
Could Somebody please explain why answer is A? How alone using statement 1, we are able to deduce value of XY?

Statement (1) says

2^(x^2+y^2) = 2^8

So, x^2+y^2 = 8

We know that x and y are positive integers

This means
(Some perfect square) + (Some perfect square) = 8

4 is the only perfect square that satisfies this condition

So x^2 = y^2 = 4 and x=y=2

Then xy=4

(1) is sufficient

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GMAT 1: 460 Q42 V13
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Re: If x and y are positive integers, what is the value of xy?  [#permalink]

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09 Apr 2019, 10:38
firas92 wrote:
brassmonkey wrote:
Could Somebody please explain why answer is A? How alone using statement 1, we are able to deduce value of XY?

Statement (1) says

2^(x^2+y^2) = 2^8

So, x^2+y^2 = 8

We know that x and y are positive integers

This means
(Some perfect square) + (Some perfect square) = 8

4 is the only perfect square that satisfies this condition

So x^2 = y^2 = 4 and x=y=2

Then xy=4

(1) is sufficient

Posted from my mobile device

I missed the logic of perfect square. thank you for your explanation.
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Re: If x and y are positive integers, what is the value of xy?  [#permalink]

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10 Apr 2019, 09:28
can someone explain why B is wrong ?
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Joined: 02 Aug 2009
Posts: 7688
Re: If x and y are positive integers, what is the value of xy?  [#permalink]

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10 Apr 2019, 09:41
anmolgmat14 wrote:
can someone explain why B is wrong ?

If x and y are positive integers, what is the value of xy?

I. $$2^(x^2+y^2)=256=2^8$$
Equating the powers we get $$x^2+y^2=8$$, so 8 is the sum of TWO perfect squares... Only possibility is $$2^2+2^2$$, thus xy=2*2=4
Sufficient

II. (2^x+y)^x−y=1
Although the question is a bit ambiguous, it seems the question is $$(2^{x+y})^{x-y}=1$$, that is $$2^{x^2-y^2}=1=2^0$$. Thus $$x^2=y^2$$..
So, x and y can take any values.. Both can be 2 and 2, or 4 and 4 and so on. Every time answer will be difficult.

A
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Re: If x and y are positive integers, what is the value of xy?  [#permalink]

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11 Apr 2019, 09:49
kiran120680 wrote:
If x and y are positive integers, what is the value of xy?

I. 2^(x^2+y^2)=256
II. (2^x+y)^x−y=1

from 1 : 2^(x^2+y^2)=256
we can say 2^(x^2+y^2) = 2^8
or say x^2+y^2= 8
given x , y are +ve integers so only possible value is x=y=2
xy=4 sufficient
#2
(2^x+y)^x−y=1

2^(x^2-y^2)=1
x=y ; x,y can be any integer value ; insufficient
IMO A
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Re: If x and y are positive integers, what is the value of xy?   [#permalink] 11 Apr 2019, 09:49
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