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If x and y are positive integers, what is the value of xy?
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06 Apr 2019, 05:48
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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
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Re: If x and y are positive integers, what is the value of xy?
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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 xy = 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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Re: If x and y are positive integers, what is the value of xy?
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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 xy = 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
award kudos if helpful
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?
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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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Re: If x and y are positive integers, what is the value of xy?
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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?
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09 Apr 2019, 09:33
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



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Re: If x and y are positive integers, what is the value of xy?
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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 deviceI 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?
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10 Apr 2019, 09:28
can someone explain why B is wrong ?



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Re: If x and y are positive integers, what is the value of xy?
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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 \((2^{x+y})^{xy}=1\), that is \(2^{x^2y^2}=1=2^0\). 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?
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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^2y^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?
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