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If x and y are positive integers, is xy even?
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26 Jun 2017, 02:43
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If x and y are positive integers, is xy even? (1) x^2 + y^2 − 1 is divisible by 4. (2) x + y is odd.
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Re: If x and y are positive integers, is xy even?
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Updated on: 25 Jul 2017, 04:36
Statement 1 X^2 +Y^2  1 is divisible by 4. can be 3^2 + 5^2  1 = 24 or 4^2 + 1^2  1 = 16 S Statement 2. X+Y = odd. it has to be one even and one odd number. Suff Ans D Sent from my SMG935F using GMAT Club Forum mobile app
Originally posted by Ejiroosa on 26 Jun 2017, 02:50.
Last edited by Ejiroosa on 25 Jul 2017, 04:36, edited 1 time in total.



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Re: If x and y are positive integers, is xy even?
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26 Jun 2017, 02:54
x^2 + y^2  1 has to be even to be divisible by 4. Hence x^2 + y^2 is odd. This means either x or y has to be even. Statement 1 is sufficient. Similarly for x+y to be odd, either x or y has to be even. Hence product xy is even. Statement 2 is also sufficient. Answer  D Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app



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If x and y are positive integers, is xy even?
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26 Jun 2017, 02:59
Bunuel wrote: If x and y are positive integers, is xy even?
(1) x^2 + y^2 − 1 is divisible by 4. (2) x + y is odd. (1) \(x^2 + y^2 − 1\) is divisible by 4.
Let (\(x^2 + y^2\) ) be \(z\).
\(z  1\) is divisible by \(4\).
Only even number is divisible by \(4\). Hence \(z  1\) should be even.
Odd  Odd = Even.
Therefore \((x^2  y^2)\) should be Odd. (\(Odd^2\) will be Odd. \(Even^2\) will be Even)
Even  Odd = Odd
Therefore either \(x\) or \(y\) should be even. Therefore \(xy\) will be even. I is Sufficient.
(2) \(x + y\) is odd.
Even + Odd = Odd.
Therefore either \(x\) or \(y\) should be even. Therefore \(xy\) will be even. II is Sufficient.
Answer (D)...



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Re: If x and y are positive integers, is xy even?
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26 Jun 2017, 03:07
If x and y are positive integers, is \(xy\)even? (1) \(x^2 + y^2 − 1\) is divisible by 4This means that either x or y has to be odd. As you know ODD * EVEN = EVENQuestion  Is xy EVEN ? is TRUE =====> Eq. (1) SUFFICIENT(2) \(x + y\) is oddAs we know, ODD + EVEN = ODDAnd ODD * EVEN = EVENQuestion  Is xy EVEN ? is TRUE =====> Eq. (2) SUFFICIENTHence, the answer is D
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Re: If x and y are positive integers, is xy even?
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26 Jun 2017, 04:30
Ans is D used 5 instead of 4.... Sent from my SMG935F using GMAT Club Forum mobile app



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Re: If x and y are positive integers, is xy even?
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17 Jul 2017, 22:45
Bunuel wrote: If x and y are positive integers, is xy even?
(1) x^2 + y^2 − 1 is divisible by 4. (2) x + y is odd. St 1 (x^2 + y^2 − 1) /4 = some integer  therefore some odd number minus 1 is divisible by 4 x^2 + y^2= some odd number... in order for this to be true either X and Y must be some even and odd mix (1)^2 +(2)^2= 5 odd knowing x and y must be different ( even and odd) x and y must odd St 2 Even + Odd = Odd so Suff D



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Re: If x and y are positive integers, is xy even?
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30 Jul 2017, 17:31
Bunuel wrote: If x and y are positive integers, is xy even?
(1) x^2 + y^2 − 1 is divisible by 4. (2) x + y is odd. We need to determine whether the product of x and y is even. Statement One Alone: x^2 + y^2 − 1 is divisible by 4. Since 4 is an even number, we need x^2 + y^2 − 1 to be even. In order for x^2 + y^2 − 1 to be even, we need x^2 + y^2 to be odd. If the sum of two squares is odd, one of them must be odd and the other must be even. This means that either x = odd and y = even OR x = even and y = odd. In either case, the product of x and y will be even. Statement one alone is sufficient to answer the question. Statement Two Alone: x + y is odd. Since x + y = odd, either x = odd and y = even OR x = even and y = odd. In either case, the product of x and y will be even. Statement two alone is sufficient to answer the question. Answer: D
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If x and y are positive integers, is xy even?
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13 Mar 2018, 21:18
Bunuel pushpitkc niks18 HatakekakashiamanvermagmatHow about this approach? \(x^2\) + \(y^2\)  1 = 4 *(m) where m is an integer since there is no remainder (given) or \(x^2\) + \(y^2\) = odd or x + y = odd (a positive odd / even no when squared will give odd and even values respectively) This is only possible when either of x or y is odd. Does that help to make St 1 suff?
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Re: If x and y are positive integers, is xy even?
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13 Mar 2018, 21:54
adkikani wrote: Bunuel pushpitkc niks18 HatakekakashiamanvermagmatHow about this approach? \(x^2\) + \(y^2\)  1 = 4 *(m) where m is an integer since there is no remainder (given) or \(x^2\) + \(y^2\) = odd or x + y = odd (a positive odd / even no when squared will give odd and even values respectively) This is only possible when either of x or y is odd. Does that help to make St 1 suff? Hello yes i think this approach is correct



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Re: If x and y are positive integers, is xy even?
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14 Mar 2018, 00:21
adkikani wrote: Bunuel pushpitkc niks18 HatakekakashiamanvermagmatHow about this approach? \(x^2\) + \(y^2\)  1 = 4 *(m) where m is an integer since there is no remainder (given) or \(x^2\) + \(y^2\) = odd or x + y = odd (a positive odd / even no when squared will give odd and even values respectively) This is only possible when either of x or y is odd. Does that help to make St 1 suff? this approach is correct good usage of basic concepts (Y)



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Re: If x and y are positive integers, is xy even?
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19 Mar 2019, 08:19
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Re: If x and y are positive integers, is xy even?
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