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Even Integer?

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Even Integer?

by hardikm » Wed Jun 01, 2011 11:13 am
Is product 2*x*5*y an even integer?
1. 2 +x+ 5 +y is an even integer
2. x -y is an odd integer

Please also write how long do u take to solve this problem? I took close to 2 minutes..

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by Frankenstein » Wed Jun 01, 2011 11:21 am
Hi,
Did he mention anything about x,y being integers or not?
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by Frankenstein » Wed Jun 01, 2011 11:24 am
Hi,
If it is not mentioned that x and y are integers, answer is E
Last edited by Frankenstein on Wed Jun 01, 2011 11:36 am, edited 1 time in total.
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by hardikm » Wed Jun 01, 2011 11:32 am
Hey Frankenstein,

question did not mention whether x and y are integers but can u provide reasoning why do u think answer is E when x and y r not.

H
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by Frankenstein » Wed Jun 01, 2011 11:44 am
hardikm wrote:Hey Frankenstein,

question did not mention whether x and y are integers but can u provide reasoning why do u think answer is E when x and y r not.

H
Hi,
Sorry, I shouldn't have posted that. If he has given that x and y are integers, then there is nothing to do.
To find out whether 2.5.x.y is an even integer, we need to find out whether x.y is integer or not.
from(1):2+x+5+y is even => x+y is odd
if x and y are integers, one of them is odd and other is even and the product is an integer
if x=2.5 and y is 4.5, x.y is not an integer
Insufficient
from(2): x-y is odd
if x and y are integers, one of them is odd and other is even and the product is an integer
if x=2.5 and y is 1.5, x.y is not an integer
Insufficient
From(1) and (2): Lets x+y = 2p+1 and x-y=2q+1, where p and q are integers
Solving we get x= p+q+1 and y = p-q.
So, x and y a re integers
Sufficient

Hence, C
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