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02 Apr 2015, 04:19
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C
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If x and y are positive integers, is x even?
(1) xy is even
(2) x + y is even
Kudos for a correct solution.
(1) xy is even
(2) x + y is even
Kudos for a correct solution.
02 Apr 2015, 05:02
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Bunuel
If x and y are positive integers, is x even?
(1) xy is even
(2) x + y is even
Kudos for a correct solution.
(1) xy is even
(2) x + y is even
Kudos for a correct solution.
x,y--->+ve; x=Even?
1. xy=Even.
y could be the only integer that is even here viz xis odd...Insufficient
2. x+y=Even
Both x and y will have to be even or both have to be odd....Insufficient
1 and 2 together:
From 1 we know *atleast* one of x or y is even.
From 2 we know if one is even then both will be even.
Hence x is even.
Sufficient
Answer: C
02 Apr 2015, 05:12
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(1) xy is even
3 possible variants:
odd * even = even,
even * odd = even,
even * even = even
- insufficient
(2) x + y is even
2 possible variants:
even + even = even,
odd + odd = even
- insufficient
(1 + 2) we have only one variant that make both statements possible, this is
even and even:
even + even = even
even * even = even
so both integers are even and these two statements are sufficient for answer on this question
Answer is C
3 possible variants:
odd * even = even,
even * odd = even,
even * even = even
- insufficient
(2) x + y is even
2 possible variants:
even + even = even,
odd + odd = even
- insufficient
(1 + 2) we have only one variant that make both statements possible, this is
even and even:
even + even = even
even * even = even
so both integers are even and these two statements are sufficient for answer on this question
Answer is C
