If x and y are positive integers, is x even?

Question

(1) xy is even

(2) x + y is even

Kudos for a correct  solution .

AmoyV · Answer

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

Harley1980 · Answer

(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

adityadon · Answer

XY is even - insufficient - as it could be 2*3 or 3*2 
X+Y is even - insufficient - as it could be 2+4 or 3+3

Combining both , if both prodcut and sum of two positive integers is even then both numbers must be even e.g 4*2=8 , 4+2=6

so answer is C

earnit · Answer

Ok, (places interchangeable) Odd +/- Even = Odd 
 Odd * Odd = Odd
These are the two ways of getting an odd output.

1) If product is even then either of the integers could be even and the other odd OR both could be even.
Ex: 2*2 = 4 2*3 = 6 so x could be either 2 or 3.

Insufficient clearly.

2) Sum of two integers is even implies either both are even or both are odd. 
Ex: 2+4 = 6 OR 3+5 = 8

Insufficient again.

Combining (1) and (2), There is only one way that two integers with product even and sum even, they both have to be even. None of them can be ODD. 
as if one is 2 and other is 3, both conditions cannot be satisfied. 
2*3 = Even but 2+3 = Not even.

Answer:C

KS15 · Answer

1. xy is even. Does not satisfy. We can have 2 combinations
x is even and y is odd OR y is even and x is odd
2 x+y is even. Does not satisfy. We can have 2 combinations
x is even and y is even OR y is odd and x is odd

Using 1 and 2, Only one combinations is possible. Both x and y are even. Answer=C

Bunuel · Answer

MAGOOSH OFFICIAL SOLUTION: isxeven_text.PNG

stonecold · Answer

Here we need to check if x is even 
Clearly statement 1 is insuff as if y is even then x can be even or odd
from statement 2 => x,y => E,E or O,D => insuff
Combining the two => x=even and y = even too
Smash that C

TestPrepUnlimited · Answer

Statement 1: 
We need only either x or y to be even to have x*y even. We could have x odd y even, or x even y odd. Insufficient.

Statement 2: 
Either x and y are both odd or both even, insufficient.

Combined: 
Statement 1 doesn't allow both odd so they must be both even, sufficient.

Ans: C

TheNightKing · Answer

Is x even?

(1) xy is even

Either x or y is even. Both could be even too.

Not Sufficient.

(2) x + y is even

Either both are even or both are odd.

Example: 2+2=4 or 5+5=10

Not Sufficient.

Combined: 
Well, Interesting. We cannot have both odd. So that's gone. We have to have both even. Because if one of them is also odd then the x+y will be odd and not even. And one of the two has to be even for xy to be even. So both are even.

Sufficient.

Answer (C)

If x and y are positive integers, is x even?

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