Is x an even integer? (1) 2y + x is an even number. (2) x^2 + x is an

Question

Is x an even integer?

(1) 2y + x is an even number.

(2) x^2 + x is an even number.

New question..

Mo2men · Answer

(1) 2y+x is an even number.

If y is any odd or even integer, then x must be integer to get Even number............Answer is Yes.

If y is fraction, for example y =1/2 and x= 1......................................................Answer is No

Insufficient

(2)  x^2+x  is an even number.

x^2+x  =  x(x+1) ...Those are in form of 2 consecutive numbers. So we are sure will get one even and other odd but x could be odd or even.

Let x =1 ...........................Answer is No

Let x =2 ...........................Answer is Yes

Insufficient

Combine 1 & 2

Use same examples when x = 1 or x =2..........We still do not get conclusive answer.

Insufficient

Answer: E

SonalSinha803 · Answer

According to statement 1, 2y + x = even. 2y is even. Thus, the only possible condition for x is to be even. Thus, answer would be yes. 
Sufficient.

Statement 2 says, x^2 + x = even. Thus, x can be odd or even as, odd + odd = even and even + even = even.

Thus, A is the answer.

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GMATBusters · Answer

Hi  SonalSinha803

As we don't know whether y is an integer, we cant say that 2y is even. 
let y =1/2 ans x = 1
2y = 1
so 2y + x = 2 = even, but x is not even.

But if y is an integer ,2y is even. Thus, the only possible condition for x is to be even. Thus, answer would be yes. 
 So A is not sufficient.

SonalSinha803 · Answer

Oh yes. Damn I missed seeing this. Thankyou so much for the clarification ?

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