Positive even integers

[aroon7]

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

1) x(y+5) is an even integer
2) 6y^2 + 41y + 25 is an even integer

[dmateer25]

1) x(y+5) is an even integer
if y is odd, x can be even or odd and the result will be even.

INSUFF


2) 6y^2 + 41y + 25 is an even integer

In order for this to be an even integer y must be odd. However, this tells us nothing about x.

INSUFF

Combined:
From statement 2 we know that y is odd. From statement 1 we know if y is odd, x can be even or odd.

INSUFF

I choose E.

[fighting_cax]

2) 6y^2 + 41y + 25 is an even integer

In order for this to be an even integer y must be odd. However, this tells us nothing about x.

I got lost in this part. How were you able to derive that y must be odd based on the equation given?

[cramya]

I got lost in this part. How were you able to derive that y must be odd based on the equation given

Hoping Dmateer will not mind

Rules:

odd+odd = even
even+even=even
even+odd = odd

Same rules above apply to subtraction also

even*even = even
odd*odd=odd
even*odd = even

6y^2+41y+25(ODD) -> even

6y^2 - >always even no matter if y is even or odd

So we now have

6y^2(EVEN) + 41y+ ODD = EVEN

6y^2(EVEN)+25(ODD) = ODD

Therefore the above reduces to
ODD + 41y = even

y has to be odd since only ODD+ODD = EVEN

For 41y to be odd, y has to be odd based on multiplication rules above

Hope this helps!

Regards,
CR

[welcome]

IMO E. What is OA?

[x2suresh]

agree with E..