Brent@GMATPrepNow wrote:

gmattesttaker2 wrote:Hello,

This is from MGMAT:

If a and b are positive integers such that a < b, is b even?

(1) b/2 - a/2 is an integer.

(2) 3b/4 - a/2 is an integer.


OA: B


I was trying to solve this as follows:

1) b/2 - a/2 = integer
(b - a)/2 = integer
b - a = even integer

So, b = a = odd
or b = a = even

Insuff.


2) 3b/4 - a/2 = integer
3b/4 - 2a/4 = integer
3b - 2a = even integer
3b - even integer = even integer

However, I was stuck after this point since 3b is odd.

Can you please assist? Thanks a lot - Sri

You were 98% there.

You got to: 3b - even integer = even integer
If something - even = even, then something is even (EVEN - EVEN = EVEN)

In other words, 3b is EVEN
If 3b is even, b must be even

Cheers,
Brent

Brent@GMATPrepNow wrote:Hi Sri,

Here's what you need to know for EVEN and ODD integers.
(EVEN)(EVEN) = EVEN
(EVEN)(ODD) = EVEN
(ODD)(ODD) = ODD

Since 3 is an odd integer, and since b is an integer, b must be even.

Now, if we remove the condition that b is an integer, then b could equal a fraction such as 2/3 in which case 3b = 2.

But since we're told that b is an integer, we can be certain that b is even.

Does that help?

Cheers,
Brent