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

[gmattesttaker2]

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

Sorry: Posted it in wrong section. Moved it to DS

[Brent@GMATPrepNow]

See https://www.beatthegmat.com/if-a-and-b-a ... tml#692892

Cheers,
Brent

[[email protected]]

Hi gmmattestaker2,

I wanted to nudge you a bit on this question...

Based on what you wrote about Fact 2...

Is the equation equal to an "even integer" or "a multiple of 4"?

Also, why is it that you think that 3B is odd?

GMAT assassins aren't born, they're made,
Rich

[gmattesttaker2]

Hi gmmattestaker2,

I wanted to nudge you a bit on this question...

Based on what you wrote about Fact 2...

Is the equation equal to an "even integer" or "a multiple of 4"?

Also, why is it that you think that 3B is odd?

GMAT assassins aren't born, they're made,
Rich

Hello Rich,

I was thinking that since 3b/4 - 2a/4 = integer, I would take the LCM.

Hence, (3b - 2a)/4 = integer

Then multiply by 4 on both sides i.e. 3b - 2a = 4*integer

Since 4 is even, 4*integer = even integer

Hence, 3b - 2a = even integer

I think this is where I got confused a bit. (Thanks to Brent for helping me by explaining it in the post given by the above link.)

So, 3b - even integer = even integer

Hence 3b has to be even since even - even = even. 3 is odd => b is even.


Is my reasoning correct here? Many thanks for your help.


Best Regards,
Sri

[[email protected]]

Hi Sri,

YES! Your logic from your last post IS correct. You've used Number Properties to prove that B is even.

If you're going to use NPs in the future (and they show up often in DS questions, so NPs are worth knowing), you must pay very careful attention to the details. Any type of careless error will likely cost you the question.

GMAT assassins aren't born, they're made,
Rich