Number property - even/odd problem

Question

Can anyone help solving this problem?

Is A + B + C even?
(1) A - B - C is even? 
(2) (A-C)/ is odd

OA will be coming soon! 
By the way, is there any specific quick approach of dealing even-odd problem? Thanks!

iamcartic · Answer

Is A + B + C even?
(1) A - B - C is even
(2) (A-C) is odd

I go with A

St1: A if odd then B+C is odd => A+B+C is even and A if even B+C is even => A+B+C is even. There can be no case where st 1 is true and we cant say what A+B+C would be.----suffic

St2: A-C is odd now nothing has been told abt B hence insuff

bhatiagp · Answer

I go with A as well

My approach :

1) A- b-c is even

means

A - ( B +C ) is even

Now even-even = even

or odd-odd = even

Therefore either ( A is even , then B + C is even ) or (if A is odd , then B + C is odd .. )

either ways

A + ( B + C ) = odd + odd = even

or if A is even than B+ C is also even hence

A+ ( B + C ) = odd + odd = even

Therefore A is correct.

Option A- C = odd, gives no information on B, hence inconclusive,

judokan · Answer

For sum or difference:
Even and even gives even 
Odd and odd gives even
Odd and even gives odd

As such

(1) is sufficient. If A-B is even, then A+B is even, vice versa. If (A-B)-C is even, (A+B)+C is even.

(2) I think you mean (A-C)/B is odd

(2) tells us two possible cases

Case (i) (A-C) is odd and B is odd, and Case (ii) (A-C) is even and B is even

In (i) if (A-C) is odd and B is odd

We can also conclude A or C is odd and the other is even

So two possible combination
(a) A (odd), B (odd), C (even)
(b) A (even), B (odd), C (odd)

In both (a) and (b) prove A + B + C is even

See Case (ii) (A-C) is even and B is even
So two possible combination
(a) A (odd), B (even), C (odd)
(b) A (even), B (even), C (even)

This also gives A+B+C even

So (2) alone is also sufficient.

pmenon · Answer

is something missing with statement 2 ? im not a fan of making assumptions

Stelladuong · Answer

It is a typical GMAT trap named unwarrant assumption. We are not given that A, B, C are integer!

OA is E!

Let's pick up numbers:

(1) Pick 9/2 - 3/2 - 1 for A - B - C respectively --> A - B - C = 2 (even) but A + B + C = 1 (Odd) --> insuff

(2) similarly, just pick up fraction like 2, 1/3, 1 for A, B,C, we got (A-C)/B odd but A+B+C is even.

(1)&(2), just the same approach.

Wondering if there is a better approach?

2010mba · Answer

That's a good question!

GMATxpert · Answer

There are a few key number properties you must know:

Adding two evens or adding two odds results in an even number
Adding an even and an odd results in an odd number

For more info, see this  Number Properties  page that I found.

Number property - even/odd problem

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