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If B is an integer, is A even? (1) AB is odd (2) A+B=even

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If B is an integer, is A even? (1) AB is odd (2) A+B=even

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If B is an integer, is A even?

(1) AB is odd
(2) A+B=even

Official answer =A. I have a hard time to answer this question. Could someone please help to resolve?

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GMAT/MBA Expert

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ziyuenlau wrote:
If B is an integer, is A even?

(1) AB is odd
(2) A+B=even

Target question: Is A even?

Given: B is an integer

Statement 1: AB is odd
If the product AB is an odd integer, then there are two possible cases:
Case a: A and B are odd integers. For example, A = 3 and B = 5.
Case b: B is an integer, and A is a FRACTION such that AB is odd. For example, A = 3/2 and B = 2
IMPORTANT: In both cases, A is definitely NOT an EVEN integer.
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Aside: We can also conclude that A is definitely NOT an EVEN integer by recognizing that IF A were an even integer, and B were an integer, then AB would be even. In other words, it would be IMPOSSIBLE for AB to be odd

Statement 2: A + B = even
There are several values of A and B that satisfy statement 2. Here are two:
Case a: A = 2 and B = 2, in which case A is EVEN
Case b: A = 1 and B = 1, in which case A is ODD
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent

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Hi ziyuenlau,

As Brent has shown, this question can be solved by TESTing VALUES. His examples are spot-on, so I won't rehash any of that math here. Instead, I want to focus on the 'design element' of DS questions - and how you have to pay careful attention to what you are told AND what you are NOT told.

In this prompt, we're told that B is an integer - so from the start that means that it could be a positive integer, a negative integer or 0. The question asks us if A is even. This is a YES/NO question, BUT we know NOTHING about A (maybe it's an integer, maybe it's a fraction, could be positive/negative/0). When there are no 'restrictions' on what a variable can be, it's often helpful to write on your pad: "A = ANYTHING." In this way, as you work through the question you'll have a constant reminder that you don't know anything about A yet - so from the start you can't assume that A is a integer. Your ability to consider all of the possibilities in DS is essential to scoring at a high level on the GMAT.

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

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ziyuenlau wrote:
If B is an integer, is A even?

(1) AB is odd
(2) A+B=even

Official answer =A. I have a hard time to answer this question. Could someone please help to resolve?
Hi ziyuenlau,

The following results involving mathematical operations between EVEN and ODD numbers must be known to you.

1. Addition and Subtraction:

a. EVEN +/- EVEN = EVEN
b. ODD +/- ODD = EVEN

So, if the Addition or Subtraction of two numbers is EVEN, you cannot conclude whether they are EVEN or ODD. They both are either EVEN or ODD.

c. EVEN + ODD = ODD

So, if the Addition or Subtraction of two numbers is ODD, you can conclude that one of them is EVEN and the other is ODD.

2. Multiplication:

a. EVEN * EVEN = EVEN
b. ODD * ODD = ODD
c. EVEN * ODD = EVEN

So, if the product of two numbers is EVEN, you cannot conclude that both the numbers are EVEN. You can conclude that AT LEAST one of the numbers is EVEN; however, if the product of two numbers is ODD, you can conclude that both the numbers are ODD.

3. Division:

a. EVEN / EVEN = EVEN or ODD; if divisible
b. ODD / ODD = ODD; if divisible
c. EVEN / ODD = EVEN; if divisible

So, if the division of two numbers is an ODD number with no remainder, you can conclude that both the numbers are either EVEN or ODD.

Hope this helps!

Relevant book: Manhattan Review GMAT Math Essentials Guide

-Jay
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GMAT/MBA Expert

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ziyuenlau wrote:
If B is an integer, is A even?

(1) AB is odd
(2) A+B=even
We need to determine whether the positive integer A is even. We must recall that the product of an even integer and any other integer is always even. Thus, if either A or B (or both) is even, then so is AB.

Statement One Alone:

AB is odd.

In order for the product of two integers to be odd, both integers must be odd. Thus, both A and B are odd. Since A is odd, A is not even. Statement one alone is sufficient to answer the question.

Statement Two Alone:

A+B=even

In order for the sum of two integers to be even, they have to be either both even or both odd. If they are both even, then A is even. However, if they are both odd, then A is not even. Statement two alone is not sufficient to answer the question.

Answer: A

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