BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

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

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Data Sufficiency |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Tue Mar 14, 2017 7:42 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Tue Mar 14, 2017 10:35 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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
Contact Rich at [email protected]
Image
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3008
Joined: Mon Aug 22, 2016 6:19 am
Location: Grand Central / New York
Thanked: 470 times
Followed by:34 members

by Jay@ManhattanReview » Wed Mar 15, 2017 12:13 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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
_________________
Manhattan Review GMAT Prep

Locations: New York | New Delhi | Seoul | Cairo | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
Top
User avatar
GMAT Instructor
Posts: 1462
Joined: Thu Apr 09, 2015 9:34 am
Location: New York, NY
Thanked: 39 times
Followed by:22 members

by Jeff@TargetTestPrep » Thu Mar 16, 2017 12:19 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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

Jeffrey Miller
Head of GMAT Instruction
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
Top
Post new topic Post Reply
• Page 1 of 1