Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 16 Jul 2019, 11:31 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # The expression ab+a is odd when the a and b are integers. Which of the

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 56244
The expression ab+a is odd when the a and b are integers. Which of the  [#permalink]

### Show Tags

1 00:00

Difficulty:   15% (low)

Question Stats: 77% (01:14) correct 23% (01:39) wrong based on 154 sessions

### HideShow timer Statistics The expression ab+a is odd when the a and b are integers. Which of the following expressions must be even?

(A) a
(B) b
(C) a + b
(D) ab - a
(E) a + b^2

_________________
Manager  D
Joined: 12 Mar 2013
Posts: 236
Re: The expression ab+a is odd when the a and b are integers. Which of the  [#permalink]

### Show Tags

Bunuel wrote:
The expression ab+a is odd when the a and b are integers. Which of the following expressions must be even?

(A) a
(B) b
(C) a + b
(D) ab - a
(E) a + b^2

ab+a is odd

a and b are integers

If a were even "ab+a" would be even despite any value of b.

B can't be odd, so "b" must be even.

Ans : B
_________________
We Shall Overcome... One day...
Manager  Joined: 19 Dec 2015
Posts: 110
Location: United States
GMAT 1: 720 Q50 V38 GPA: 3.8
WE: Information Technology (Computer Software)
Re: The expression ab+a is odd when the a and b are integers. Which of the  [#permalink]

### Show Tags

1
Given : ab + a is always odd. the expression can be simplified as :

ab + a = a(b+1) = odd. Only a multiplication of an odd to another odd number will yield an odd. => odd * odd = odd.

Thus, a= odd, and b+1 = odd => b = even. Hence B.
Intern  S
Joined: 29 Jul 2015
Posts: 12
Location: India
Concentration: Marketing, Strategy
WE: Information Technology (Retail Banking)
The expression ab+a is odd when the a and b are integers. Which of the  [#permalink]

### Show Tags

Bunuel wrote:
The expression ab+a is odd when the a and b are integers. Which of the following expressions must be even?

(A) a
(B) b
(C) a + b
(D) ab - a
(E) a + b^2

a b ab a ab+a
e o e e e
o e e o o (2nd line)
e e e e e
o o 0 0 e

Only the 2nd line gives us an odd value so "a" has to be odd and "b" has to be even

Testing all the options with these inputs will give us option B as the answer.
Manager  Joined: 18 May 2016
Posts: 67
GMAT 1: 720 Q49 V39 GPA: 3.7
WE: Analyst (Investment Banking)
Re: The expression ab+a is odd when the a and b are integers. Which of the  [#permalink]

### Show Tags

A very quick solution:

ab + a = a (b + 1)
For the above equation to be odd, both a and (b+1) must be odd
If b+1 must be odd, b must be even

_________________

My debrief: Self-study: How to improve from 620(Q39,V36) to 720(Q49,V39) in 25 days!
CEO  V
Joined: 12 Sep 2015
Posts: 3847
Re: The expression ab+a is odd when the a and b are integers. Which of the  [#permalink]

### Show Tags

Top Contributor
Bunuel wrote:
The expression ab+a is odd when the a and b are integers. Which of the following expressions must be even?

(A) a
(B) b
(C) a + b
(D) ab - a
(E) a + b²

GIVEN: ab+a is odd
Factor to get: a(b+1) is ODD

This means a and b+1 must be ODD, which means b must be EVEN
So, we already know that a is odd and b is even

So, a quick approach will be to take each answer choice and replace a with 1 (odd) and replace b with 0 (even)
We get:

(A) 1 = ODD (ELIMINATE)
(B) 0 = EVEN. keep
(C) 1 + 0 = 1, which is ODD (ELIMINATE)
(D) (1)(0) - 1 = -1, which is ODD (ELIMINATE)
(E) 1 + 0² = 1, which is ODD (ELIMINATE)

Cheers,
Brent
_________________ Re: The expression ab+a is odd when the a and b are integers. Which of the   [#permalink] 15 Feb 2019, 10:48
Display posts from previous: Sort by

# The expression ab+a is odd when the a and b are integers. Which of the  