If a, b, and c are integers and ac + b is odd, is b odd?

Question

(1) ac + ab is even
(2) b + c is odd

Zarrolou · Accepted Answer

If a, b, and c are integers and ac + b is odd, is b odd? 
 ac+b=odd

A) ac + ab is even 
 ac+b+ac+ab=odd+even ,  2ac+b(1+a)=odd . The first term will be even so the second term must be odd in order to obtain even+odd=odd.
 b(1+a)=odd , since an odd number results from odd*odd, both terms must be odd.
Sufficient

B) b + c is odd 
B could be even or odd.
Not sufficient

Bunuel · Answer

If a, b, and c are integers and ac + b is odd, is b odd?

Given that \(ac + b=odd\), determine whether b is odd.

(1) ac + ab is even --> \(ac+ab=even\). Subtract this equation from the equation above: \(b-ab=odd-even=odd\) --> \(b(1-a)=odd\) --> \(b=odd\). Sufficient.

(2) b + c is odd. Clearly insufficient.

Answer: A.

Similar questions to practice:
the-product-of-integers-x-y-and-z-is-even-is-z-even-130140.html
if-m-is-an-integer-is-m-odd-129702.html
if-x-and-y-are-integers-is-xy-even-137508.html
if-x-and-y-are-integers-is-the-value-of-x-y-1-even-149236.html
if-x-y-and-z-are-integers-and-xy-z-is-an-odd-integer-is-81562.html
if-a-and-b-are-integers-is-b-even-99211.html
if-x-is-an-integer-is-x-even-142751.html
is-a-b-c-even-130399.html
is-x-y-z-t-even-133065.html

Hope it helps.

Bluelagoon · Answer

kamaal karte ho tum bunnel yaar, haath main le ke talwar kar rahe ho waar, baar baar

Hope you like the shayari, pun intended

JimGMATAnswers · Answer

A) ac + ab is even
ac+b+ac+ab=odd+even, 2ac+b(1+a)=odd. The first term will be even so the second term must be odd in order to obtain even+odd=odd.
b(1+a)=odd, since an odd number results from odd*odd, both terms must be odd.
Sufficient

B) b + c is odd
B could be even or odd.
Not sufficient

Kinshook · Answer

Given: 
a, b, and c are integers 
ac + b is odd

Asked: Is b odd?

ac + b is odd 
=> b is odd and ac is even 
or b is even and a & c are odd

(1) ac + ab is even
a (c+b) is even => a is even or c+b is even
If a is even => b is odd
If c+b is even => c & b are even Not feasible
or c & b are odd => b is odd
SUFFICIENT

(2) b + c is odd
b is even and c is odd => a is odd 
b is odd and c is even => a may or may not be even
NOT SUFFICIENT

IMO A

bumpbot · Answer

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

If a, b, and c are integers and ac + b is odd, is b odd?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

If a, b, and c are integers and ac + b is odd, is b odd?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards