GMAT Changed on April 16th - Read about the latest changes here

 It is currently 25 May 2018, 07:29

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If a, b and c are integers such that ab + c is an odd integer, is a an

Author Message
TAGS:

Hide Tags

Manager
Joined: 24 May 2016
Posts: 164
If a, b and c are integers such that ab + c is an odd integer, is a an [#permalink]

Show Tags

Updated on: 26 May 2016, 02:24
6
This post was
BOOKMARKED
00:00

Difficulty:

85% (hard)

Question Stats:

41% (01:45) correct 59% (02:42) wrong based on 51 sessions

HideShow timer Statistics

If a, b and c are integers such that ab + c is an odd integer, is a an even integer?

(1) ab + ac is an even integer.
(2) b + ac is an odd integer.

Originally posted by EBITDA on 26 May 2016, 02:19.
Last edited by Bunuel on 26 May 2016, 02:24, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 45422
Re: If a, b and c are integers such that ab + c is an odd integer, is a an [#permalink]

Show Tags

26 May 2016, 02:30
2
KUDOS
Expert's post
If a, b and c are integers such that ab + c is an odd integer, is a an even integer?

Given that $$ab + c=odd$$, determine whether a is even.

(1) ab + ac is an even integer. $$ab+ac=even$$. Subtract this equation from the equation above: $$(ab+ac)-(ab + c)=ac-c=even-odd=odd$$ --> $$c(a-1)=odd$$ --> both multiples must be odd --> $$a-1=odd$$ --> $$a=odd+1=even$$. Sufficient.

(2) b + ac is an odd integer. a=even, b=odd and c=odd OR a=odd, b=odd and c=even. Not sufficient.

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 45422
Re: If a, b and c are integers such that ab + c is an odd integer, is a an [#permalink]

Show Tags

26 May 2016, 02:31
Bunuel wrote:
If a, b and c are integers such that ab + c is an odd integer, is a an even integer?

Given that $$ab + c=odd$$, determine whether a is even.

(1) ab + ac is an even integer. $$ab+ac=even$$. Subtract this equation from the equation above: $$(ab+ac)-(ab + c)=ac-c=even-odd=odd$$ --> $$c(a-1)=odd$$ --> both multiples must be odd --> $$a-1=odd$$ --> $$a=odd+1=even$$. Sufficient.

(2) b + ac is an odd integer. a=even, b=odd and c=odd OR a=odd, b=odd and c=even. Not sufficient.

Similar questions to practice:
if-a-b-and-c-are-integers-and-ac-b-is-odd-is-b-odd-154000.html
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.
_________________
Director
Joined: 29 Jun 2017
Posts: 504
GPA: 4
WE: Engineering (Transportation)
Re: If a, b and c are integers such that ab + c is an odd integer, is a an [#permalink]

Show Tags

31 Aug 2017, 07:59
we know , ab+c=odd
1) ab+ac = even
ab+c +ac -ac
ab+ac + c-ac
even + c-ac
c-ac = odd
c(1-a) = odd
oddxodd=odd
1-a=odd
a = even

so A or D can be the answer

2) Now b+ac =odd
ok
b+ac + ab+c = even { ab+c = odd , odd+odd = even}
b+ab + ac+c = even
b(a+1) +c(a+1) = even
(b+c) (a+1) = even

either b+c = even a+1 = odd so a is even
or a+1 is even so a is odd

_________________

Give Kudos for correct answer and/or if you like the solution.

Re: If a, b and c are integers such that ab + c is an odd integer, is a an   [#permalink] 31 Aug 2017, 07:59
Display posts from previous: Sort by