Find all School-related info fast with the new School-Specific MBA Forum

It is currently 02 Jul 2015, 15:59

Close

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
Your Progress

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If a, b, and c are all integers, is ab+bc+ca

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
avatar
Status: Trying.... & desperate for success.
Joined: 17 May 2012
Posts: 78
Location: India
Concentration: Leadership, Entrepreneurship
Schools: NUS '15
GMAT 1: Q33 V27
GPA: 2.92
WE: Analyst (Computer Software)
Followers: 0

Kudos [?]: 36 [0], given: 61

If a, b, and c are all integers, is ab+bc+ca [#permalink] New post 16 Sep 2012, 00:12
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

38% (02:10) correct 62% (01:19) wrong based on 125 sessions
If a, b, and c are all integers, is ab+bc+ca+(a*a) odd?

(1) a is odd.
(2) (b+c) is odd.



- From HULT free tests
[Reveal] Spoiler: OA
1 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 15 Jun 2010
Posts: 363
Schools: IE'14, ISB'14, Kellogg'15
WE 1: 7 Yrs in Automobile (Commercial Vehicle industry)
Followers: 10

Kudos [?]: 213 [1] , given: 50

Reviews Badge
Re: If a, b, and c are all integers, is ab+bc+ca [#permalink] New post 16 Sep 2012, 01:01
1
This post received
KUDOS
navigator123 wrote:
If a, b, and c are all integers, is ab+bc+ca+(a*a) odd?

(1) a is odd.
(2) (b+c) is odd.
- From HULT free tests


From Question stem : a^2+ab+ac+bc
=(a+c)(a+b). product of 2 numbers.
St1: Insufficient: Let say a is odd, c even & b even, so (a+b) =odd & (a+b)=odd , So (a+b)(a+c) = odd, which gives YES
Let say a is odd, c odd & b even, So (a+b)= odd & (a+c)=even, So (a+b)(a+c)= even, which gives NO.

St 2: Sufficient: if b+c = odd, any one of b & c should be even and another odd. so a can be either odd or even. Let say b=O & C=E and A=O
(a+b)=E, (a+c) = E, hence (a+b)(a+c)= E, which gives NO
Now Let say b=O & C=E and A=E, (a+b)=O, (a+c)=E, Hence (a+b)(a+c)= E, which gives NO
So any one of the factors (a+b) or (a+c) will be either E or O which will always give an Even number.
_________________

Regards
SD
-----------------------------
Press Kudos if you like my post.
Debrief 610-540-580-710(Long Journey): from-600-540-580-710-finally-achieved-in-4th-attempt-142456.html

1 KUDOS received
Intern
Intern
avatar
Joined: 04 Aug 2013
Posts: 5
Followers: 0

Kudos [?]: 2 [1] , given: 1

If a, b, and c are all integers, is ab+bc+ca+a2 odd? [#permalink] New post 19 Feb 2014, 16:05
1
This post received
KUDOS
If a, b, and c are all integers, is ab+bc+ca+a2 odd?

(1) a is odd.
(2) (b+c) is odd.
Expert Post
1 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 5682
Location: Pune, India
Followers: 1413

Kudos [?]: 7328 [1] , given: 186

Re: If a, b, and c are all integers, is ab+bc+ca+a2 odd? [#permalink] New post 19 Feb 2014, 21:59
1
This post received
KUDOS
Expert's post
mhknair wrote:
If a, b, and c are all integers, is ab+bc+ca+a2 odd?

(1) a is odd.
(2) (b+c) is odd.


Looking at the statements, I would try to club b and c together.

Given Expression: a(b+c) + a^2 + bc
There are 3 terms: a(b+c), a^2, bc

(1) a is odd.
a^2 is certainly odd. But we don't know anything about the other two terms.
Say b and c are both even. Then 2 terms (a(b+c) and bc) are even and one (a^2) is odd so sum is odd.
Say b and c are both odd. Then 2 terms (a^2 and bc) are odd and one (a(b+c)) is even so sum is even.
Not sufficient.

(2) (b+c) is odd.
If b+c is odd, it means one of b and c is odd and the other is even. So bc will be even
Now if a is odd, two terms are odd (a(b+c) and a^2) while the third term (bc) is even. So sum will be even.
If a is even, all three terms are even so sum will be even.
In any case, the sum will be even so this statement alone is sufficient.

Answer (B)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Intern
Intern
avatar
Joined: 19 Feb 2014
Posts: 18
Concentration: Finance
GRE 1: 1580 Q800 V780
WE: Securities Sales and Trading (Investment Banking)
Followers: 1

Kudos [?]: 5 [0], given: 1

Re: If a, b, and c are all integers, is ab+bc+ca+a2 odd? [#permalink] New post 20 Feb 2014, 00:18
mhknair wrote:
If a, b, and c are all integers, is ab+bc+ca+a2 odd?

(1) a is odd.
(2) (b+c) is odd.


Simpler: Regroup to get \((ab + ac) + bc + a^2\). Since a is odd, we know \(\underbrace{ab + ac}_{odd} + bc + \underbrace{a^2}_{odd}\). Next, since b+c is odd we know either b or c is odd and the other is even -- so bc must be even. Odd + even + odd is even.

Alternatively: Regroup to get \((a^2 + ab + ac) + bc\). Since a and (b+c) are odd, we know \(a+b+c\) is even and \(\underbrace{a(a+b+c)}_{even} + bc\). Next, since b+c is odd we know b or c is odd and the other is even -- so bc must be even. Even + even is even.
Intern
Intern
avatar
Joined: 27 Mar 2013
Posts: 28
Followers: 0

Kudos [?]: 47 [0], given: 33

If a, b, and c are all integers, is ab+bc+ca+a2 odd? [#permalink] New post 26 Sep 2014, 04:15
If a, b, and c are all integers, is ab+bc+ca+a2 odd?

(1) a is odd.

(2) (b+c) is odd.
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 28252
Followers: 4464

Kudos [?]: 45049 [0], given: 6640

Re: If a, b, and c are all integers, is ab+bc+ca [#permalink] New post 26 Sep 2014, 05:38
Expert's post
Re: If a, b, and c are all integers, is ab+bc+ca   [#permalink] 26 Sep 2014, 05:38
    Similar topics Author Replies Last post
Similar
Topics:
4 Experts publish their posts in the topic The numbers a, b, and c are all non-zero integers. Is a > 0? Bunuel 6 02 Mar 2015, 07:15
5 Experts publish their posts in the topic If a, b and c are all positive integers, is abc an even number? ezinis 5 30 Dec 2010, 20:34
If a,b,c,d and x are all non zero integers, is the product mohansb 3 11 Oct 2007, 22:56
Positive integers a, b and c are all less than 10. If the kevincan 5 24 Jul 2006, 06:44
Positive integers a, b and c are all less than 10. If the kevincan 4 24 Jul 2006, 05:18
Display posts from previous: Sort by

If a, b, and c are all integers, is ab+bc+ca

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.