Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

It is currently 22 May 2017, 09:23

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

1 KUDOS received
Manager
Manager
avatar
Status: Trying.... & desperate for success.
Joined: 17 May 2012
Posts: 78
Location: India
Concentration: Leadership, Entrepreneurship
Schools: NUS '15
GPA: 2.92
WE: Analyst (Computer Software)
Followers: 0

Kudos [?]: 88 [1] , given: 61

If a, b, and c are all integers, is ab+bc+ca [#permalink]

Show Tags

New post 16 Sep 2012, 01:12
1
This post received
KUDOS
7
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

40% (02:12) correct 60% (01:13) wrong based on 326 sessions

HideShow timer Statistics

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: 361
Schools: IE'14, ISB'14, Kellogg'15
WE 1: 7 Yrs in Automobile (Commercial Vehicle industry)
Followers: 11

Kudos [?]: 398 [1] , given: 50

Reviews Badge
Re: If a, b, and c are all integers, is ab+bc+ca [#permalink]

Show Tags

New post 16 Sep 2012, 02:01
1
This post received
KUDOS
2
This post was
BOOKMARKED
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): http://gmatclub.com/forum/from-600-540-580-710-finally-achieved-in-4th-attempt-142456.html

1 KUDOS received
Intern
Intern
avatar
Joined: 04 Aug 2013
Posts: 4
Followers: 0

Kudos [?]: 7 [1] , given: 1

If a, b, and c are all integers, is ab+bc+ca+a2 odd? [#permalink]

Show Tags

New post 19 Feb 2014, 17:05
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
3 KUDOS received
Veritas Prep GMAT Instructor
User avatar
S
Joined: 16 Oct 2010
Posts: 7368
Location: Pune, India
Followers: 2281

Kudos [?]: 15068 [3] , given: 224

Re: If a, b, and c are all integers, is ab+bc+ca+a2 odd? [#permalink]

Show Tags

New post 19 Feb 2014, 22:59
3
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 [?]: 8 [0], given: 1

Re: If a, b, and c are all integers, is ab+bc+ca+a2 odd? [#permalink]

Show Tags

New post 20 Feb 2014, 01:18
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.
Verbal Forum Moderator
Verbal Forum Moderator
User avatar
Joined: 29 Apr 2015
Posts: 896
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
Followers: 56

Kudos [?]: 1424 [0], given: 302

GMAT ToolKit User Premium Member
Re: If a, b, and c are all integers, is ab+bc+ca [#permalink]

Show Tags

New post 11 Aug 2015, 14:32
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


I doubt that this is a 700+, is it? I had this as the 2nd question on a GMAT Scholarship Competition Exam.
_________________

Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!

PS Please send me PM if I do not respond to your question within 24 hours.

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 15374
Followers: 648

Kudos [?]: 204 [0], given: 0

Premium Member
Re: If a, b, and c are all integers, is ab+bc+ca [#permalink]

Show Tags

New post 21 Sep 2016, 01:20
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Intern
Intern
avatar
Joined: 18 Apr 2013
Posts: 6
Followers: 0

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

If a, b, and c are all integers, is ab+bc+ca+a^2 odd? [#permalink]

Show Tags

New post 14 Jan 2017, 06:49
If a, b, and c are all integers, is \(ab+bc+ca+a^2\) odd?

(1) a is odd.

(2) (b+c) is odd.
Math Forum Moderator
User avatar
G
Joined: 13 Apr 2015
Posts: 1446
Location: India
Concentration: Strategy, General Management
WE: Information Technology (Consulting)
Followers: 43

Kudos [?]: 766 [0], given: 728

GMAT ToolKit User Premium Member CAT Tests
Re: If a, b, and c are all integers, is ab+bc+ca+a^2 odd? [#permalink]

Show Tags

New post 14 Jan 2017, 07:50
Is \(ab+bc+ca+a^2\) odd
= a(b + c) + bc + a^2
= a(b + c + a) + bc

St1: a is odd. --> No info about b and c.
Clearly insufficient.

St2: (b+c) is odd. --> Possible when one value is odd and the other value is even.
Hence if b + c is odd then b *c is even.

Consider a(b + c + a) + bc --> If a is even then the expression is Even + Even = Even.
If a is odd then the expression is --> Odd*(Odd + Odd) + Even = Even + Even = Even.
Thus, \(ab+bc+ca+a^2\) is always even.
Sufficient.

Answer: B
SVP
SVP
User avatar
B
Joined: 05 Jul 2006
Posts: 1747
Followers: 6

Kudos [?]: 357 [0], given: 49

GMAT ToolKit User
Re: If a, b, and c are all integers, is ab+bc+ca+a^2 odd? [#permalink]

Show Tags

New post 14 Jan 2017, 07:54
roastedchips wrote:
If a, b, and c are all integers, is \(ab+bc+ca+a^2\) odd?

(1) a is odd.

(2) (b+c) is odd.


STEM

a(b+c+a) + bc = ??

from 1

clearly insuff

from 2

b+c = odd thus one of them is even and the other is odd

now in a(b+c+a) , we know b+c = odd thus if a is odd the b+c+a = even and thus a(b+c+a) is even too and if a is even then a(a+b+c) is even too , i,e, in all cases it is even
bc = even ( since b+c = odd) thus a(b+c+a) +bc is always even and the answer to the question is definite no

B
Expert Post
Math Expert
User avatar
P
Joined: 02 Sep 2009
Posts: 38796
Followers: 7712

Kudos [?]: 105735 [0], given: 11578

Re: If a, b, and c are all integers, is ab+bc+ca [#permalink]

Show Tags

New post 14 Jan 2017, 08:48
Director
Director
avatar
G
Joined: 26 Mar 2013
Posts: 943
Followers: 7

Kudos [?]: 200 [0], given: 122

Premium Member Reviews Badge CAT Tests
Re: If a, b, and c are all integers, is ab+bc+ca [#permalink]

Show Tags

New post 15 Jan 2017, 06:21
If a, b, and c are all integers, is ab+bc+ca+(a*a) odd?

(1) a is odd.

Clearly Insufficient. We do not know any info about other terms. It could Even or Odd.

(2) (b+c) is odd.

Re-arrange the question:

ab+ac+bc+a^2 = a (b+c)+ bc+a^2

when (b+c) = odd.......it means one is even and other is odd........So 'bc' is always Even

Let examine the question: a (b+c)+ bc+a^2

Let a =Odd........................O*O+E+O= O+E+0= EVEN

Let a =Even.......................E *O+E+E=E+E+E=EVEN

In both cases the answer to question is NO

Sufficient

Answer: B
Top Contributor
VP
VP
User avatar
G
Joined: 12 Sep 2015
Posts: 1422
Location: Canada
Followers: 136

Kudos [?]: 1595 [0], given: 327

Re: If a, b, and c are all integers, is ab+bc+ca [#permalink]

Show Tags

New post 05 Apr 2017, 08:21
Top Contributor
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.



Target question: Is ab + bc + ca + a² odd?
This is a good candidate for rephrasing the target question.
ab + bc + ca + a² = b(a + c) + a(c + a)
= (b + a)(c + a)
So, we get....
REPHRASED target question: Is (b+a)(c+a) odd?

When I SCAN the two statements, I see that it might be useful to systematically list the possible outcomes. To do this, I'll list each possible case, and plug in 0 for any EVEN integer and plug in 1 for any ODD integer. We get:
case a: a = odd, b = odd, c = odd. Here, (b+a)(c+a) = EVEN
case b: a = odd, b = odd, c = even. Here, (b+a)(c+a) = EVEN
case c: a = odd, b = even, c = odd. Here, (b+a)(c+a) = EVEN
case d: a = odd, b = even, c = even. Here, (b+a)(c+a) = ODD
case e: a = even, b = odd, c = odd. Here, (b+a)(c+a) = ODD
case f: a = even, b = even, c = odd. Here, (b+a)(c+a) = EVEN
case g: a = even, b = odd, c = even. Here, (b+a)(c+a) = EVEN
case h: a = even, b = even, c = even. Here, (b+a)(c+a) = EVEN

Statement 1: a is odd
This means we're dealing with case a, b, c, or d
For cases a, b and c, (b+a)(c+a) is EVEN
For case d, (b+a)(c+a) is ODD
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT


Statement 2: (b+c) is odd
This means we're dealing with case b, c, f or g
In ALL of these cases, (b+a)(c+a) is EVEN
This means we can be certain that (b+a)(c+a) is EVEN
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

Answer:
[Reveal] Spoiler:
B


RELATED VIDEOS



_________________

Brent Hanneson – Founder of gmatprepnow.com

Image

Re: If a, b, and c are all integers, is ab+bc+ca   [#permalink] 05 Apr 2017, 08:21
    Similar topics Author Replies Last post
Similar
Topics:
2 Are A, B, and C consecutive integers? C-B = A-B A, B, and C are all i hazelnut 5 28 Apr 2017, 18:45
4 Experts publish their posts in the topic Is √abcd an integer, where a,b,c,d are all prime numbers? rajarshee 8 06 Nov 2015, 04:08
7 Experts publish their posts in the topic The numbers a, b, and c are all non-zero integers. Is a > 0? Bunuel 11 30 Dec 2016, 06:15
6 Experts publish their posts in the topic The numbers a, b, and c are all non-zero integers. Is a > 0? Bunuel 7 26 Jul 2016, 01:40
5 Experts publish their posts in the topic If a, b and c are all positive integers, is abc an even number? ezinis 5 20 Apr 2015, 19:17
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| 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®.