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

 It is currently 24 Apr 2018, 03:22

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 all integers, is ab + bc + ca + a^2 odd?

Author Message
TAGS:

Hide Tags

Manager
Status: Trying.... & desperate for success.
Joined: 17 May 2012
Posts: 70
Location: India
Schools: NUS '15
GPA: 2.92
WE: Analyst (Computer Software)
If a, b, and c are all integers, is ab + bc + ca + a^2 odd? [#permalink]

Show Tags

16 Sep 2012, 01:12
1
KUDOS
11
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

48% (01:01) correct 52% (01:15) wrong based on 340 sessions

HideShow timer Statistics

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

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

- From HULT free tests
[Reveal] Spoiler: OA
Senior Manager
Joined: 15 Jun 2010
Posts: 343
Schools: IE'14, ISB'14, Kellogg'15
WE 1: 7 Yrs in Automobile (Commercial Vehicle industry)
Re: If a, b, and c are all integers, is ab + bc + ca + a^2 odd? [#permalink]

Show Tags

16 Sep 2012, 02:01
1
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

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8031
Location: Pune, India
Re: If a, b, and c are all integers, is ab + bc + ca + a^2 odd? [#permalink]

Show Tags

19 Feb 2014, 22:59
4
KUDOS
Expert's post
1
This post was
BOOKMARKED
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.

_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Intern Joined: 19 Feb 2014 Posts: 18 Concentration: Finance GRE 1: 1580 Q800 V780 WE: Securities Sales and Trading (Investment Banking) Re: If a, b, and c are all integers, is ab + bc + ca + a^2 odd? [#permalink] Show Tags 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. Retired Moderator Joined: 29 Apr 2015 Posts: 874 Location: Switzerland Concentration: Economics, Finance Schools: LBS MIF '19 WE: Asset Management (Investment Banking) Re: If a, b, and c are all integers, is ab + bc + ca + a^2 odd? [#permalink] Show Tags 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. SC Moderator Joined: 13 Apr 2015 Posts: 1618 Location: India Concentration: Strategy, General Management WE: Analyst (Retail) Re: If a, b, and c are all integers, is ab + bc + ca + a^2 odd? [#permalink] Show Tags 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 Retired Moderator Joined: 05 Jul 2006 Posts: 1737 Re: If a, b, and c are all integers, is ab + bc + ca + a^2 odd? [#permalink] Show Tags 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 SVP Joined: 26 Mar 2013 Posts: 1613 Re: If a, b, and c are all integers, is ab + bc + ca + a^2 odd? [#permalink] Show Tags 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 SVP Joined: 12 Sep 2015 Posts: 2308 Location: Canada Re: If a, b, and c are all integers, is ab + bc + ca + a^2 odd? [#permalink] Show Tags 05 Apr 2017, 08:21 Expert's post 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 EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 11507 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Re: If a, b, and c are all integers, is ab + bc + ca + a^2 odd? [#permalink] Show Tags 21 Dec 2017, 12:11 Hi All, This question can be solved by TESTing VALUES. By extension, if you recognize the Number Properties involved, then you'll only have to TEST 'odds' vs. 'evens' (and NOT have to work through multiple iterations of each option). We're told that A, B and C are all INTEGERS. We're asked if (A)(B) + (B)(C) + (C)(A) + A^2 is ODD. This is a YES/NO question. 1) A is ODD With this Fact, we have to consider whether B and C are odds, evens or a mix of the two... IF... A = 1, then we have.... (1)(B) + (B)(C) + (C)(1) + (1)^2 IF... B=0 and C=0.... (1)(0) + (0)(0) + (0)(1) + (1)^2 = 1 and the answer to the question is YES. IF... B=1 and C=1.... (1)(1) + (1)(1) + (1)(1) + (1)^2 = 4 and the answer to the question is NO. Fact 1 is INSUFFICIENT 2) (B+C) is ODD With this Fact, we know that ONE of these two variables is ODD and the other is EVEN. The "A" can be odd or even... IF... B=0 and C=1, then we have.... (A)(0) + (0)(1) + (1)(A) + (A)^2 IF.... A=0.... (0)(0) + (0)(1) + (1)(0) + (0)^2 = 0 and the answer to the question is NO. IF.... A=1.... (1)(0) + (0)(1) + (1)(1) + (1)^2 = 2 and the answer to the question is NO. IF... B=1 and C=0, then we have.... (A)(1) + (1)(0) + (0)(A) + (A)^2 IF.... A=0.... (0)(1) + (1)(0) + (0)(1) + (0)^2 = 0 and the answer to the question is NO. IF.... A=1.... (1)(1) + (1)(0) + (0)(1) + (1)^2 = 2 and the answer to the question is NO. The answer to the question is ALWAYS NO. Fact 2 is SUFFICIENT Final Answer: [Reveal] Spoiler: B GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Re: If a, b, and c are all integers, is ab + bc + ca + a^2 odd?   [#permalink] 21 Dec 2017, 12:11
Display posts from previous: Sort by

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

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne 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®.