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

 It is currently 30 Jun 2015, 21:19

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If a + b+ c are integers, is abc divisible by 4?

 Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
Intern
Joined: 18 Mar 2012
Posts: 48
GMAT 1: 690 Q V
GPA: 3.7
Followers: 0

Kudos [?]: 85 [0], given: 117

If a + b+ c are integers, is abc divisible by 4? [#permalink]  26 Jan 2013, 11:04
3
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

58% (02:53) correct 42% (01:47) wrong based on 165 sessions
If a + b+ c are integers, is abc divisible by 4?

(1) a + b + 2c is even
(2) a + 2b + c is odd
[Reveal] Spoiler: OA
Manager
Joined: 27 Feb 2012
Posts: 138
Followers: 1

Kudos [?]: 32 [0], given: 22

Re: If a + b+ c are integers, is abc divisible by 4? [#permalink]  26 Jan 2013, 12:28
alexpavlos wrote:
If a + b+ c are integers, is abc divisible by 4?

1) a + b + 2c is even
2) a + 2b + c is odd

Can anyone please show me what is the festet and most "elegant" way of solving this? Do you just try each scenario?

Thanks!
Alex

Subtract both of then b - c is odd ....one of b or c is odd and other even
Add 2a + 3b + 3c = odd ....one of b or c is odd and other even
Combine...
Let b = odd
c = even
a = odd
Satisfies both premises and Ans for main statement Yes

Let b = even c = odd a = even
Again satisfies both but Ans for main statement No.

So Ans E
_________________

---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Please +1 KUDO if my post helps. Thank you.

Current Student
Joined: 27 Jun 2012
Posts: 418
Concentration: Strategy, Finance
Followers: 57

Kudos [?]: 470 [0], given: 182

Re: If a + b+ c are integers, is abc divisible by 4? [#permalink]  26 Jan 2013, 13:04
Note that
$$O + E =O$$, $$E + E = E$$, and $$O + O= E$$

To prove whether abc is divisible by 4 when
two of the numbers even (divisible by 2)
One of the numbers is divisible by 4

1) a + b + 2c is even
INSUFFICIENT:
a*b*c not divisible by 4-> Each a, b and c can be ODD (i.e. a*b*c is ODD), but 'a + b + 2c = O+O+2*O=E' will be EVEN.
a*b*c divisible by 4-> If a, b and c are EVEN, 'a + b + 2c' will be even.

2) a + 2b + c is odd
INSUFFICIENT:
a*b*c not divisible by 4-> consider a & b as ODD and c as even (only divisible by 2), 'a + 2b + c' will be ODD and a*b*c will be EVEN, but will be only divisible by 2 (not 4).
a*b*c is EVEN & divisible by 4-> consider a & b as EVEN and c as ODD, 'a + 2b + c' will be ODD, but a*b*c will be divisible by 4.

Combining (1) and (2)
INSUFFIENT: Adding the statements gives 2a + 3b + 3c = ODD, which tells b & c are ODD. However it doesn't tell whether 'a' is even.
If a is even then 2a is divisible by 4. If a is ODD then 2a is NOT divisible by 4.

Hence choice(E) is the answer.
_________________

Thanks,
PraPon

Tough 700+ Level RCs: Passage1 | Passage2 | Passage3 | Passage4 | Passage5 | Passage6 | Passage7
Reading Comprehension notes: Click here
VOTE: vote-best-gmat-practice-tests-excluding-gmatprep-144859.html
PowerScore CR Bible - Official Guide 13 Questions Set Mapped: Click here

Manager
Joined: 24 Sep 2012
Posts: 90
Location: United States
Concentration: Entrepreneurship, International Business
GMAT 1: 730 Q50 V39
GPA: 3.2
WE: Education (Education)
Followers: 4

Kudos [?]: 86 [0], given: 3

Re: If a + b+ c are integers, is abc divisible by 4? [#permalink]  20 Feb 2013, 15:33
The easiest way to solve this problem would require the below knowledge

Odd+Odd=Even
Even+Even=Even
Odd+Even=Odd
Even+Odd=Odd

Now the first question just states that a,b,c are integers. We still do not know whether they are even or odd. To be divisible by 4, one of the below 2 scenarios need to occur

1. Either 2 numbers are even
2. One number is a multiple of 4

Now let's take the given statements one by one

1. This tells us that

a+b+2c is even. Since, 2c is always even irrespective of whether c is even or odd, we have no information about c. However, since 2c is even, we know that a+b also needs to be even for the sum to be even. This gives rise to two scenarios

i. a=even, b=even
ii. a=odd and b= odd

Since, we have no further information to determine which of the two is true, we cannot proceed with this. INSUFFICIENT.

2. This tells us that a+2b+c=odd

Since, we know that 2b is always even irrespective of whether b is even or odd, we have no idea about b. However, since 2b is even and the sum is odd, a+c needs to be odd since only a sum of even and odd adds up to an odd number. This can happen only in two ways

i. a=odd and c=even
ii a=even and c=odd

Since, again we have no further info, we cannot proceed further with these statements. INSUFFICIENT.

Together, we still get the four conclusions that we got from 1 and 2.

i. a=even, b=even
ii. a=odd and b= odd
i. a=odd and c=even
ii a=even and c=odd

However, there is no overlap between these four distinct scenarios. Hence, INSUFFICIENT.

Answer=E

This approach might initially confuse you but the more you practice this approach, the lesser time this will take to solve such problems.

Hope it helps!

alexpavlos wrote:
If a + b+ c are integers, is abc divisible by 4?

1) a + b + 2c is even
2) a + 2b + c is odd

Can anyone please show me what is the festet and most "elegant" way of solving this? Do you just try each scenario?

Thanks!
Alex

_________________

Thanks
Kris
Instructor at Aspire4GMAT

Visit us at http://www.aspire4gmat.com

Post your queries
Join our free GMAT course

New blog: How to get that 700+
New blog: Data Sufficiency Tricks

Press Kudos if this helps!

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 5678
Location: Pune, India
Followers: 1413

Kudos [?]: 7313 [0], given: 186

Re: If a + b+ c are integers, is abc divisible by 4? [#permalink]  20 Feb 2013, 20:39
Expert's post
alexpavlos wrote:
If a + b+ c are integers, is abc divisible by 4?

1) a + b + 2c is even
2) a + 2b + c is odd

Can anyone please show me what is the festet and most "elegant" way of solving this? Do you just try each scenario?

Thanks!
Alex

I am assuming that the question means that a, b and c are integers. This is how I would evaluate the statements:

1) a + b + 2c is even
This means that 'a' and 'b' are either both odd or both even. abc may or may not divisible by 4. Not sufficient.

2) a + 2b + c is odd
This means that one of 'a' and 'c' is odd and the other is even. abc may or may not divisible by 4. Not sufficient.

If 'a' and 'b' both are odd, c must be even. If c is divisible by 4, abc is divisible by 4. Otherwise not. Not sufficient. I needn't even consider the case when 'a' and 'b' are both even.

Answer (E)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews SVP Joined: 06 Sep 2013 Posts: 2046 Concentration: Finance GMAT 1: 770 Q0 V Followers: 26 Kudos [?]: 312 [0], given: 355 Re: If a + b+ c are integers, is abc divisible by 4? [#permalink] 27 Feb 2014, 13:38 Good question +1. (Note: Although I don't know why you put a+b+c are integers, should be a,b,c are integers) Anyways, let's nail 1) a+b+2c is Even This means that a+b must be even So either a,b, are both even or a,b both odd Insufficient 2) a+2b+c is odd So this tells us that either a odd and c even, or the other way around. Still not sufficient 1+2) Both together we have the following a+b Even a+c Odd Add em up: 2a + b+ c is Odd Therefore b+c is odd So either b odd and c even, or the other way around Let's see first case b odd, c even, a odd. Not divisible by 4 b even, c odd, a even. Divisible by 4. Therefore E Hope its clear Cheers J Intern Joined: 05 Jan 2015 Posts: 3 Followers: 0 Kudos [?]: 2 [0], given: 48 Re: If a + b+ c are integers, is abc divisible by 4? [#permalink] 01 Feb 2015, 04:51 Can someone please explain how can "abc" be divisible by 4 when either of the below scenarios occurs? -when two of the numbers are even -when one of the numbers is divisible by 4 I thought a number is divisible by 4 only if the number formed by the last "two digits" is divisible by 4. Am I missing something here? Math Expert Joined: 02 Sep 2009 Posts: 28203 Followers: 4455 Kudos [?]: 44894 [1] , given: 6630 Re: If a + b+ c are integers, is abc divisible by 4? [#permalink] 01 Feb 2015, 05:26 1 This post received KUDOS Expert's post CEZZAR89 wrote: Can someone please explain how can "abc" be divisible by 4 when either of the below scenarios occurs? -when two of the numbers are even -when one of the numbers is divisible by 4 I thought a number is divisible by 4 only if the number formed by the last "two digits" is divisible by 4. Am I missing something here? Does those statements contradict each other? For a number to be divisible by 2 the last digit must be divisible by 2 (so the last digit must be even); For a number to be divisible by 4 the last two digits must be divisible by 4 (04, 08, 12, 16, ..., 96); For a number to be divisible by 8 the last three digits must be divisible by 8 (008, 012, 016, ..., ); etc. If out of two integers, x and y, both are even (x=2m, y=2n), then xy will be a multiple of 4: xy = 2m*2n = 4(mn). For example, 2*6 = 12 = {multiple of 4}. If out of two integers, x and y, one is a multiple of 4 (for example, if x=4m), then xy will be a multiple of 4: xy = 4m*y = 4(my). For example, 4*5 = 20 = {multiple of 4}. _________________ Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 5678 Location: Pune, India Followers: 1413 Kudos [?]: 7313 [1] , given: 186 Re: If a + b+ c are integers, is abc divisible by 4? [#permalink] 01 Feb 2015, 21:44 1 This post received KUDOS Expert's post CEZZAR89 wrote: Can someone please explain how can "abc" be divisible by 4 when either of the below scenarios occurs? -when two of the numbers are even -when one of the numbers is divisible by 4 I thought a number is divisible by 4 only if the number formed by the last "two digits" is divisible by 4. Am I missing something here? a, b and c are not the digits of a three digit number. abc is actually a*b*c where a, b and c are independent numbers. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

Re: If a + b+ c are integers, is abc divisible by 4?   [#permalink] 01 Feb 2015, 21:44
Similar topics Replies Last post
Similar
Topics:
6 If a, b and c are integers, is abc divisible by 4? 7 29 Sep 2013, 18:14
Is a*b*c divisible by 24? (1) a,b, and c are consecutive 3 28 May 2012, 04:06
2 Is a*b*c divisible by 24? (1) a,b, and c are consecutive 9 12 Dec 2010, 19:06
Is a*b*c divisible by 24 ? 1. a, b, and c are consecutive 20 28 Nov 2007, 06:36
Is a*b*c divisible by 32? 9 24 May 2007, 00:48
Display posts from previous: Sort by

If a + b+ c are integers, is abc divisible by 4?

 Question banks Downloads My Bookmarks Reviews Important topics

 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®.