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

It is currently 23 Oct 2014, 12:37

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

Is a*b*c divisible by 24? (1) a,b, and c are consecutive

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
avatar
Joined: 18 Jul 2010
Posts: 21
Schools: Northwestern, Booth, Duke, Berkley, Stanford, Harvard, IMD, IESE,
WE 1: Business Development with top IT Outsourcing and Consulting firm (Fortune 10 Company)
Followers: 1

Kudos [?]: 3 [0], given: 8

Is a*b*c divisible by 24? (1) a,b, and c are consecutive [#permalink] New post 12 Dec 2010, 19:06
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

70% (01:53) correct 30% (01:16) wrong based on 47 sessions
Is a*b*c divisible by 24?

(1) a, b, and c are consecutive even integers
(2) a*b is divisible by 12

Please provide your thoughts on this one. The question comes from one of the GMAT Club Tests on Number Props.

[Reveal] Spoiler:
Here's the answer from the GMAT Club Test:

Statement (1) by itself is sufficient. One of any three consecutive even integers is divisible by 3. Because this integer is even, it is also divisible by 6. When multiplied by two more even integers, it renders a product that is divisible by 24.

Statement (2) by itself is insufficient. We need to know something about c.

Correct me if I'm wrong, but I thought Zero is not divisible 24? If either a, b, or c is zero, then a*b*c= 0, which is not divisible
[Reveal] Spoiler: OA
Kaplan Promo CodeKnewton GMAT Discount CodesManhattan GMAT Discount Codes
Manager
Manager
User avatar
Status: Fighting the beast.
Joined: 25 Oct 2010
Posts: 182
Schools: Pitt, Oregon, LBS...
Followers: 28

Kudos [?]: 263 [0], given: 36

Re: Data Suff - Number Property... [#permalink] New post 12 Dec 2010, 20:00
tarn151 wrote:
Please provide your thoughts on this one. The question comes from one of the GMAT Club Tests on Number Props.

Is a*b*c divisible by 24?

1) a,b, and c are consecutive even integers
2) a*b is divisible by 12

[Reveal] Spoiler:
Here's the answer from the GMAT Club Test:

Statement (1) by itself is sufficient. One of any three consecutive even integers is divisible by 3. Because this integer is even, it is also divisible by 6. When multiplied by two more even integers, it renders a product that is divisible by 24.

Statement (2) by itself is insufficient. We need to know something about c.

Correct me if I'm wrong, but I thought Zero is not divisible 24? If either a, b, or c is zero, then a*b*c= 0, which is not divisible



The answer is A. Why?

First, you need to factor out the number 24. 24 is composed of 4*6 or 2*2*2*3. So, in order for a*b*c to be divisible by 24, it must contain at least 3 2's and a 3 as its factors.

1) a, b and c are consecutive positive integers. This means two things: a, b and c have at least 3 2's, because they are all even, and one of them must be divisible by 3. Product of any 3 consecutive integers will be divisible by 3. Try it: 1,2,3 are divisible by 3. 4,5,6 are divisible by 3. 8,10,12 are divisible by 3. In addition, it is good to know that any set of 3 consecutive integers will be divisible by 3 or 3! Also, set of 8 consecutive integers will be divisible by 8! Any set of n consecutive integers will be divisible by n!
So, since a, b, and c contain at least 2*2*2*3, it must be divisible by 24.

2) If ab is divisible by 12, we know nothing about c. If c is 1, a*b*c is not divisible by 24. If c is 2, it is. So the answer is: maybe. Not sufficient.

Finals answer: A.

Hope this helps, friend.
_________________

[highlight]Monster collection of Verbal questions (RC, CR, and SC)[/highlight]
massive-collection-of-verbal-questions-sc-rc-and-cr-106195.html#p832142

[highlight]Massive collection of thousands of Data Sufficiency and Problem Solving questions and answers:[/highlight]
1001-ds-questions-file-106193.html#p832133

Expert Post
2 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23398
Followers: 3611

Kudos [?]: 28839 [2] , given: 2854

Re: Data Suff - Number Property... [#permalink] New post 13 Dec 2010, 01:09
2
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
tarn151 wrote:
Please provide your thoughts on this one. The question comes from one of the GMAT Club Tests on Number Props.

Is a*b*c divisible by 24?

1) a,b, and c are consecutive even integers
2) a*b is divisible by 12

[Reveal] Spoiler:
Here's the answer from the GMAT Club Test:

Statement (1) by itself is sufficient. One of any three consecutive even integers is divisible by 3. Because this integer is even, it is also divisible by 6. When multiplied by two more even integers, it renders a product that is divisible by 24.

Statement (2) by itself is insufficient. We need to know something about c.

Correct me if I'm wrong, but I thought Zero is not divisible 24? If either a, b, or c is zero, then a*b*c= 0, which is not divisible



Note that an integer a is a multiple of an integer b (integer a is a divisible by an integer b) means that \frac{a}{b}=integer: so, as 0 divided by any integer (except zero itself) yields an integer then yes, zero is a multiple of every integer (except zero itself).

Also on GMAT when we are told that a is divisible by b (or which is the same: "a is multiple of b", or "b is a factor of a"), we can say that:
1. a is an integer;
2. b is an integer;
3. \frac{a}{b}=integer.

BACK TO THE ORIGINAL QUESTION:
Is a*b*c divisible by 24?

(1) a, b, and c are consecutive even integers --> a=2k-2, b=2k and c=2k+2 for some integer k --> abc=(2k-2)2k(2k+2)=8(k-1)k(k+1), now (k-1), k, (k+1) are 3 consecutive integers, which means that one of them must be a multiple of 3, thus abc is divisible by both 8 and 3, so by 24. Sufficient.

Or even without the formulas: th product of 3 consecutive even integers will have 2*2*2=8 as a factor, plus out of 3 consecutive even integers one must be a multiple of 3, thus abc is divisible by both 8 and 3, so by 24.

(2) a*b is divisible by 12, clearly insufficient as no info about c (if ab=12 and c=1 answer will be NO but if ab=24 and c=any integer then the answer will be YES).

Answer: A.

Hope it's clear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Senior Manager
Senior Manager
User avatar
Status: Bring the Rain
Joined: 17 Aug 2010
Posts: 408
Location: United States (MD)
Concentration: Strategy, Marketing
Schools: Michigan (Ross) - Class of 2014
GMAT 1: 730 Q49 V39
GPA: 3.13
WE: Corporate Finance (Aerospace and Defense)
Followers: 7

Kudos [?]: 43 [0], given: 46

Re: Data Suff - Number Property... [#permalink] New post 13 Dec 2010, 05:19
Thanks for the explanation.
_________________

Go Blue!

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Expert Post
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4877
Location: Pune, India
Followers: 1154

Kudos [?]: 5369 [0], given: 165

Re: Data Suff - Number Property... [#permalink] New post 13 Dec 2010, 21:39
Expert's post
tarn151 wrote:
Please provide your thoughts on this one. The question comes from one of the GMAT Club Tests on Number Props.

Is a*b*c divisible by 24?

1) a,b, and c are consecutive even integers
2) a*b is divisible by 12

[Reveal] Spoiler:
Here's the answer from the GMAT Club Test:

Statement (1) by itself is sufficient. One of any three consecutive even integers is divisible by 3. Because this integer is even, it is also divisible by 6. When multiplied by two more even integers, it renders a product that is divisible by 24.

Statement (2) by itself is insufficient. We need to know something about c.

Correct me if I'm wrong, but I thought Zero is not divisible 24? If either a, b, or c is zero, then a*b*c= 0, which is not divisible


The product of two consecutive integers will be divisible by 2. e.g. 3*4 or 1*2 or (-5)(-4) etc because one of the numbers will always be even.

The product of 3 consecutive integers will be divisible by 3 because there will be a multiple of 3 in 3 consecutive numbers e.g. 2*3*4 or 7*8*9 etc

The product of 4 consecutive integers will be divisible by 4 because there will be a multiple of 4 in 4 consecutive numbers e.g. 1*2*3*4 or 8*9*10*11 etc

and so on....

Stmnt 1: a,b, and c are consecutive even integers

Since a, b and c are even, each one of them has a 2 to give us an 8. Also, if we take their 2s out, we are left with 3 consecutive integers which will definitely have a multiple of 3 e.g. 6*8*10 gives us 2*2*2*(3*4*5).
Hence 3 consecutive even integers' product is divisible by 8 and by 3. Hence it is divisible by 24. Sufficient.

Stmnt 2: a*b is divisible by 12
Remember, this statement does not give any relation between a, b and c. Do not assume here that they are still even consecutive integers. If a*b is divisible by 12, it doesn't say anything about c. Also, we don't know if a*b is itself divisible by 24. Hence not sufficient.

Answer (A).
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Intern
Intern
avatar
Joined: 09 May 2011
Posts: 4
Followers: 0

Kudos [?]: 0 [0], given: 8

Re: Data Suff - Number Property... [#permalink] New post 15 Jul 2011, 03:06
Cant the three numbers be
a = -2, b= 0, c = 2.
The question does not say the numbers have to be positive?
Intern
Intern
avatar
Joined: 09 May 2011
Posts: 4
Followers: 0

Kudos [?]: 0 [0], given: 8

Re: Data Suff - Number Property... [#permalink] New post 15 Jul 2011, 03:14
Cant the three numbers be
a = -2, b= 0, c = 2.
The question does not say the numbers have to be positive or non-zero.
GMAT Instructor
avatar
Joined: 24 Jun 2008
Posts: 978
Location: Toronto
Followers: 261

Kudos [?]: 709 [0], given: 3

Re: Data Suff - Number Property... [#permalink] New post 15 Jul 2011, 09:22
eshabhide wrote:
Cant the three numbers be
a = -2, b= 0, c = 2.
The question does not say the numbers have to be positive or non-zero.


Yes, they could be, but that doesn't change the answer here. Zero is divisible by every positive integer.
_________________

Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.

Private GMAT Tutor based in Toronto

Manager
Manager
User avatar
Joined: 20 Jul 2011
Posts: 152
GMAT Date: 10-21-2011
Followers: 0

Kudos [?]: 36 [0], given: 15

Re: Data Suff - Number Property... [#permalink] New post 04 Sep 2011, 22:32
Quote:
Please provide your thoughts on this one. The question comes from one of the GMAT Club Tests on Number Props.

Is a*b*c divisible by 24?

1) a,b, and c are consecutive even integers
2) a*b is divisible by 12

[Reveal] Spoiler:
[Reveal] Spoiler: OA


From statement 1
Prime factors of 24: 2,2,2,3
Consecutive even integers that results in 24 when multiplied together: 2, 4, 6
--> sufficient

From statement 2
a*b is a multiple of 12
a*b can be: 12, 24, 36, 48, etc...
--> insufficient

Answer: A
_________________

"The best day of your life is the one on which you decide your life is your own. No apologies or excuses. No one to lean on, rely on, or blame. The gift is yours - it is an amazing journey - and you alone are responsible for the quality of it. This is the day your life really begins." - Bob Moawab


Last edited by gmatopoeia on 05 Sep 2011, 23:24, edited 1 time in total.
Manager
Manager
User avatar
Joined: 13 Apr 2010
Posts: 173
Location: singapore
Schools: Wharton,NY Stern,INSEAD,Stanford
Followers: 2

Kudos [?]: 30 [0], given: 25

GMAT ToolKit User
Re: Data Suff - Number Property... [#permalink] New post 05 Sep 2011, 22:25
+1 for A
Plug-in Numbers 2,4,6 for "1"
We dont the value of "C" so it is not sufficient.
_________________

Regards,
Nagesh
My GMAT Study Plan: my-gmat-study-plan-112833.html
Idioms List : gmat-idioms-104283.html?hilit=idioms#p813231
--------------------------------------
Consider Kudos if you like my posts

Re: Data Suff - Number Property...   [#permalink] 05 Sep 2011, 22:25
    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic Is a*b*c divisible by 24? (1) a,b, and c are consecutive dexerash 3 28 May 2012, 04:06
3 Is a*b*c divisible by 24 ? 1. a, b, and c are consecutive study 6 03 Nov 2008, 00:18
Is a*b*c divisible by 24 ? 1. a, b, and c are consecutive JDMBA 20 28 Nov 2007, 06:36
Experts publish their posts in the topic Is abc divisible by 24? 1) a, b, c are consecutive even GMATBLACKBELT 5 14 Nov 2007, 21:39
Is ABC divisible by 24? 1. A B C are consecutive integers 2. bmwhype2 4 29 Oct 2007, 11:31
Display posts from previous: Sort by

Is a*b*c divisible by 24? (1) a,b, and c are consecutive

  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®.