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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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

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.

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).

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.

Re: Data Suff - Number Property... [#permalink]
15 Jul 2011, 09:22

Expert's post

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. _________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Re: Data Suff - Number Property... [#permalink]
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.

I am not panicking. Nope, Not at all. But I am beginning to wonder what I was thinking when I decided to work full-time and plan my cross-continent relocation...

Over the last week my Facebook wall has been flooded with most positive, almost euphoric emotions: “End of a fantastic school year”, “What a life-changing year it’s been”, “My...