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:

How many positive three-digit integers are divisible by both [#permalink]
16 May 2012, 11:04

1

This post received KUDOS

5

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

5% (low)

Question Stats:

83% (02:20) correct
17% (01:34) wrong based on 174 sessions

How many positive three-digit integers are divisible by both 3 and 4?

A. 75 B. 128 C. 150 D. 225 E. 300

I know how to solve this one... but it takes me ages to find what would be the largest three digit number divisible by 12. Any tips or trick on how I can quickly get to that number?

Re: How many positive three-digit integers are divisible by both [#permalink]
16 May 2012, 11:18

3

This post received KUDOS

Expert's post

4

This post was BOOKMARKED

alexpavlos wrote:

How many positive three-digit integers are divisible by both 3 and 4?

A. 75 B. 128 C. 150 D. 225 E. 300

I know how to solve this one... but it takes me ages to find what would be the largest three digit number divisible by 12. Any tips or trick on how I can quickly get to that number?

Thanks!

A number to be divisible by both 3 and 4 should be divisible by the least common multiple of 3 and 4 so by 12.

How to find the largest three-digit multiple of 12: 1,000 is divisible by 4, so is 1,000-4=996, which is also divisible by 3, so 996 is the largest three-digit integer divisible by 12.

Re: How many positive three-digit integers are divisible by both [#permalink]
26 Jun 2012, 09:09

4

This post received KUDOS

cant say that my method is good, but still...

first, look at answer choices. u can see that these choices range widely. now divide 999 by 12 and get 83. so, u need an answer choice that is at most 83.

only 75 is less than 83. so, A is the answer. _________________

Happy are those who dream dreams and are ready to pay the price to make them come true

I am still on all gmat forums. msg me if you want to ask me smth

Re: How many positive three-digit integers are divisible by both [#permalink]
01 Oct 2012, 05:31

Multiplying 3 by 4 we get the smallest no. that is divisible by both 3 as well as 4 ... Therefore any number that is divisible by 12 is also divisible by 3 and 4 ...

Our numbers are to begin from 100 and end at 999 ...

The first three digit no. that is divisible by 12 is 108 , and the last three digit no. is 996

Now we can set up an A.P. using 108 as our first number, 996 as our last number D= 12 ..

so we get 108 , 120 , 132 .........996 ...

The nth term is 996 and to calculate the value of n we use the following formula :

Tn = a + (n-1)d

Therefore 996 = 108 + (n-1) 12

996 - 108 = (n-1) 12

888/12 = n-1

74 = n-1

n = 75 .. ( A ) _________________

"When you want to succeed as bad as you want to breathe, then you’ll be successful.” - Eric Thomas

Re: How many positive three-digit integers are divisible by both [#permalink]
01 Oct 2012, 08:32

LalaB wrote:

cant say that my method is good, but still...

first, look at answer choices. u can see that these choices range widely. now divide 999 by 12 and get 83. so, u need an answer choice that is at most 83.

only 75 is less than 83. so, A is the answer.

It is good, because with the given list of choices, it works. With another choice below 83, it would have been another story. _________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

Re: How many positive three-digit integers are divisible by both [#permalink]
15 Dec 2014, 14:24

Hi Bunuel i have one question. so we need to check manually and find out the least and greatest numbers that is divisible by 3 and 4? like in this case 108 is the least number. so we have to test for each number from 100-108 is divisible by 3 and 4 or not? is this the only method?

thanks-

Bunuel wrote:

alexpavlos wrote:

How many positive three-digit integers are divisible by both 3 and 4?

A. 75 B. 128 C. 150 D. 225 E. 300

I know how to solve this one... but it takes me ages to find what would be the largest three digit number divisible by 12. Any tips or trick on how I can quickly get to that number?

Thanks!

A number to be divisible by both 3 and 4 should be divisible by the least common multiple of 3 and 4 so by 12.

How to find the largest three-digit multiple of 12: 1,000 is divisible by 4, so is 1,000-4=996, which is also divisible by 3, so 996 is the largest three-digit integer divisible by 12.

Hope it helps.

_________________

--------------------------------------------------------------------------------------------- Kindly press +1 Kudos if my post helped you in any way

On September 6, 2015, I started my MBA journey at London Business School. I took some pictures on my way from the airport to school, and uploaded them on...

When I was growing up, I read a story about a piccolo player. A master orchestra conductor came to town and he decided to practice with the largest orchestra...

I’ll start off with a quote from another blog post I’ve written : “not all great communicators are great leaders, but all great leaders are great communicators.” Being...