• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

• FREE GMAT Exam
Know how you'd score today for $0 Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Get 300+ Practice Questions
25 Video lessons and 6 Webinars for FREE

Available with Beat the GMAT members only code

## Difficult Math Problem #109 - Number Theory

This topic has 2 member replies
800guy Master | Next Rank: 500 Posts
Joined
27 Jun 2006
Posted:
354 messages
Followed by:
5 members
Upvotes:
11

#### Difficult Math Problem #109 - Number Theory

Wed Mar 14, 2007 8:42 am
How many integers less than 1000 have no factors (other than 1) in common with 1000?

(1) 400
(2) 410
(3) 411
(4) 412
(5) None of the above

from diff math doc. oa coming after some people respond with explanations

gabriel Legendary Member
Joined
20 Dec 2006
Posted:
986 messages
Followed by:
1 members
Upvotes:
51
Wed Mar 14, 2007 9:14 am
800guy wrote:
How many integers less than 1000 have no factors (other than 1) in common with 1000?

(1) 400
(2) 410
(3) 411
(4) 412
(5) None of the above

from diff math doc. oa coming after some people respond with explanations
So we need numbers that have factors other than 2 or 5..... that wuld be equal to.. total- ( numbers with 2 or 5 as a factor )

Now, the number of integers that have 2 as a factor and less than 1000 is 499.....

now while counting factors of 5 we do not have to include numbers like 10,20,30... bcoz they are already included in the list of integers with 2 as a factor... so we only consider the odd multiples of 5... ie 5,15,25... which wuld be equal to 100.. therefore tha answer is 999-( 499+100) = 400.. therefore the answer is A....

800guy Master | Next Rank: 500 Posts
Joined
27 Jun 2006
Posted:
354 messages
Followed by:
5 members
Upvotes:
11
Fri Mar 16, 2007 8:59 am
here's the oa:

1000 - multiples of 2 and/or 5

multiples of 2 = 500 (all even #)
multiples of 5 = (995 -5)/10 + 1 [ Using AP formula]
= 100

Answer = 1000 - (500 + 100)
= 400

You cannot calculate for all multiples of 5 because you have already removed all even integers (including 10, 20, and 30). The difference in the AP series should be 10 instead of 5 because you're looking for the integers that have 5 as a unit's digit. Therefore we divide by 10 and not 5.

### Top First Responders*

1 GMATGuruNY 72 first replies
2 Rich.C@EMPOWERgma... 45 first replies
3 Brent@GMATPrepNow 43 first replies
4 Jay@ManhattanReview 27 first replies
5 ErikaPrepScholar 9 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 GMATGuruNY

The Princeton Review Teacher

133 posts
2 Rich.C@EMPOWERgma...

EMPOWERgmat

118 posts
3 Jeff@TargetTestPrep

Target Test Prep

105 posts
4 Max@Math Revolution

Math Revolution

93 posts
5 Scott@TargetTestPrep

Target Test Prep

92 posts
See More Top Beat The GMAT Experts