• Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer

Difficult Math Problem #109 - Number Theory

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

Difficult Math Problem #109 - Number Theory

Post 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

  • +1 Upvote Post
  • Quote
  • Flag
800guy Master | Next Rank: 500 Posts Default Avatar
Joined
27 Jun 2006
Posted:
354 messages
Followed by:
5 members
Upvotes:
11
Post 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.

  • +1 Upvote Post
  • Quote
  • Flag
gabriel Legendary Member
Joined
20 Dec 2006
Posted:
986 messages
Followed by:
1 members
Upvotes:
51
Post 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....

  • +1 Upvote Post
  • Quote
  • Flag

Best Conversation Starters

1 Roland2rule 170 topics
2 lheiannie07 110 topics
3 ardz24 56 topics
4 LUANDATO 50 topics
5 swerve 48 topics
See More Top Beat The GMAT Members...

Most Active Experts

1 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

155 posts
2 image description Scott@TargetTestPrep

Target Test Prep

122 posts
3 image description GMATGuruNY

The Princeton Review Teacher

121 posts
4 image description Rich.C@EMPOWERgma...

EMPOWERgmat

110 posts
5 image description DavidG@VeritasPrep

Veritas Prep

81 posts
See More Top Beat The GMAT Experts