tough number properties

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ashish1354: Master | Next Rank: 500 Posts; Posts: 100; Joined: Wed Jul 30, 2008 9:52 am; Thanked: 4 times

by ashish1354 » Tue Sep 23, 2008 3:37 am

How many integers less than 1000 have no factors (other than 1) in common with 1000?

my question is whether we need to consider integers starting from 0 till 999

& if we do do we need to include 0??

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Source: Beat The GMAT — Problem Solving | Tue Sep 23, 2008 3:37 am

Morgoth: Master | Next Rank: 500 Posts; Posts: 316; Joined: Mon Sep 22, 2008 12:04 amFollowed by: 1 member; Thanked: 36 times

by Morgoth » Tue Sep 23, 2008 4:00 am

I guess you have to consider 0. Since 0 is a factor of no number and multiple of every number.

But on GMAT you generally get things like positive integers or positive factors in the question stem itself. So, you dont have to consider 0 then.

0 is an integer neither positive nor negative.

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

Re: tough number properties

by Ian Stewart » Tue Sep 23, 2008 5:42 am

ashish1354 wrote:How many integers less than 1000 have no factors (other than 1) in common with 1000?

my question is whether we need to consider integers starting from 0 till 999

& if we do do we need to include 0??

If the question simply says 'How many integers less than 1000', you'd even need to consider negative numbers, so the answer would be 'an infinite number'. You won't see a question like that on the GMAT- if you saw such a question, it would say 'positive integers', in which case you would not, of course, consider zero, since zero is not positive.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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4meonly: Legendary Member; Posts: 891; Joined: Sat Aug 16, 2008 4:21 amFollowed by: 1 member; Thanked: 27 times; GMAT Score:660(

by 4meonly » Tue Sep 23, 2008 5:55 am

What is the answer?
400?

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pre-gmat: Master | Next Rank: 500 Posts; Posts: 105; Joined: Tue Jul 15, 2008 7:03 pm; Thanked: 5 times

by pre-gmat » Tue Sep 23, 2008 2:32 pm

Yeah I guess answer should be 400.

here's my reasoning...

1000 has 2,5 as prime factors.

so first eliminate all even numbers which leaves 500 odd integers and now out of 500 eliminate any number divisible by 5 which is 100 and therefore leaves us with 400.
We haev already covered the case of 2 and 5 together being factor.

Let me know the OA.

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