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PS-How many Positive integers?

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Director
Joined: 04 Jan 2008
Posts: 898

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28 Mar 2009, 23:09
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How many positive integers, from 2 to 100, inclusive, are not divisible by odd integers greater than 1?

A. 5
B. 6
C. 8
D. 10
E. 50

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Director
Joined: 04 Jan 2008
Posts: 898
Re: PS-How many Positive integers? [#permalink]

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29 Mar 2009, 03:13
How to approach?
I have the OE but i need some quick soln
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Manager
Joined: 19 May 2008
Posts: 164
Location: Mumbai
Re: PS-How many Positive integers? [#permalink]

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29 Mar 2009, 03:19
I think this should be simple - 2, 4, 8, 16, 32 and 64.

Senior Manager
Joined: 28 Aug 2006
Posts: 304
Re: PS-How many Positive integers? [#permalink]

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29 Mar 2009, 06:17
nitya34 wrote:
How many positive integers, from 2 to 100, inclusive, are not divisible by odd integers greater than 1?

A. 5
B. 6
C. 8
D. 10
E. 50

The question clearly says that we need to find numbers which do not have odd factors.

So the number must be of the form $$2^n$$

Hence the numbers in the given range are $$2, 2^2, 2^3, 2^4, 2^5 \quad and \quad 2^6$$

So totally 6 numbers exits.
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Re: PS-How many Positive integers? [#permalink]

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29 Mar 2009, 09:12
Thanks
It looks simple now
OA-B
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Manager
Joined: 19 Aug 2006
Posts: 241
Re: PS-How many Positive integers? [#permalink]

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29 Mar 2009, 11:20
We have a range of 2...100.

Only some of the even integers will not be divisible by odd numbers in this range.
Let's try to list a few even numbers in the range: 2,4,6,8,10,12,14,16,18,20....
Out of these 2,4,8,16 are not divisible by odd factors - it can be deduced that the numbers we seek are multiples of 2: 2,4,8,16,32,64.
Re: PS-How many Positive integers?   [#permalink] 29 Mar 2009, 11:20
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