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# If M is a positive odd integer between 2 and 30, then M is

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Intern
Joined: 10 Aug 2004
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If M is a positive odd integer between 2 and 30, then M is [#permalink]  07 Dec 2007, 03:17
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If M is a positive odd integer between 2 and 30, then M is divisible by how many different positive prime numbers?

1) M is not divisible by 3
2) M is not divisible by 5
CEO
Joined: 17 Nov 2007
Posts: 3578
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
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Kudos [?]: 2149 [0], given: 359

Expert's post
A

1. any prime (except 2 and 3) are fulfill condition. for example, 5,7,13.... with 1 different prime number.
The least integer with two different prime numbers is 5*7=35 - out of the set [2,30] - suff.

2. any prime (except 2 and 5) are fulfill condition. for example, 3,7,13.... with 1 different prime number.
The least integer with two different prime numbers is 3*7=21 - in the set [2,30] - insuff.
Manager
Joined: 04 Nov 2007
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All possible m are: 3, 5, 7, 9, 11, 13, 15, 17, 19

a. m is not divisible by 3, thus delete 3, 9 and 15. The rest of the odd numbers are all prime numbers which means they are all divisible by exactly 2 numbers: 1 and itself. Sufficient

b. m is not divisible by 5, thus delete 15. Except 9, all of the rest are prime numbers, which are divisible by two numbers: 1 and itself. 9 is divisible by three numbers: 3, 1 and 9. Thus, b is insufficient

Ans = A
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