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

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SVP
Joined: 04 May 2006
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If m is a positive odd integer between 2 and 30, then m is [#permalink]

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23 Jul 2008, 19:37
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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.
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Senior Manager
Joined: 23 May 2006
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23 Jul 2008, 19:58
List down all the positive odd numbers b/w 2 and 30:
3,5,7,9,11,13,15,17,19,21,23,25,27,29

S1. 3,9,15,21,27 are out from the list
This leaves only 25 which can be divided by 5 - hence one prime number only

S2 leaves 3,9,21,27
3 can be divided by 3 only
9 can be divided by 3 only
21 can be divided by 3 and 7
27 can be divided by 3 only
Hence maybe case

IMO A

Last edited by x97agarwal on 24 Jul 2008, 18:00, edited 1 time in total.
Director
Joined: 27 May 2008
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23 Jul 2008, 21:54
my approach, list all possible numbers

3,5,7,9,11,13,15,17,19,21,23,25,27,29

only 15 (3*5) and 21( 3*7) are multiple of two different prime numbers...

statement 1 : can eliminate both 15 and 21 --- Suff
statement 2 : can only eliminate 15, 21 stays --- not suff
Director
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23 Jul 2008, 22:21
GMBA85 wrote:
durgesh79 wrote:
my approach, list all possible numbers

3,5,7,9,11,13,15,17,19,21,23,25,27,29

only 15 (3*5) and 21( 3*7) are multiple of two different prime numbers...

statement 1 : can eliminate both 15 and 21 --- Suff
statement 2 : can only eliminate 15, 21 stays --- not suff

How about 25? Which is 5*5.

Its "different" prime numbers .... 5 and 5 are same prime numbers
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Joined: 19 Mar 2008
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24 Jul 2008, 01:58
(1) tells us m can be 5, 7, 11, 13, 15, 17, 19, 23, 25, 29
not sufficient

(2) tells us m can be 3, 7, 9, 11, 13, 17, 19, 21, 23, 27, 29
not sufficient

(1) + (2) tells us m can be 7, 11, 13, 17, 19, 23, 29
sufficient

After working with this time-consuming method, I believe that there is a shortcut.

Is it a rule that between 2 and 30, if the number is not a multiple of 3 or 5, it is a prime number?
SVP
Joined: 28 Dec 2005
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24 Jul 2008, 03:50
A for me . After eliminating from the list all multiples of 3, the leftover numbers can only be divided by one unique prime number.

From B, after eliminating all relevant #s from the list, you still have 21, which is divisiable by two primes, and numbers like 3, which is divisible by only one prime
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Joined: 04 May 2006
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26 Jul 2008, 19:56
OA is A friends, thanks. I have just come back after relax. Easy one right?
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27 Jul 2008, 20:45
sondenso wrote:
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.

from 1: 5x7 = 35, which is out of the range. so only one prime divides m. suff..
from 2: any odd prime in the range or 21 (3x7). so either 1 or 2 primes divide(s) m. nsf.

A.
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Re: GmatPrep.DS2   [#permalink] 27 Jul 2008, 20:45
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