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Source: — Problem Solving |

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by Brent@GMATPrepNow » Sat Jun 04, 2011 10:54 am
MBA.Aspirant wrote:What's the least positive integer that is not a factor of 25! and is not a prime number?

26
28
36
56
58
25! = 25 x 24 x 23 22 x . . . . x 3 x 2 x 1

A) 26 = 2 x 13
13 and 2 can be found in 25! : 25 x 24 x 23 22 x . . . x 13 x . . . x 3 x 2 x 1
Therefore 26 is a factor of 25!

B) 28 = 2 x 2 x 7
2, 2 and 7 can be found in 25!: 25 x 24 x 23 22 x . . . x 7 x . . .x (2)(2) x 3 x 2 x 1
Therefore 28 is a factor of 25!

etc, etc, etc

E) 59 = 2 x 29.
Since 29 cannot be found anywhere in 25!, 58 cannot be a divisor of 25!

So, the answer is E
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by Frankenstein » Sat Jun 04, 2011 10:56 am
Hi,
26 =13.2(will be there in 25!)
28=2.14(will be there in 25!)
36=2.18(will be there in 25!))
56=4.14(will be there in 25!)
58=2.29(29 is prime and will not be in 25!)
Hence, E
Cheers!

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by Frankenstein » Sat Jun 04, 2011 11:00 am
Hi,
If you do not have options, the way in which we solve this question is follows:
Look for the smallest prime greater than 25. It is 29.
We need the smallest integer which is not prime. So, we will multiply this prime with the smallest number(2) that makes it composite.
So, the number is 29.2=58
Cheers!

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by cans » Sat Jun 04, 2011 8:27 pm
a)2*13 -> factor
b)2*14 -> factor
c)2*18 -> factor
D)4*14-> factor
e)2*29 -> not factor
IMO E
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by MBA.Aspirant » Sun Jun 05, 2011 5:45 am
Brent@GMATPrepNow wrote:
MBA.Aspirant wrote:What's the least positive integer that is not a factor of 25! and is not a prime number?

26
28
36
56
58
25! = 25 x 24 x 23 22 x . . . . x 3 x 2 x 1

A) 26 = 2 x 13
13 and 2 can be found in 25! : 25 x 24 x 23 22 x . . . x 13 x . . . x 3 x 2 x 1
Therefore 26 is a factor of 25!

B) 28 = 2 x 2 x 7
2, 2 and 7 can be found in 25!: 25 x 24 x 23 22 x . . . x 7 x . . .x (2)(2) x 3 x 2 x 1
Therefore 28 is a factor of 25!

etc, etc, etc

E) 59 = 2 x 29.
Since 29 cannot be found anywhere in 25!, 58 cannot be a divisor of 25!

So, the answer is E
Cool - thanks for the tip!
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