Divisibility problem

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tonebeeze: Master | Next Rank: 500 Posts; Posts: 158; Joined: Mon Nov 02, 2009 5:49 pmFollowed by: 3 members; Thanked: 2 times

by tonebeeze » Mon Jan 03, 2011 7:10 pm

How many divisors does positive integer N have?

1. The difference between the largest and the smallest divisor of N is 21

2. N+1 has 2 divisors

OA is A

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Source: Beat The GMAT — Data Sufficiency | Mon Jan 03, 2011 7:10 pm

anshumishra: Legendary Member; Posts: 543; Joined: Tue Jun 15, 2010 7:01 pmFollowed by: 3 members; Thanked: 147 times

by anshumishra » Mon Jan 03, 2011 7:20 pm

tonebeeze wrote:How many divisors does positive integer N have?

1. The difference between the largest and the smallest divisor of N is 21

2. N+1 has 2 divisors

OA is A

Statement 1:
Sufficient
Please note that the largest divisor is the number itself (and smallest is 1), so we know the number.

Statement 2:
Insufficient
you can check with different values of n, that thsi will give different results.

Hence, A

Thanks
Anshu

(Every mistake is a lesson learned )

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Mon Jan 03, 2011 7:22 pm

tonebeeze wrote:How many divisors does positive integer N have?

1. The difference between the largest and the smallest divisor of N is 21

2. N+1 has 2 divisors

Statement 1: The difference between the largest and the smallest divisor of N is 21
Largest divisor of any positive integer is the integer itself and smallest divisor of any positive integer is 1. Thus, (Integer - 1) = 21 => The integer is 22. We can easily determine the number of divisors of 22.

Sufficient.

Statement 2: N+1 has 2 divisors
This implies (N + 1) is a prime. But there is infinite number of positive integers N such that (N + 1) is prime.

Not Sufficient.

The correct answer is A.

Anurag Mairal, Ph.D., MBA
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aleph777: Master | Next Rank: 500 Posts; Posts: 131; Joined: Fri Jun 18, 2010 10:19 am; Location: New York, NY; Thanked: 10 times

by aleph777 » Tue Jan 04, 2011 8:08 am

Another point I think worth mentioning is that "divisors" is synonymous with "factors." So you're simply looking for the number of factors of N.

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