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Quant Question...Answer Pls

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Joined: 12 Oct 2011
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Quant Question...Answer Pls [#permalink] New post 06 Nov 2011, 09:03
For any positive integer n, the length of n is defined as the number of prime factors whose product is n. For example, the length of 75 is 3, since 75 = 3x5x5. How many two-digit positive integers have length 6 ?

A) None
B) One
C) Two
D) Three
E) Four

My answer is B....but the official answer is C........Anyone Pls explain??
Intern
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Status: Accepted - SMU, Singapore (Class of 2013)
Joined: 08 Sep 2011
Posts: 27
Location: Singapore
Concentration: Finance, General Management
GMAT 1: 620 Q46 V29
GMAT 2: 710 Q50 V35
WE: Information Technology (Computer Software)
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Re: Quant Question...Answer Pls [#permalink] New post 06 Nov 2011, 09:10
rvind wrote:
For any positive integer n, the length of n is defined as the number of prime factors whose product is n. For example, the length of 75 is 3, since 75 = 3x5x5. How many two-digit positive integers have length 6 ?

A) None
B) One
C) Two
D) Three
E) Four

My answer is B....but the official answer is C........Anyone Pls explain??



2x2x2x2x2x2=64
2x2x2x2x2x3=96

hence two such two-digit numbers
Ans. C
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Re: Quant Question...Answer Pls [#permalink] New post 06 Nov 2011, 09:12
It is two. C

The minimal possible value for a length of 6 is by taking all the primes as 2.

2 * 2 * 2 * 2 * 2 * 2 = 64.

The next alteration we do is to replace a number by 3.

2 * 2 * 2 * 2 * 2 * 3 = 96.

So it is still possible. Another replacement of 3 will make it a 3 digit.
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Re: Quant Question...Answer Pls   [#permalink] 06 Nov 2011, 09:12
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