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Intern
Joined: 12 Oct 2011
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06 Nov 2011, 10:03
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

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Concentration: Finance, General Management
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06 Nov 2011, 10:10
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

2x2x2x2x2x2=64
2x2x2x2x2x3=96

hence two such two-digit numbers
Ans. C
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06 Nov 2011, 10:12
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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