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Positive integer

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Positive integer

by arbiter » Sun Aug 23, 2009 7:17 am
For any positive integer n, the length of n is defined as the number of prime factors whose product is n. For ex, the length of 75 is 3, since 75=3*5*5. how many 2 digit positive integers have length 6?
a> none
b> one
c>two
d>three
e>four

OA is [spoiler]c>two[/spoiler]
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Re: Positive integer

by umaa » Sun Aug 23, 2009 7:23 am
arbiter wrote:For any positive integer n, the length of n is defined as the number of prime factors whose product is n. For ex, the length of 75 is 3, since 75=3*5*5. how many 2 digit positive integers have length 6?
a> none
b> one
c>two
d>three
e>four

OA is [spoiler]c>two[/spoiler]
The length should be 6. So, the least prime number is 2.

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

Replace a 2 with a 3.

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

You can't replace another 3 in the multiplication. Because it will give,

2*2*2*2*3*3 = 144 - 3 digit number. We need only 2 digit numbers.

So, the answer is 2 (c)
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