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DS: "length"

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DS: "length"

by haidgmat » Sun Sep 05, 2010 5:58 pm
For any positive integer n, the length n is defined as the number of prime factors whose product is n. For example, the length of 75 is 3, since 75= 3 X 5 X 5. How many two-digit positive integers have length 6?

a. None
b. One
c. Two
d. Three
e. Four

Ans- C
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by Rahul@gurome » Sun Sep 05, 2010 7:09 pm
Solution:
Let us check the minimum value which will have length 6.
Obviously it will be 2^6 = 64 which is a 2 digit positive integer.
The next higher value can be 2^5 * 3 = 96 which is again a 2 digit positive integer.
The third higher value will be (2^4) * (3^2) = 16*9 = 144 which is a 3 digit number.

So there are only 2, two-digit positive integers with length 6.

The correct answer is c.
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