YTT 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 = 3 * 5 * 5. How many two-digit positive integers have length 6?
A. None
B. One
C. Two
D. Three
E. Four
Let's first find the smallest value with length 6.
This is the case when each prime factor is 2.
We get 2 x 2 x 2 x 2 x 2 x 2 = 64. This is a 2-digit positive integer. PERFECT
To find the next largest number with length 6, we'll replace one 2 with a 3
We get
3 x 2 x 2 x 2 x 2 x 2 = 96. This is a 2-digit positive integer. PERFECT
To find the third largest number with length 6, we'll replace another 2 with a 3
We get
3 x
3 x 2 x 2 x 2 x 2 = 144. This is a 3-digit positive integer. NO GOOD
So there are only
two two-digit positive integers with length 6.
Answer: C
Cheers,
Brent
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Brent Hanneson – Creator of gmatprepnow.com
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