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For any positive integer n, the length of n is defined as the number of prime factors whose product is n...

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For any positive integer n, the length of n is defined as the number of prime factors whose product is n...

by BTGmoderatorLU » Wed Sep 02, 2020 11:10 am

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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

The OA is C
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Re: For any positive integer n, the length of n is defined as the number of prime factors whose product is n...

by Brent@GMATPrepNow » Mon Sep 07, 2020 7:09 am
BTGmoderatorLU wrote: ↑
Wed Sep 02, 2020 11:10 am
 Source: GMAT Prep

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

The OA is C
Let's first find the smallest value with length 6.
This is the case when each prime factor is 2.
We get 2x2x2x2x2x2 = 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 3x2x2x2x2x2 = 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 3x3x2x2x2x2 = 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
Brent Hanneson - Creator of GMATPrepNow.com
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