BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

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

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Moderator
Posts: 7187
Joined: Thu Sep 07, 2017 4:43 pm
Followed by:23 members

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

by BTGmoderatorDC » Sun Jan 09, 2022 8:36 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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


OA C

Source: GMAT Prep
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

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

by Brent@GMATPrepNow » Mon Jan 10, 2022 6:25 am
BTGmoderatorDC wrote: ↑
Sun Jan 09, 2022 8:36 pm
 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


OA C

Source: GMAT Prep
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
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Post new topic Post Reply
• Page 1 of 1