OG 11 PS question

Expert replies

varunkh70: Senior | Next Rank: 100 Posts; Posts: 51; Joined: Thu May 01, 2008 7:26 am; Thanked: 1 times

by varunkh70 » Sat Jun 27, 2009 2:18 am

If the integer n has exactly three positive divisors, including 1 and n, how many positive divisors does n^2 have?

OA later. any shortcuts?

~Varun

Like this post

Source: Beat The GMAT — Problem Solving | Sat Jun 27, 2009 2:18 am

ssmiles08: Master | Next Rank: 500 Posts; Posts: 472; Joined: Sun Mar 29, 2009 6:54 pm; Thanked: 56 times

Re: OG 11 PS question

by ssmiles08 » Sat Jun 27, 2009 4:29 am

varunkh70 wrote:If the integer n has exactly three positive divisors, including 1 and n, how many positive divisors does n^2 have?

OA later. any shortcuts?

~Varun

IMO 5

i took n as 4.

4^2 = 16

16 = 2^4

(4+1) = 5 Total factors

Like this post

varunkh70: Senior | Next Rank: 100 Posts; Posts: 51; Joined: Thu May 01, 2008 7:26 am; Thanked: 1 times

by varunkh70 » Sat Jun 27, 2009 5:05 am

thanks but how did that 4+1 come ther?

Like this post

ssmiles08: Master | Next Rank: 500 Posts; Posts: 472; Joined: Sun Mar 29, 2009 6:54 pm; Thanked: 56 times

by ssmiles08 » Sat Jun 27, 2009 5:24 am

varunkh70 wrote:thanks but how did that 4+1 come ther?

anytime you have a number, you want to find its total factors, you first break it down into primes, ex. 12 = 2^2 * 3^1

Then, you add 1 to their exponents and multiply each other. Here in this case for 12, it would be (2+1)*(1+1) = 3*2 = 6 total factors.

Ian has discussed it in detail here:

https://www.beatthegmat.com/what-s-your- ... 64-15.html

Like this post

shanmugam.d: Junior | Next Rank: 30 Posts; Posts: 29; Joined: Thu Apr 30, 2009 1:32 pm; Thanked: 2 times

by shanmugam.d » Sat Jun 27, 2009 6:42 am

Yeah it should be 5
- a number can have exactly 3 factor if it is a square of a prime number
- hence square of a number which is a prime square will be in the form:

- say x is a prime no., n = x^2
- n^2 =(x^2)^2
- n^2 =(x^4) hence it has 4+1 factors

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review