If the integer n has exactly 3 positive divisors, including 1 and n, how many positive divisors does n^2 have?
(A) 4
(B) 5
(C) 6
(D) 8
(E) 9
I don't understand why answer is B. Book explanation not clear.
Thanks!
OG 11th Edition PS#241-Need explanation
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Last edited by joyseychow on Wed Apr 29, 2009 1:36 am, edited 1 time in total.
- Vemuri
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Interesting question. I am not very good with number theories, so I could not come up with a number that has exactly 3 divisors. So, my solution is more theoretical.
Given, n has 1, n & some number 'x' as its divisors. So, n^2 will have 1, n, n^2, x & x^2 as its divisors. So, there are 5 divisors in all.
BTW, please use spoiler when giving answer. This will allow others to give a fair try at the question before providing the explanation.
Given, n has 1, n & some number 'x' as its divisors. So, n^2 will have 1, n, n^2, x & x^2 as its divisors. So, there are 5 divisors in all.
BTW, please use spoiler when giving answer. This will allow others to give a fair try at the question before providing the explanation.
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Interesting question indeed.
This problem can be easily solved once we know this key concept.
1. A prime number N has ONLY 2 divisors N and 1.
2. Square of a prime number has 3 divisors
ie N^2 has N^2, N and 1 as its divisors.
Now u can easily solve this problem.
let the number be 4. It has the following divisors 4, 2 and 1.
Square of this number is 16. Lets find the divisors of 16 as follows.
1 -------- 16
2 -------- 8
4 -------- 4
So the divisors are 1, 2, 4, 8, 16
So the number of divisors = 5
HT Helps
-V
This problem can be easily solved once we know this key concept.
1. A prime number N has ONLY 2 divisors N and 1.
2. Square of a prime number has 3 divisors
ie N^2 has N^2, N and 1 as its divisors.
Now u can easily solve this problem.
let the number be 4. It has the following divisors 4, 2 and 1.
Square of this number is 16. Lets find the divisors of 16 as follows.
1 -------- 16
2 -------- 8
4 -------- 4
So the divisors are 1, 2, 4, 8, 16
So the number of divisors = 5
HT Helps
-V
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- Master | Next Rank: 500 Posts
- Posts: 125
- Joined: Mon Dec 15, 2008 9:24 pm
Thanks V for the in depth explanation! Will remember the concept.vittalgmat wrote:Interesting question indeed.
This problem can be easily solved once we know this key concept.
1. A prime number N has ONLY 2 divisors N and 1.
2. Square of a prime number has 3 divisors
ie N^2 has N^2, N and 1 as its divisors.
Now u can easily solve this problem.
let the number be 4. It has the following divisors 4, 2 and 1.
Square of this number is 16. Lets find the divisors of 16 as follows.
1 -------- 16
2 -------- 8
4 -------- 4
So the divisors are 1, 2, 4, 8, 16
So the number of divisors = 5
HT Helps
-V