- Hi all,The answers given by Viv are correct. The explanations are also perfect. I have given slightly more detailed explanations here - http://iimcat.blogspot.com/2010/10/discussion-on-number-theory-questions.html . The questions are as follows
1. What is the smallest number that has exactly 12 factors?

a. 2

^{11}b. 60

c. 120

d. 96

e. 144

2. If f(x) is the number of primes less than or equal to x, find the value of f(90) - f(80) = ?

a. 3

b. 2

c. 1

d. 4

e. 0

3. The difference between the ages of two brothers is a prime number. Sum of their ages is also a prime number. If the elder brother is 28 years old, how many different values can the age of the younger brother take?

a. 2

b. 3

c. 4

d. 1

e. 0

Will send across the last 4 questions from the challenge quiz later today. I am hoping that we can go from there to having a more detailed discussion on Number Theory. This is a vast topic, and is a wonderful one to discuss on email. If any one of you want to take up one topic and discuss it, drop me an email. We can always accommodate one serious guest post every week. That way, the discussion can be more fun also.Cheers,Rajesh**From:**vivek kumar**Sent:**Tuesday, October 19, 2010 11:44 AM**Subject:**Re: [2IIM CAT Prep] Questions from Challenge QuizHi Rajesh,

1. b 60 = 2^2 x 3 x 5, powers 3x2x2 = 12

2. b 83 n 89 are the primes between 80 and 90.

3. b Age of younger brother can be 9, 15 n 25.

Kindly lemme know if they are right.

Regards

Viv

**From:**"rajesh@..." <rajesh@...>**To:**ascent4cat@yahoogroups.com**Sent:**Tue, October 19, 2010 10:53:15 AM**Subject:**[2IIM CAT Prep] Questions from Challenge Quiz

Hi all,I have given below three questions from Number Theory from the quiz that is on our website (We have already discussed three out of these). The questions can be found here - http://challenge.2iim.com/test_1/ . I will post the solutions for this in a day or two.Happy cracking.1. What is the smallest number that has exactly 12 factors?

a. 2

^{11}b. 60

c. 120

d. 96

e. 144

2. If f(x) is the number of primes less than or equal to x, find the value of f(90) - f(80) = ?

a. 3

b. 2

c. 1

d. 4

e. 0

3. The difference between the ages of two brothers is a prime number. Sum of their ages is also a prime number. If the elder brother is 28 years old, how many different values can the age of the younger brother take?

a. 2

b. 3

c. 4

d. 1

e. 0

Cheers,Rajesh B (B.Tech IITM, PGDM IIMB)

Director, 2IIM,

93825 48484