- Hi all,Given below are a few questions on LCM and HCF. As ever, they are also available on our blog - http://iimcat.blogspot.com/2010/11/number-theory-questions-lcm-hcf.html1. How many pairs of positive integers x,y exist such that HCF of, x,y = 35 and sum of x and y = 1085?

2. How many pairs of positive integers x,y exist such that HCF(x,y) + LCM (x,y) = 91?

3. Sum of two numbers x,y = 1050. What is the maximum value of the HCF between x and y?

4. Sum of two even numbers a and b = 240. If HCF (a,b) is greater than a and b, what is the minimum value of HCF (a,b)?Happy cracking.Cheers,Rajesh99626 48484**New CAT2011 batches starting @ Chennai**

Nov 13th @ Velachery, Nov 20th @ Mylapore - 1. Phi(31) = 30.

2. 8 + 4 + 4 = 16.

3. 1050/2 = 525.

4. HCF(a, b) cannot be greater than a and b.

Please confirm the answers. I am sure that there can be some silly error which i a reluctant to recheck.**From:**Rajesh Balasubramanian <rajesh@...>**To:**ascent4cat@yahoogroups.com**Sent:**Wed, November 10, 2010 9:24:37 AM**Subject:**[2IIM CAT Prep] Questions on Number Theory - LCM HCFHi all,Given below are a few questions on LCM and HCF. As ever, they are also available on our blog - http://iimcat.blogspot.com/2010/11/number-theory-questions-lcm-hcf.html1. How many pairs of positive integers x,y exist such that HCF of, x,y = 35 and sum of x and y = 1085?

2. How many pairs of positive integers x,y exist such that HCF(x,y) + LCM (x,y) = 91?

3. Sum of two numbers x,y = 1050. What is the maximum value of the HCF between x and y?

4. Sum of two even numbers a and b = 240. If HCF (a,b) is greater than a and b, what is the minimum value of HCF (a,b)?Happy cracking.Cheers,Rajesh99626 48484**New CAT2011 batches starting @ Chennai**

Nov 13th @ Velachery, Nov 20th @ Mylapore Ans1: If HCF is 35 then the numbers should be in the form 35k, where k is a prime number. Since it is given x+y=1085, we can write 35(a+b)=1085 or a+b = 31. Now only one pair of prime number satisfy this condition(2,29)..hence answere is one pair.(though my gut feeling tells me i am overlooking something so please correct me if i am wrong)ANS2:- 16 pairsAns3 :- 525Ans4:...I dont know whether it was to be solved or not but HCF cannot be greater than the numbers..please check and send us the question back.**Opinion is like an AssHole, everybody has one!****Divakar Narayan Singh**--- On

**Wed, 10/11/10, Rajesh Balasubramanian**wrote:*<rajesh@...>*

From: Rajesh Balasubramanian <rajesh@...>

Subject: [2IIM CAT Prep] Questions on Number Theory - LCM HCF

To: ascent4cat@yahoogroups.com

Date: Wednesday, 10 November, 2010, 9:24 AMHi all,Given below are a few questions on LCM and HCF. As ever, they are also available on our blog - http://iimcat.blogspot.com/2010/11/number-theory-questions-lcm-hcf.html1. How many pairs of positive integers x,y exist such that HCF of, x,y = 35 and sum of x and y = 1085?

2. How many pairs of positive integers x,y exist such that HCF(x,y) + LCM (x,y) = 91?

3. Sum of two numbers x,y = 1050. What is the maximum value of the HCF between x and y?

4. Sum of two even numbers a and b = 240. If HCF (a,b) is greater than a and b, what is the minimum value of HCF (a,b)?Happy cracking.Cheers,Rajesh99626 48484**New CAT2011 batches starting @ Chennai**

Nov 13th @ Velachery, Nov 20th @ Mylapore- Hi Divakar

a + b = 31 such that HCF(a, b) = 1. Now it is not compulsory that a and b are prime. eg. (a, b) can be (1, 30), (2, 29), (3, 28), .....(30, 1) i.e. total 30 pairs.

Now observe closely that HCF of all these pairs is 1 and their sum is 31.

Hope it is clear.**From:**divakar narayan <divakar_narayan@...>**To:**ascent4cat@yahoogroups.com**Sent:**Wed, November 10, 2010 7:59:52 PM**Subject:**Re: [2IIM CAT Prep] Questions on Number Theory - LCM HCFAns1: If HCF is 35 then the numbers should be in the form 35k, where k is a prime number. Since it is given x+y=1085, we can write 35(a+b)=1085 or a+b = 31. Now only one pair of prime number satisfy this condition(2,29)..hence answere is one pair.(though my gut feeling tells me i am overlooking something so please correct me if i am wrong)ANS2:- 16 pairsAns3 :- 525Ans4:...I dont know whether it was to be solved or not but HCF cannot be greater than the numbers..please check and send us the question back.**Opinion is like an AssHole, everybody has one!****Divakar Narayan Singh**--- On

**Wed, 10/11/10, Rajesh Balasubramanian**wrote:*<rajesh@...>*

From: Rajesh Balasubramanian <rajesh@...>

Subject: [2IIM CAT Prep] Questions on Number Theory - LCM HCF

To: ascent4cat@yahoogroups.com

Date: Wednesday, 10 November, 2010, 9:24 AMHi all,

2. How many pairs of positive integers x,y exist such that HCF(x,y) + LCM (x,y) = 91?

3. Sum of two numbers x,y = 1050. What is the maximum value of the HCF between x and y?

4. Sum of two even numbers a and b = 240. If HCF (a,b) is greater than a and b, what is the minimum value of HCF (a,b)?Happy cracking.Cheers,Rajesh99626 48484**New CAT2011 batches starting @ Chennai**

Nov 13th @ Velachery, Nov 20th @ Mylapore