## Questions on Number Theory - LCM HCF

Expand Messages
• Hi all, Given below are a few questions on LCM and HCF. As ever, they are also available on our blog -
Message 1 of 4 , Nov 9 7:54 PM
• 0 Attachment
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.html

1. 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,
Rajesh
99626 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
Message 2 of 4 , Nov 9 11:25 PM
• 0 Attachment
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 HCF

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.html

1. 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,
Rajesh
99626 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)=1085or a+b = 31. Now
Message 3 of 4 , Nov 10 6:29 AM
• 0 Attachment
 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)=1085or 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:From: Rajesh Balasubramanian Subject: [2IIM CAT Prep] Questions on Number Theory - LCM HCFTo: ascent4cat@yahoogroups.comDate: Wednesday, 10 November, 2010, 9:24 AM  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.html 1. 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 48484New 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.
Message 4 of 4 , Nov 10 10:28 PM
• 0 Attachment
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 HCF

 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)=1085or 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:From: Rajesh Balasubramanian Subject: [2IIM CAT Prep] Questions on Number Theory - LCM HCFTo: ascent4cat@yahoogroups.comDate: Wednesday, 10 November, 2010, 9:24 AM  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.html 1. 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 48484New CAT2011 batches starting @ Chennai Nov 13th @ Velachery, Nov 20th @ Mylapore

Your message has been successfully submitted and would be delivered to recipients shortly.