How many pairs of positive integers x, y exist such that HCF of x, y = 35 and sum of x and y = 1085?
  • a)
    12
  • b)
    8
  • c)
    15
  • d)
    30
  • e)
    16
Correct answer is option 'C'. Can you explain this answer?
Related Test: Test: LCM & GCD - 1

GMAT Question

NIKITA AGRAWAL
Aug 12, 2019
Let HCF of (x, y) be h. Then we can write x = h * a and y = h * b.
Furthermore, note that HCF (a, b) = 1. This is a very important property. One that seems obvious when it is mentioned but a property a number of people overlook.
So, we can write x = 35a; y = 35b
x + y = 1085 => 35(a + b) = 1085. => (a + b) = 31. We need to find pairs of co-prime integers that add up to 31. (Another way of looking at it is to find out integers less than 31 those are co-prime with it or phi(31) as had mentioned. More on this wonderful function in another post).
Since 31 is prime. All pairs of integers that add up to 31 will be co-prime to each other. Or, there are totally 15 pairs that satisfy this condition.
The question is "How many pairs of positive integers x, y exist such that HCF of x, y = 35 and sum of x and y = 1085?"
Hence the answer is "15"

This discussion on How many pairs of positive integers x, y exist such that HCF of x, y = 35 and sum of x and y = 1085?a)12b)8c)15d)30e)16Correct answer is option 'C'. Can you explain this answer? is done on EduRev Study Group by GMAT Students. The Questions and Answers of How many pairs of positive integers x, y exist such that HCF of x, y = 35 and sum of x and y = 1085?a)12b)8c)15d)30e)16Correct answer is option 'C'. Can you explain this answer? are solved by group of students and teacher of GMAT, which is also the largest student community of GMAT. If the answer is not available please wait for a while and a community member will probably answer this soon. You can study other questions, MCQs, videos and tests for GMAT on EduRev and even discuss your questions like How many pairs of positive integers x, y exist such that HCF of x, y = 35 and sum of x and y = 1085?a)12b)8c)15d)30e)16Correct answer is option 'C'. Can you explain this answer? over here on EduRev! Apart from being the largest GMAT community, EduRev has the largest solved Question bank for GMAT.
This discussion on How many pairs of positive integers x, y exist such that HCF of x, y = 35 and sum of x and y = 1085?a)12b)8c)15d)30e)16Correct answer is option 'C'. Can you explain this answer? is done on EduRev Study Group by GMAT Students. The Questions and Answers of How many pairs of positive integers x, y exist such that HCF of x, y = 35 and sum of x and y = 1085?a)12b)8c)15d)30e)16Correct answer is option 'C'. Can you explain this answer? are solved by group of students and teacher of GMAT, which is also the largest student community of GMAT. If the answer is not available please wait for a while and a community member will probably answer this soon. You can study other questions, MCQs, videos and tests for GMAT on EduRev and even discuss your questions like How many pairs of positive integers x, y exist such that HCF of x, y = 35 and sum of x and y = 1085?a)12b)8c)15d)30e)16Correct answer is option 'C'. Can you explain this answer? over here on EduRev! Apart from being the largest GMAT community, EduRev has the largest solved Question bank for GMAT.