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Retired Moderator
Joined: 16 Apr 2020
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WE:Education (Education)
If x and y are two positive integers such that x + y = 1085 and HCF (x
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07 Mar 2022, 00:41
07 Mar 2022, 00:41
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If x and y are two positive integers such that x + y = 1085 and HCF (x, y) = 35. Then how many pairs of positive integers x and y exist?
A. 8
B. 12
C. 15
D. 30
E. 31
A. 8
B. 12
C. 15
D. 30
E. 31
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Given Kudos: 172
Location: India
WE:Education (Education)
If x and y are two positive integers such that x + y = 1085 and HCF (x
[#permalink]
25 Mar 2022, 06:46
25 Mar 2022, 06:46
OA Explanation:
Since the HCF (x,y) is 35
Let x = 35a and y = 35b
Her, a and b should be different positive integers
As per the question;
x + y = 1085
35a + 35b = 1085
35(a + b) = 1085
(a + b) = 31
How many pairs?
(1 + 30), (2 + 29), (3 + 28), (4 + 27), .........., (14 + 17), (15 + 16)
So a total of 15 pairs
Hence, option C
Since the HCF (x,y) is 35
Let x = 35a and y = 35b
Her, a and b should be different positive integers
As per the question;
x + y = 1085
35a + 35b = 1085
35(a + b) = 1085
(a + b) = 31
How many pairs?
(1 + 30), (2 + 29), (3 + 28), (4 + 27), .........., (14 + 17), (15 + 16)
So a total of 15 pairs
Hence, option C
gmatclubot
If x and y are two positive integers such that x + y = 1085 and HCF (x [#permalink]
25 Mar 2022, 06:46
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