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Question

The sum of two numbers is 629 and their HCF is 37. The number of pairs satisfying the above condition is

A
5
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B
6
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C
10
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D
8
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Solution

The correct option is D 8
H.C.F=37
So, two numbers are 37x and 37y, where x and y are co-prime numbers.
So,37x+37y=629
x+y=17
So, possible values are
(1,16),(2,15),(3,14),(4,13),(5,12),(6,11),(7,10),(8,9)
Now, we will not write (9,8) or (10,7) as it will form the same number formed by above pair.
8 pairs are satisfied by the above condition.

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