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Question

If 4x17y=1 & x,y500, find how many positive integer solutions are possible?

A
29
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B
28
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C
27
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D
Cannot be determined
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Solution

The correct option is A 29
4x17y=1
Or 4x1=17y
Or 4x1 must be multiple of 17 and y and x500
Max multiple of 17 in the set 4x1 i.e.
(3,7,11,.........1999)
to be divisible by 17 is (17,34,51........1989)
Using AP formula we get n=29
Hence, the answer is 29.

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