the sum of two numbers is 528 and their h c f..., HCF & LCM, General Mathematics

Question:The sum of two numbers is 528 and their H.C.F. is 33. The number of pairs of such numbers satisfying the above condition is:

A 6 
B 12 
C 8 
D 4

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+ AnswerD

+ Explanationsolution:
Let the required numbers be `33a and 33b`. Then, 
`33a +33b=528` 
or `a+b=16.`
Now, two co-primes with sum 16 are: 
`(1,15),(3,13),(5,11) & (7,9)`
`:.` Numbers with sum 528 and H.C.F. 33 are:
`(33 xx 1, 33 xx 15),(33 xx 3, 33 xx 13),(33 xx 5, 33 xx 11),(33 xx 7, 33 xx 9)`.
The number of such pairs is 4.

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