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Question

The sum of two numbers is 204 and their HCF is 17. Find the number of all the possible pairs of such numbers.

A
119
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B
120
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C
121
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D
117
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Solution

The correct option is D 119
Let the two numbers be x and y respectively.

It is given that the sum of the two numbers is 204, therefore,
x+y=204

Also 17 is their HCF, thus both numbers must be divisible by 17.

So, let x=17a and y=17b, then

17a+17b=20417(a+b)=204a+b=20417a+b=12
Therefore, required possible pair of values of x and y which are prime to each other are (1,11) and (5,7).

Thus, the required numbers are (17,187) and (85,119).

Hence, the number of possible pairs is 2.

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