Question : The sum of the two numbers is 1224 and their HCF is 68. The number of pairs of numbers satisfying the above condition is:
Option 1: 3
Option 2: 4
Option 3: 6
Option 4: 2

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Question : If the sum of two numbers is 60 and their HCF and LCM are 5 and 60, respectively, then the sum of the reciprocals of the numbers will be:
Option 1: $\frac{1}{11}$
Option 2: $\frac{1}{6}$
Option 3: $\frac{1}{4}$
Option 4: $\frac{1}{5}$

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Answer 1

Correct Answer: 3

Solution : Given: The sum of the two numbers is 1224 and their HCF is 68.
Let the two numbers be $68 x$ and $68 y$ .
According to the question,
$68 x + 68 y = 1224$
⇒ $x + y = 18$
So, the possible pairs of values which are co-prime to each other are (1, 17), (5, 13), and (7, 11).
$∴$ Number of required pairs is 3.
Hence, the correct answer is 3.

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Question : The sum of the two numbers is 1224 and their HCF is 68. The number of pairs of numbers satisfying the above condition is:Option 1: 3Option 2: 4Option 3: 6Option 4: 2

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Question : The sum of the two numbers is 1224 and their HCF is 68. The number of pairs of numbers satisfying the above condition is:
Option 1: 3
Option 2: 4
Option 3: 6
Option 4: 2