Subject
Quantitative Aptitude
Topic
Number
The sum of two numbers is 192 and their HCF is 32. Find how many such pairs can be formed.
The sum of two numbers is 192 and their HCF is 32. Find how many such pairs can be formed.
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9Explanation
If HCF of two numbers is 32, then the two numbers are 32X & 32Y where X & Y are co-prime numbers. Now the sum of the two numbers is 192. So we can say, 32X + 32Y = 192 ⇒ X + Y = 6 The possible pairs of X & Y are: (1, 5), (2, 4), (3, 3) [As we are not considering the ordered pairs so (4, 2), (5, 1) pairs have been excluded.] Now, X & Y are co-prime numbers. Two integers A and B are said to be relatively prime or co-prime if the only positive integer that divides both of them is 1. ∴Among the three pairs there is only one co-prime pair (1, 5). ∴Only one such pair can be formed. The two numbers of the pair are 32 & (32 × 5) = 160Related questions
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