Latest CAT Aptitude Question SOLUTION: How many pairs of positive integers m,n satisfies (1/m)+(4/n)=1/12, where n is an odd integer less than 60.

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How many pairs of positive integers m,n satisfies (1/m)+(4/n)=1/12, where n is an odd integer less than 60.

Asked In CAT Devendra Marghade (12 years ago)

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chaitanya  (12 years ago)

1/m = 1/12 - 4/n

Since m is positive,
n must be greater than 48.
Possible odd values of n such that 48 < n < 60 are 49, 51, 53, 55, 57 and 59 of which only 49, 51 and 57 give integral values of m.
So,there are 3 solutions

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chaitanya  (12 years ago)

The given condition is 1/m + 4/n = 1/12
= (n + 4m)12 = mn
= 12n + 48m = mn
= mn – 12n + 48m = 0
= n(m – 12) + 48 (m – 12) = 12 * 48 = 576
= (m – 12) (n + 48) = 576
Now, the prime factors of 576 which satisfy m = 12n / (n – 48) are 49, 51, and 57.

so totally three prime factors

Is this solution Helpfull? Yes (9) | No (1)  

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