Latest Elitmus Aptitude Question SOLUTION: how many pairs of positive integers m,n satisfy 1/m + 4/n = 1/12 op: 3,4,5,6,7

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(#M40151537) ELITMUS Category question Keep an EYE

how many pairs of positive integers m,n satisfy
1/m + 4/n = 1/12

op: 3,4,5,6,7

Asked In Elitmus rohit sharma (9 years ago)

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siddharth prakash singh  (9 years ago)

I think question is incomplete. There was condition given as n is odd integers less than 60.
on solving above eq we get
12n + 48m =mn
mn - 12n - 48m = 0
adding 576 both sides, we get
mn - 12n - 48m + 576 =576
(m-12)(n-48)=576
since 576= 2^6*3^2
so there are 7*3 = 21 factors.
(so there are 21 natural no solutions of given ques without condition of n is odd integers less than 60. But there is not such option given hence ques is incomplete)
now if n-48 is even then
n=even+48 =even
but we req to have n as odd ( missing condition in above ques)
so n-48 = odd
now
(n-48) * (m-12)= 2^6*3^2
(n-48) * (m-12)= 1*(2^6*3^2),,,, [n-48=1] so [n=49

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padam singh ahlawat  (9 years ago)

1/m+4/n=1/12
1/m=1/12-4/n
n-48/12n
m= 12n/n-48
positive integral values of m for odd integral values of n are :
n=37,49,51
therefore 3 pairs are possible

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rohit sharma  (9 years ago)

* n is odd integer and < 60

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sivaramakrishna  (9 years ago)

so...576=2^6*3^2
n-48 should be odd
so..n-48 should be either 3^0 or 3^1 or 3^2.
total 3 ways.

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