IIIT PGEE 2019

Question

How many pairs of positive integers do $m$ and $n$ satisfy in $\frac{1}{m}+\frac{4}{n}=\frac{1}{12}, $ where $n$ is odd and less than $60?$

• A. 3
• B. 5
• C. 7
• D. 9

Comments

see this https://aptitude.gateoverflow.in/4768/cat-2007-06?show=4773#a4773

Answer 1

Answer : 3 pairs

1/m + 4/n = 1/12

1/m = 1/12 - 4/n = (n-48)/12n

m= 12n / (n-48)

so we can say that n>48

given that n is odd and less than 60 i.e  possible odd values of n are 49,51,53,55,57,59

48<n<60

when n=49

m=12*49=588

when n=51

m=12*51/3=204

when n=53

m= non integer value

when n=55

m=non integer value

when n=57

m=76

when n=59

m=non integer value

so the pairs are (49,588) , (51,204) and (57,76)

Answer 2

vThere are the pair of sets with 49,51,57.