K+N

[N:Dure]

If 72.42 = k (24 + n/100), where k and n are positive integers and n < 100, then k+n =

a) 17
b) 16
c) 15
d) 14
e) 13

[anshumishra]

If 72.42 = k (24 + n/100), where k and n are positive integers and n < 100, then k+n =

a) 17
b) 16
c) 15
d) 14
e) 13

72.42 = k (24 + n/100) = 3(24+ 14/100)

=> k + n = 17

Hence Answer is A

[N:Dure]

Well played! but any easier way to get to that? cause 17 isn't only 14+3

[anshumishra]

Well played! but any easier way to get to that? cause 17 isn't only 14+3

Yes 17 could be 15 +2, 13 + 4, 11 + 6 etc.., but we got 17 as a summation of n and k.

When you have two equations in two variables , it is easy to solve both of them. Here we have One equation in two variables (AND, a big hint that n,k are integer), So the fastest way is intelligent guess.

72.42 = 72 + 0.42 = k (24 + n/100)

Wouldn't it be nice if : 24K = 72 and nk/100 = 0.42

Let's see : 24 k = 72 => k =3
3n = 42 => n = 14.

Therefore, k+n = 17.

Do you see any problem in the approach ( If you get one of the multiple choice right, why should you further solve it, just to prove that there are no other integral solution ) ?