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K+N

by N:Dure » Thu Dec 23, 2010 5:59 pm
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
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by anshumishra » Thu Dec 23, 2010 6:07 pm
N:Dure wrote: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
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by N:Dure » Thu Dec 23, 2010 6:34 pm
Well played! but any easier way to get to that? cause 17 isn't only 14+3
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by anshumishra » Thu Dec 23, 2010 6:47 pm
N:Dure wrote: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 ) ?
Thanks
Anshu

(Every mistake is a lesson learned )
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