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A good practice prob:

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by \'manpreet singh » Wed Sep 04, 2013 9:23 pm
If 42.42 = k(14 + m/50), where k and m are positive integers and m < 50, then what is the value of
k + m ?

(A) 6
(B) 7
(C) 8
(D) 9
(E) 10

Ans E
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by vipulgoyal » Wed Sep 04, 2013 9:30 pm
If 14k = 42 and mk/50 = 42/100 = 21/50, then it will satisfy the given equation.

14k = 42 => k = 3
mk = 21 => 3m = 21 => m =7

Hence; m+k = 10.
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by [email protected] » Wed Sep 04, 2013 11:40 pm
Hi manpreet singh,

Vipulgoyal's solution is correct. I wanted to take a moment to point out the pattern that exists in this question, so that you can look for other patterns in the future.

The answer choices for this question are remarkably small (6 - 10).

If you combine this information with what you're given in the equation, you'll see that...

14K + 14(m/50) = 42.42

The ONLY way to keep the numbers small and integers is if

14K = 42, so the K MUST = 3.

From there, it's just a bit of math to either solve for M (since 14M/50 = .42) or TEST THE ANSWERS to figure out which value for M (3 through 7, based on K = 3) would match.

Sometimes TESTING THE ANSWERS is faster than doing the conventional math.

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