If 42.42 = k(14 + m/50), where k and m are positive

VJesus12 wrote: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

The OA is E.

What is the equation I should use to solve this PS question? How do I find k and m? Experts, I need your help.

We have 42.42 = k(14 + m/50).

4242/100 = k(14 + m/50)

2121/50 = k(14 + m/50)

2121 = k(700 + m)

3*7*101 = k(700 + m); 101 cannot be broken as it is a prime number.

* If k = 3, then m = 7 < 50, thus k + m = 10. The correct answer is E.

Since this is a PS question, we need not deliberate on this further as only one among the five options is correct; however, for the sake of understanding, we discuss the other possibilities.

* If k = 1, then (700 + m) = 2121 => m = 1421; it is not possible since m < 50.
* If k = 3, then (700 + m) = 303 => m = –397; it is not possible since m is positive.
* If k = 101, then (700 + m) = 21 => m = –679; it is also not possible since m is positive.

So, k = 3 and m = 7, thus k + m = 10.

The correct answer: E

Hope this helps!

-Jay
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Hi VJesus12,

We're told that 42.42 = (K)(14 + M/50), where K and M are POSITIVE INTEGERS and M < 50. We're asked for the value of K + M. This question can be solved with some basic arithmetic.

To start, you should think about (K)(14) and what THAT product could be.... (3)(14) = 42... which is remarkably close to what we're after, so we can 'lock in' the value for K. That leaves us with....

.42 = (3)(M/50)
21/50 = (3)(M/50)
7/50 = M/50
7 = M

Thus, K+M = 3+7 = 10

Final Answer: E

GMAT assassins aren't born, they're made,
Rich