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Need an elegant solution

by nuranes » Sun Mar 16, 2014 12:34 am
Help...
Have the foll. question:

6. If 42.42 = k(14 + m/50), where kand 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

Need a solution which does not use the substitution method...

Thanks...
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by GMATGuruNY » Sun Mar 16, 2014 3:49 am
nuranes wrote:If 42.42 = k(14 + m/50), where kand 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
42.42 = k(14 + m/50)

4242/100 = k * (700+m)/50

2121/50 = [k * (700+m)]/ 50

2121 = k * (700 + m)

3 * 707 = k * (700+m).

Thus:
k=3, m=7, and k+m = 10.

The correct answer is E.
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by theCodeToGMAT » Sun Mar 16, 2014 9:35 am
42.42 = k(14 + m/50)

4242 = 1400k + 2mk

Since, k & M are integers.. then the possible combination is:

4242 ==> 1400*3 + 2*7*3

k = 3, m = 7

k + m = 10

[spoiler]{E}[/spoiler]
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by [email protected] » Sun Mar 16, 2014 9:20 pm
Hi nuranes,

This question has a number of built-in limitations that you can take advantage of that will allow you to really minimize the amount of math that is required.

We're told that K and M are POSITIVE INTEGERS and M < 50.

We're also told that 42.42 = K(14+m/50), which we can rewrite as...

42.42 = 14K + KM/50

Since both variables are positive integers, K MUST be 1, 2, or 3 (otherwise the total we go over 42.42...

Since M < 50, then M/50 is < 1, so it's likely that K = 3. This tells us that...

.42 = 3M/50

Now the math will only take a few steps...

21 = 3M

7 = M

The value of K + M = 10

Final Answer: E

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