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

Question

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

Source:   Nova GMAT  
Difficulty Level:   650

Mo2men · Accepted Answer

42.42 = 14K + Km/50...we can rewrite the number as follows:

42+ 0.42= 14K + Km/50........Since K is integer, then 42=14K..........K=3

0.42=Km/50......42/100=3m/50......m=7

k+m=3+7=10

Answer: E

amanvermagmat · Answer

42.42 = 42 + 0.42 = 42 + 42/100 = 42 + 21/50

Now this slightly resembles the right hand side, but still we need to change it to the form: k (14+m/50)
where k and m are positive integers. And we can see that 42 = 14*3

So, 42 + 21/50 = 3 (14 + 7/50) ... (taking out 3 common)
Hence k=3, m=7. Required sum = 3+7 = 10.

Hence  E answer

ishitam · Answer

Please explain the highlighted part.

As in , how is 42.42 = 42 + 0.42?

Mo2men · Answer

It is the same when you say 3.5. It is sum of 3 plus 0.5 . Part of the number is integer number (42) and part is decimal number (0.42)

Hope it helps.

Heseraj · Answer

We have

\frac{4242}{100}= 14k+\frac{km}{50} => 4242 = 1400k + \frac{100km}{50} => 4200+42 = 1400*(3) + 2km => 4200 + 42 = 4200 + 2(3)m => 42=6m => m=\frac{42}{6}=7

Therefore, m+k=3+7=10

Option E

In the beginning, it might seems rough but practice brings all to life.

Please   Kudos   should you like the detailed solution.

laddaboy · Answer

42.42 = 4242/100 = 2121/50 = 14K + KM/50 = (14K*50+KM)/50

=> 2121 = 14K*50 + KM = K(700+M)
3*7*101 = K(700+M) 
Since M < 50

3*707=K(700+M)

K =3 M=7 => K+M = 10

shashankism · Answer

42.42 = k(14+m/50 )
42 = 14k and 0.42 = km/50 
-> k = 3

also 
0.42 = 3*m/50 
m = 7

k+m = 10

Answer E

EMPOWERgmatRichC · Answer

Hi All,

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 would be larger than 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

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

DarleneTran · Answer

-->If N is divided by D and equals Q with the remainder R (N= DQ + R)
We can interpret 42.42 = 14k + km/50 into divisibility. According to that, we know:
+42 is divided by 14 and the result is k-->k= 3
+The remainder is 0.42 which relates to km/50-->m=3, we have k=3 from the above calculation.
-->k + m= 10

MH321 · Answer

42.42=k(14+m/50)
700k+km=50*4242/100
k(700+m)=2121
k=2121/(700+m)

Clearly, 2121 is divisible by 707. Therefore, m=7 and the numerator will be divisible by 707. 
And now, placing m=7, we get k=3

The answer is 7+3=10

Posted from my mobile device

MH321 · Answer

42.42=k(14+m/50)
700k+km=50*4242/100
k(700+m)=2121
k=2121/(700+m)

Clearly, 2121 is divisible by 707. Therefore, m=7 and the numerator will be divisible by 707. 
And now, placing m=7, we get k=3

The answer is 7+3=10

bumpbot · Answer

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If 42.42 = k(14 + m/50), where k and m are positive integers and m < 5

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