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

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Intern
Joined: 10 Jun 2018
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If 42.42 = k(14 + m/50), where k and m are positive integers [#permalink]  10 Aug 2018, 15:16
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Question Stats:

61% (02:14) correct 38% (02:48) wrong based on 13 sessions
If $$42.42 = k(14 + \frac{m}{50})$$, 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
[Reveal] Spoiler: OA
Intern
Joined: 07 Jul 2018
Posts: 9
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Kudos [?]: 5 [0], given: 1

Re: If 42.42 = k(14 + m/50), where k and m are positive integers [#permalink]  10 Aug 2018, 16:47
Retired Moderator
Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Kudos [?]: 2976 [1] , given: 394

Re: If 42.42 = k(14 + m/50), where k and m are positive integers [#permalink]  11 Aug 2018, 04:42
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Expert's post
This does not look like an authentic GRE question!

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

or $$4242 = 100 \times k(14 + m/50)$$

or $$4242 = 1400k + 2km$$

Clearly we have 1 equation and 2 variables so it is unsolvable but it is also given that k and m are integers. The only option left is plugging.

This is where it gets tricky see k and m are integers less than 50 so the term 2km will be smaller than the term 1400k. So ideally we want to get close 4242 with a suitable value of k.

Choosing k=3.

$$1400*k=1400*3=4200$$

Now remaining 42 needs to come from $$2km$$ or $$2km=42$$ or $$2\times 3 \times m=42$$ or $$m=7$$.

Hence k=3 and m=7.

$$k+m=10$$

Hence option E is correct!
_________________

Sandy
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Re: If 42.42 = k(14 + m/50), where k and m are positive integers   [#permalink] 11 Aug 2018, 04:42
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