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

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

57% (02:02) correct 42% (03:17) wrong based on 7 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
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Re: If 42.42 = k(14 + m/50), where k and m are positive integers [#permalink] New post 10 Aug 2018, 16:47
Is E is the answer?
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Re: If 42.42 = k(14 + m/50), where k and m are positive integers [#permalink] New post 11 Aug 2018, 04:42
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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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If 42.42 = k(14 + m/50), where k and m are positive integers

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