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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