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If 42.42 = k(14 + m/50), where k and m are positive integers
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10 Aug 2018, 15:16
10 Aug 2018, 15:16
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Question Stats:
66% (02:11) correct
33% (02:47) wrong based on 21 sessions
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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
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Re: If 42.42 = k(14 + m/50), where k and m are positive integers
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10 Aug 2018, 16:47
10 Aug 2018, 16:47
Is E is the answer?
Re: If 42.42 = k(14 + m/50), where k and m are positive integers
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11 Aug 2018, 04:42
11 Aug 2018, 04:42
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Expert Reply
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!
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!
