Question: If mn ≠ 0 and 25 percent of n equals \(37\frac{1}{2}\) percent of m, what is the value of \(\frac{12n}{m}\) ?
(A) 18
(B) \(\frac{32}{3}\)
(C) 8
(D) 3
(E) \(\frac{9}{8}\)
“If mn ≠ 0 and 25 percent of n equals \(37\frac{1}{2}\) percent of m, what is the value of \(\frac{12n}{m}\) ?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide 2022”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.
Solution and Explanation
Approach Solution 1:
It is given in the question that 25% of n = 37 \(\frac{1}{2}\) % of m.
So we have:
\((\frac{25}{100})\)n = \((\frac{37.5}{100})\)m
Multiplying both sides by 100, we get:
25n = 37.5m
Multiplying both sides again by 10, we get:
250n = 375m
Dividing both sides by 25, we get:
10n = 15m
that implies, 2n = 3m
Multiplying both sides by 6 to get the 12n in the numerator of \(\frac{12n}{m}\)
We get, 12n = 18m
Later dividing both sides by m, to get the value of \(\frac{12n}{m}\)
\(\frac{12n}{m}\) = 18
Hence, the required value of \(\frac{12n}{m}\) is 18.
Correct Answer: A
Approach Solution 2:
It is given in the problem,
12.5% = \(\frac{1}{8}\)
So, according to the given problem,
12.5 % *3 = 37.5% = \(\frac{3}{8}\)
that implies, 25 % of n = 37.5 % of m
that implies,\(\frac{n}{4}\) =\(\frac{3m}{8}\)
that implies, \(\frac{n}{m}\) = \(\frac{12}{8}\) =\(\frac{3}{2}\)
that implies, \(\frac{12n}{m}=12*\frac{3}{2}\) = 18
Hence, the required value of\(\frac{12n}{m}\) is 18.
Correct Answer: A
Approach Solution 3:
We have 25 percent of n equals 37 1/2 percent of m.
=> 25% of n = 37 1/2 % of m
=> (25n/100) = (75/2)% of m
=> (25n/100) = (75/2)/100 of m
=> 25n = 75m/2
=> n = 3m/2
=> n/m = 3/2
=> 12n/m = 12*(3/2) = 18
Correct Answer: A
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