12n/m = ?

[AbeNeedsAnswers]

If mn ≠ 0 and 25 percent of n equals 37 1/2 percent of m, what is the value of 12n/m?

A) 18
B) 32/3
C) 8
D) 3
E) 9/8

A

[Jay@ManhattanReview]

If mn ≠ 0 and 25 percent of n equals 37 1/2 percent of m, what is the value of 12n/m?

A) 18
B) 32/3
C) 8
D) 3
E) 9/8

A

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

The correct answer: A

Hope this helps!

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-Jay
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[ceilidh.erickson]

One strategy you should always employ on PS: scan the answer choices & think logically / try to estimate before diving into solving.

If 25% of n = 37.5% of m, (i.e. a smaller percentage of n = a larger percentage of m), then n must be larger than m. (Assuming positive values. If n and m were negative, this would make n less than m, but with a larger absolute value. This is the same idea for our analysis here).

Therefore, n/m must be greater than 1, so 12n/m must be greater than 12. Or another way to estimate it: 12 times a larger number divided by the smaller number must be larger than 12.

Eliminate any answer choice less than 12:
A) 18 --> maybe
B) 32/3 --> this is a little less than 11 (33/3). Eliminate.
C) 8 --> eliminate
D) 3 --> eliminate
E) 9/8 --> barely greater than 1. Eliminate.

The only answer greater than 12 is A, so that must be the answer! We didn't have to calculate.

Estimation like this will of course not get you all the way to the right answer on every single problem, but it's a good practice to get into. It can save time on questions like this, and help to prevent mistakes on other problems.

More here: https://www.manhattanprep.com/gmat/blog ... -pen-down/

And please edit your post to list your source!

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Hi AbeNeedsAnswers,

Sometimes the 'key' to answering a Quant question quicker is to 'convert' whatever data you've been given into a different format. For this question, I'm going to convert the percents into small fractions.

We're told that 25% of N = 37.5% of M....

That can be rewritten as....

(1/4)(N) = (3/8)(M)

If we multiply both sides by 8, we get...

2N = 3M

The question asks for the value of 12N/M

Since 2N = 3M....
12N = (6)(2N) =
6(3M) =
18M

So the question is really asking for the value of 18M/M.... and since M cannot be 0, the value of that fraction is 18.

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

[Matt@VeritasPrep]

(1/4)n = (3/8)m

n = (3/2)m

Substituting (3/2)m for n, we get

12n/m =>

12 * (3/2)m / m =>

12 * (3/2) =>

18.

[Matt@VeritasPrep]

Alternatively, just pick valid numbers for n and m, then plug them into 12n/m.

Say n = 3 and m = 2. From there, 12n/m = 12*3/2, or 18.

[Scott@TargetTestPrep]

If mn ≠ 0 and 25 percent of n equals 37 1/2 percent of m, what is the value of 12n/m?

A) 18
B) 32/3
C) 8
D) 3
E) 9/8

We are given that 25 percent of n = 37 1/2 percent of m. So, we have:

(25/100)n = (37.5/100)m

We can multiply both sides by 100:

25n = 37.5m

We can multiply both sides by 10:

250n = 375m

We can divide both sides by 25:

10n = 15m

2n = 3m

We can multiply both sides by 6 to get the 12n in the numerator of (12n)/m:

12n = 18m

Now divide both sides of the equation by m:

(12n)/m = (18m)/m = 18

Answer: A

[Brent@GMATPrepNow]

If mn ≠ 0 and 25 percent of n equals 37 1/2 percent of m, what is the value of 12n/m?

A) 18
B) 32/3
C) 8
D) 3
E) 9/8

A

Useful conversions:
25% = 1/4
37.5% = 3/8

25 percent of n equals 37(1/2) percent of m
In other words, 1/4 of n equals 3/8 of m
We get: n/4 = 3m/8

What is the value of 12n/m?
Take n/4 = 3m/8
Cross-multiply to get: (8)(n) = (3m)(4)
Simplify: 8n = 12m
Divide both sides by m to get: 8n/m = 12 [ALMOST THERE!!!]
Multiply both sides by 1.5 to get: 12n/m = 18

Answer: A

Cheers,
Brent