If mn ≠ 0 and 25 percent of n equals 37(1/2) percent of m, what is the

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25 % of n = 37 (1/2) % of m , this means n>m

n/m > 1 ; 12 (n/m) > 12

there is only 1 option greater than 12. i.e 18

Answer = 18

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

Finally, divide both sides by m, obtaining the value of (12n)/m:

(12n)/m = 18

Answer: A
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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:

Cheers,
Brent

I'm totally stuck with arithmetic in this question. I will be very grateful for explanation why exactly I get another result. Can't see it on my own.
I start with (1/4)*n=(37/100)*(1/2)*m and get (1/4)*n=(37/200)*m. Then I continue with 200n=37*4*m and divide both sides by 2 and get 100n=75n. This equation I divide by 100, resulting in n=(3/4)m. Here I substitude for m and get that 12n=12*(3/4)m=9m, and it comes that 9m/m=9.
Where am I lost?

37(1/2) % of m = 37.5 % of m = 75/2 * of m

You have incorrectly assumed it to be (37/100)*(1/2)*m = 18.5% of m.

Hope this helps.

25n/100 = 37.5m/100
25n = 37.5m
25n/m = 37.5
12.5n / m = 18.45
12n/m = 18 (no need to calculate all other option not at all close to 18)

Answer: Option A

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Why n/4 = (75/2)m is not giving us the result? By converting it to the fraction, the process should be same but it the result is the same?

you are missing the % part here, when you do 25% of n it becomes n / 4. But when you are calculating % on the rightside you are missing to divide by 100. Your right hand side should give you (37*2) + 1 and then divide by 100 which is (74+1)/ 2 * 100 which is 75/200.

n/4 = 75m/200

n/2 = 75m/100
n/2 = 3m/4
12n/m = 6 *12/4 = 18

I’ll try to explain a reasoning-based approach to solving this question. This approach would require a clear understanding of what percentages represent.

Let's compare incomes - mine with Jeff Bezos's. He's the richest man in the world in 2021 according to Forbes. I am ... not.

So,
1. Would his income be a fraction of mine?
2. Or, would my income be a fraction of his?

The latter, right? Not just that, my income would be a very small fraction of his. In percentage terms, 100% of my income would be equivalent to ~0.0...1% of Bezos's income. Makes sense?

Now, let’s talk about cakes for a bit.

We have two cakes.
Half of the first cake weighs the same as the full second cake.
Based on this statement, can you understand which cake would be bigger?
A fraction of one cake weighs the same as a full cake. So the first cake must have been the bigger one. After all, we just needed a fraction of the first to be equivalent to the full second one.

Next,
Say, a quarter of the first cake weighs the same as half of the second cake.
Now, can you understand which cake would be bigger?
A smaller portion of the first cake weighs the same as a larger portion of the second. So, the first cake must be bigger.

Back to the question.

A smaller percentage of n is equivalent to a larger percentage of m.
Based on this information, can you understand which of n and m would be greater?
'n' would be greater.

We need to figure out 12xn/m. If n > m, n/m > 1.

So, we're looking for 12 times [something more than 1]. Thus, the result will be greater than 12. Answer choices, 32/3, 8, 3, and 9/8 are all smaller than 12 and can be eliminated. We're left with only one answer choice that's greater than 12. So, 12n/m must be 18.

If mn ≠ 0 and 25 %of n equals 37.5 % of m, what is the value of 12n/m ?

12.5% = 1/8

12.5 % *3 = 37.5%= 3/8

25 % of n = 37.5 % of m

n/4 = 3m/8

n/m = 12/8 = 3/2

12n/m = 12* 3/2 = 18

Option A is the answer.

Thanks,
Clifin

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