If mn ≠ 0 and 25 percent of n equals

BTGmoderatorLU wrote:Source: Official Guide
$$\text{If } mn\neq0\text{ and }25\text{ percent of } n\text{ equals }37\frac{1}{2}\text{ percent of }m, \text{ what is the value of }\frac{12n}{m}?$$
$$\text{A. }18$$
$$\text{B. }\frac{32}{3}$$
$$\text{C. }8$$
$$\text{D. }3$$
$$\text{E. }\frac{9}{8}$$

The OA is 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: (1/4)(n) = (3/8)(m)
Simplify: 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

BTGmoderatorLU wrote:Source: Official Guide
$$\text{If } mn\neq0\text{ and }25\text{ percent of } n\text{ equals }37\frac{1}{2}\text{ percent of }m, \text{ what is the value of }\frac{12n}{m}?$$
$$\text{A. }18$$
$$\text{B. }\frac{32}{3}$$
$$\text{C. }8$$
$$\text{D. }3$$
$$\text{E. }\frac{9}{8}$$

The OA is A.

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