"What Percent of 30 Is 12?" — GMAT® Worked Solution

Source: Official Guide for GMAT® Review, 11th Edition

What percent of 30 is 12?

(A) 2.5%

(B) 3.6%

(C) 25%

(D) 40%

(E) 250%

Try it before reading on.

Two Ways In

Some test takers read this question and write $\frac{12}{30}$ without hesitating, reduce it to $\frac{2}{5}$ , and answer from a fraction they already know. If that came to you immediately, there's nothing here to fix. This page is for the version of the question where the first move doesn't arrive on its own, or where you landed on an answer but would like to be sure of it before moving on.

Percent questions show up throughout the quant section, and they reward a small set of fixed word translations that can be memorized once and applied every time. The rest of this solution builds that system.

The Four Translations

Four words do nearly all the work in percent translation questions:

Word	Translation
what	a new variable
percent	divide by 100
of	multiply
is	equals

Two of these deserve a second look. "What" becomes a variable you make up, usually $P$ for percent, and it has to be a new one: if the problem already uses $x$ , pick a different letter, because reusing a variable that means something else is where translation errors start. "Percent" means whatever came right before it divided by 100, so 20% is $\frac{20}{100}$ and $P$ % is $\frac{P}{100}$ .

Translating the Question One Word at a Time

Start at the left of "What percent of 30 is 12?" and move right, writing as you go:

"What" → write $P$
"percent" → turn that into $\frac{P}{100}$
"of" → write a multiplication sign
"30" → write 30
"is" → write an equals sign
"12" → write 12

Assembled in order, the question becomes:

$\frac{P}{100} \times 30 = 12$

Nothing has been solved yet, and no percent needs to feel intuitive yet. The sentence is now an equation, and the equation carries the rest.

Solving for P

Multiply both sides by 100:

$P \times 30 = 1200$

Then divide both sides by 30:

$P = 40$

The answer is (D).

The Fraction Route, and Why Both Are Worth Having

The intuitive route runs through $\frac{12}{30}$ : divide top and bottom by 6, get $\frac{2}{5}$ , and $\frac{2}{5}$ is 40% if you know your fifths. That route is fast when it comes to you, and knowing the common fraction-percent equivalences by heart is what makes it come to you. The conversions worth memorizing are the thirds, fourths, fifths, eighths, ninths, and elevenths. Sixths and sevenths rarely earn their spot, since long division can always back you up.

The long division backup for this question is small enough to show in full, $\frac{12}{30} = \frac{2}{5} = 0.4$ :

    0.4
   ----
5 ) 2.0
    2.0
    ---
     0

It's slower than memory, and it's the route that works when nothing else does. Test takers aiming above the 90th percentile tend to want both: the memorized equivalences for speed, and division they can trust when a conversion isn't on the list.

Why This Problem Matters

The answer choices are built around a flipped reading of the question. Computing $\frac{30}{12}$ gives 2.5, and that number appears twice: as (A) 2.5%, the flipped ratio read as a decimal, and as (E) 250%, the flipped ratio converted to a percent. Both answer the question "30 is what percent of 12?" The words "of 30 is" fix the direction, and the translation system fixes it mechanically, because $\frac{P}{100} \times 30 = 12$ only builds one way.

There's a second benefit to the memorized equivalences that has nothing to do with this question. Walking into the exam knowing that $\frac{2}{5}$ is 40%, fluidly, in both directions, is a confidence lift in the middle of a section that tends to take confidence out. Small stored facts pay psychological dividends along with the mathematical ones.