"How Many Minutes Does It Take John to Type Y Words..." — GMAT® Worked Solution

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

How many minutes does it take John to type $Y$ words if he types at the rate of $X$ words per minute?

(A) $\dfrac{X}{Y}$

(B) $\dfrac{Y}{X}$

(C) $XY$

(D) $\dfrac{60X}{Y}$

(E) $\dfrac{Y}{60X}$

Try it before reading on.

Step 1: Draw Rows and Columns

Word problems run on a setup, not a lightning strike of insight, and the setup that handles rates is a spreadsheet minus the lines: the formula across the top, one row per instance of that formula in the problem. For rates, the formula is Rate × Time = Work. The chart starts empty:

Step 2: Fill In What the Sentences Give

Two sentences, two cells. "At the rate of $X$ words per minute" fills the Rate column, and "$Y$ words" fills the Work column. Units written right next to each variable:

One cell is empty, and it sits in the Time column, which is convenient: "how many minutes" is exactly what the question wants. The chart points at the answer before any algebra has happened.

Step 3: Name the Missing Cell and Solve

Call the time $t$ minutes:

The header row converts directly into an equation:

$X \times t = Y$

Divide both sides by $X$:

$t = \frac{Y}{X}$

The answer is (B).

The units double as a check: words per minute times minutes leaves words, which matches the Work column. Had the setup been reversed, the units would come out wrong, and that's the kind of slip this chart catches on the page instead of in the score.

The Numbers Version

Variables feel slippery to plenty of smart people, and numbers work just as well here. Pick $X = 20$ words per minute and $Y = 60$ words, written somewhere separate from the chart. The chart reads $20 \times t = 60$, so $t = 3$ minutes.

Then replace $X$ with 20 and $Y$ with 60 in every answer choice, and keep the one that produces 3. Choice (B) is the only one that does. If algebra is the friction, this route is a fine default, and the chart setup stays identical either way.

Why This Problem Matters

More than 5% of test takers select (C) $XY$ on this question, which is the two givens multiplied together in the wrong roles. The math here is easy, and that's the danger: a problem that looks this simple invites rushing, and rushing under time pressure is how $Y/X$ becomes $XY$ before anyone notices.

Two habits protect against it. First, label what's given clearly while transcribing the problem, whether with rows and columns or another system that serves the same purpose of stopping organizational misses. Second, write units from the very beginning of prep, on the questions where they seem unnecessary. Speed built on skipping those steps is progress in the wrong direction, because the biggest score killer in the quant section is missing questions you know how to do. Start good and slow, and repetition should bring the speed without the misses.

Ready for the next one? "√(16 × 20 + 8 × 32) = ?" — GMAT® Worked Solution.

Want the full strategy? Read: GMAT® Quant Solution Paths: Theory, Plugging In, and Brute Force

From Episode 9 of Real GMAT® Problems (The GMAT® Strategy Podcast).