"Darra Ran on a Treadmill That Had a Readout" — GMAT® Worked Solution

From Episode 39 of Real GMAT® Problems (The GMAT® Strategy Podcast). For the full strategy behind percent word problems on the GMAT®, read: Translating Percent Word Problems on the GMAT®: A One-Word-at-a-Time System.

The Problem

Source: Retired GMAT® practice test

Darra ran on a treadmill that had a readout indicating the time remaining in her exercise session. When the readout indicated 24 minutes 18 seconds, she had completed 10% of her exercise session. The readout indicated which of the following when she had completed 40% of her exercise session?

(A) 10 minutes 48 seconds

(B) 14 minutes 52 seconds

(C) 14 minutes 58 seconds

(D) 16 minutes 6 seconds

(E) 16 minutes 12 seconds

Write What Is Given and What Is Asked

This problem is less about translation and more about reading carefully. Two words do most of the work here, and missing either one leads to a wrong answer.

The readout shows time REMAINING — not time elapsed. That is one trap.

The question asks for the readout when 40% is complete — meaning 60% remains. That is the second trap.

Write it all out before doing any math:

Given:

• Readout = time remaining (not elapsed)
• 24 min 18 sec remaining = 10% complete = 90% remaining

Asked:

• Readout when 40% complete = 60% remaining

That single line — "90% remaining" — is the bridge between the given and what is asked. Without it, the math goes off the rails.

Step 1: Set Up the First Equation

Let T be the total workout time in seconds.

90% of T is the time remaining when she has completed 10%:

⁹⁰⁄₁₀₀ × T = 24 minutes 18 seconds

Step 2: Convert 24 min 18 sec to Seconds

Use a labeled conversion. 1 minute = 60 seconds.

24 minutes × ^{60 seconds}⁄_{1 minute} = 1,440 seconds

Add the 18 seconds:

1,440 + 18 = 1,458 seconds

So:

⁹⁰⁄₁₀₀ × T = 1,458 seconds

Step 3: Solve for Total Workout Time T

Multiply both sides by ¹⁰⁰⁄₉₀:

T = 1,458 × ¹⁰⁰⁄₉₀

Simplify ¹⁰⁰⁄₉₀ = ¹⁰⁄₉:

T = 1,458 × ¹⁰⁄₉

1,458 ÷ 9 = 162

T = 162 × 10 = 1,620 seconds

That is the total workout length: 1,620 seconds (or 27 minutes).

Step 4: Calculate the Readout at 40% Complete

When Darra has completed 40%, the readout shows 60% of T remaining (NOT 40%).

Remaining = ⁶⁰⁄₁₀₀ × 1,620 seconds

Simplify ⁶⁰⁄₁₀₀ = ³⁄₅:

Remaining = ³⁄₅ × 1,620

1,620 ÷ 5 = 324

Remaining = 324 × 3 = 972 seconds

Step 5: Convert 972 Seconds Back to Minutes and Seconds

972 seconds × ^{1 minute}⁄_{60 seconds}

Divide 972 by 60:

972 ÷ 60 = 16 with a remainder

16 × 60 = 960. So 972 − 960 = 12 seconds left over.

Remaining = 16 minutes 12 seconds

The answer is (E).

Why This Problem Matters

About 31% of test takers miss this one — similar miss rate to Problem 2, but for a completely different reason.

The biggest wrong answer pattern: about 12% of test takers pick (A), 10 minutes 48 seconds.

Here is how that mistake happens. The test taker correctly sets up the first equation: 90% of T = 24 min 18 sec. They solve for T. Then they take 40% of T — not 60% — and convert back to minutes and seconds. The arithmetic is right. The setup forgot that the readout shows remaining time, not elapsed time.

This is the kind of mistake that has nothing to do with knowing the math. It is an attention-to-detail mistake. The fix is in the notation.

Three habits that prevent this:

Write "remaining" next to every time value you record. Not just on the given (24 min 18 sec remaining), but on the answer too (60% remaining = the readout we want). Two words. Saves a wrong answer.

Convert with labeled fractions. When converting between minutes and seconds, write the conversion factor with units (^{60 seconds}⁄_{1 minute}). The labels cancel like variables, which lets you see whether the conversion is going the right direction.

Resist the urge to skip computation steps under time pressure. The average time on this problem is around 2 minutes 37 seconds — quite a bit longer than Problem 2 at 1 minute 58 seconds. Most of that extra time is the unit conversion. There are no real shortcuts. Trying to do it in your head is what creates errors.

One more pattern worth noting: this problem looks short. Five sentences total. The brevity makes test takers move quickly, which is where the slip happens. On a quant problem with unusual wording — "time remaining," "completed," percentages relative to a partial workout — slow down by a beat in the setup phase and you usually save time overall.

Previous problem: If x is m% of y, then in terms of m, y is what percent of x?

Back to the strategy article: Translating Percent Word Problems on the GMAT®: A One-Word-at-a-Time System