"In a Small Snack Shop the Average Revenue Was $400 per Day" — GMAT® Worked Solution

From Episode 43 of Real GMAT® Problems (The GMAT® Strategy Podcast). For the full strategy behind GMAT® word problems, read: GMAT® Word Problems: Half Math, Half English, and the Setup That Prevents Translation Mistakes.

The Problem

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

In a small snack shop, the average (arithmetic mean) revenue was $400 per day over a 10-day period. During this period, if the average daily revenue was $360 for the first 6 days, what was the average daily revenue for the last 4 days?

(A) $420

(B) $440

(C) $450

(D) $460

(E) $480

Half Math, Half English Setup

Write what is given and what is asked before doing any computation.

• 10-day average = $400
• 6-day average = $360 (first six days)
• 4-day average = ? (last four days)

The structure is now visible. We have three averages, two of them given, one of them asked. The path forward is to use the average formula to convert what we know into totals — then subtract.

Step 1: Find the 10-Day Total

Average formula: sum / count = average.

Multiply both sides by 10:

sum = 400 × 10 = $4,000

That is the total revenue across all 10 days.

Step 2: Find the First-6-Day Total

Same formula. Multiply 360 × 6.

6 × 0 = 0. 6 × 6 = 36, write 6, carry 3. 6 × 3 = 18, plus the carried 3 = 21.

The product is 2,160. That is the total revenue across the first six days.

Step 3: Find the Last-4-Day Total

The last four days account for whatever is left over.

4,000 − 2,160 = 1,840

That is the total revenue across the last four days.

Step 4: Find the Last-4-Day Average

Now apply the average formula in the other direction.

1,840 / 4 = ?

4 goes into 18 four times (16), remainder 2. Bring down the 4 to make 24. 4 goes into 24 six times exactly, remainder 0. Bring down the 0. 4 goes into 0 zero times.

1,840 / 4 = 460.

The average daily revenue for the last four days is $460.

The answer is (D).

Why This Problem Matters

About 8 percent of test takers miss this question. What is interesting in the data is that the wrong answers are spread fairly evenly across the four incorrect choices — there is no single trap answer cluster.

When wrong answers are spread out, it usually means people are not making one specific conceptual mistake. They are getting confused about which average is which, losing track of a number partway through, or rushing the long multiplication and landing somewhere off by a small amount.

The fix for that pattern is the half math, half English step. Writing "10-day average = $400" and "6-day average = $360 (first six days)" on the page — with labels — removes the confusion. The brain does not have to remember which 360 belongs to which group while also doing arithmetic.

A note on the computation. The math in this problem is long multiplication (360 × 6), long subtraction (4,000 − 2,160), and long division (1,840 ÷ 4). None of it is hard. If any of those felt heavy, it is worth a quick reset on the basics — the Math Basics episodes we reference in the podcast series cover the mechanics. Most people need 10 to 20 reps to get fluent, not hundreds.

The bigger point is the workflow. Half math, half English, then equations from the formula, then computation. This same sequence handles the harder questions in the episode with only minor modifications.

Next problem: A Beverage Distributor Charges $60 per Case for 1 to 5 Cases — GMAT® Worked Solution

Back to the strategy article: GMAT® Word Problems: Half Math, Half English, and the Setup That Prevents Translation Mistakes

Episode page: Real GMAT® Problems — Ep. 43 — Word Problems