"M Is the Average and the Median of the First 10 Positive Multiples of 5" — GMAT® Worked Solution
From Episode 42 of Real GMAT® Problems (The GMAT® Strategy Podcast). For the full strategy behind GMAT® statistics questions, read: GMAT® Statistics: The Average, the Median, and the Shortcut That Saves You Time.
The Problem
Source: Official Guide for GMAT® Review, 11th Edition
If m is the average (arithmetic mean) of the first 10 positive multiples of 5 and if M is the median of the first 10 positive multiples of 5, what is the value of M − m?
(A) −5
(B) 0
(C) 5
(D) 25
(E) 27.5
Listing the Set
The first 10 positive multiples of 5 are:
5, 10, 15, 20, 25, 30, 35, 40, 45, 50
The list is already in order from smallest to largest. That matters for the median.
The Brute Force Path
It is worth knowing how this looks when computed directly, even when a shortcut is available.
For the mean, we add the values and divide by 10:
5 + 10 + 15 + 20 + 25 + 30 + 35 + 40 + 45 + 50 = 275
275 / 10 = 27.5
For the median, we look at the middle of an ordered list. There are 10 values, which is an even count, so the median is the average of the two middle values — the 5th and the 6th.
The 5th value is 25. The 6th value is 30.
(25 + 30) / 2 = 55 / 2 = 27.5
So both the mean and the median are 27.5.
M − m = 27.5 − 27.5 = 0
The answer is (B).
The Shortcut
The first 10 positive multiples of 5 form an evenly spaced set. Every consecutive pair of terms differs by 5.
In any evenly spaced set, the mean is equal to the median. This is a property of arithmetic sequences.
Once we see "first 10 positive multiples of 5" and recognize it as evenly spaced, we can conclude that M and m have to be equal. The difference is 0 without computing either value.
| Method | Time | |
|---|---|---|
| Brute force | List, add, divide, find middle two, average | About 90 seconds |
| Shortcut | Recognize evenly spaced set, apply property | About 10 seconds |
Both paths land at (B). The shortcut just saves the time for harder questions later in the section.
Why This Problem Matters
This is a warm-up problem. About 10 percent of test takers miss it, often by computing the mean correctly and then averaging the wrong pair for the median — or by reaching for the average choice (27.5) instead of the difference.
Two takeaways are worth keeping.
First, the evenly spaced set property is one of the highest-leverage shortcuts in GMAT® statistics. It shows up on integer sequences, multiples problems, consecutive even or odd numbers, and a range of other setups. Recognizing the pattern is the move.
Second, knowing the brute force version still matters. When the shortcut does not apply — or when you cannot tell whether a set is evenly spaced — the average formula and the ordered-list approach are what get you the answer.
A small note for those rusty on percent and fraction arithmetic: the average formula (sum / count) is one of the foundational tools across most quant question types. The Math Basics lessons we reference in this podcast series cover the supporting computation skills if any of the long addition or long division here felt heavy.
Next problem: Five Pieces of Wood Have an Average Length of 124 Centimeters — GMAT® Worked Solution
Back to the strategy article: GMAT® Statistics: The Average, the Median, and the Shortcut That Saves You Time
Episode page: Real GMAT® Problems — Ep. 42 — Statistics