"A Team Won 80% of Its First 100 Games and 50% of Its Remaining Games..." — GMAT® Worked Solution

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

During a certain season, a team won 80% of its first 100 games and 50% of its remaining games. If the team won 70% of its games for the entire season, what was the total number of games that the team played?

(A) 180

(B) 170

(C) 156

(D) 150

(E) 105

Try it before reading on.

Step 1: Write What's Given and Asked

Before setting up any equations, write down what the problem tells you and what it asks for.

Given:

• The team won 80% of its first 100 games
• The team won 50% of its remaining games
• The team won 70% of all games for the entire season

Asked: total number of games played in the season

Writing this out takes a few seconds and gives you a clear picture of what you're working with before you start computing.

Step 2: Recognize the Comparison and Set Up a Table

This problem has a clear part-to-whole structure: the first 100 games versus the remaining games, and both contribute to the total season. That's a signal to use rows and columns.

Set up the table with rows for each part of the season and columns for wins and total games:

Step 3: Fill In What You Know

Start with the information you can compute directly. 80% of the first 100 games is 80 wins:

Step 4: Assign Variables and Fill the Remaining Cells

The number of remaining games isn't given, so assign a variable. Let $r$ equal the number of remaining games. The team won 50% of those, which is $\frac{50}{100}r$ wins. Fill in the remaining row:

Step 5: Fill the Total Row

The total games played is $100 + r$, and the total wins (70% of all games) is $\frac{70}{100}(100 + r)$:

Step 6: Write the Equation

The wins from the first part plus the wins from the remaining part equal the total wins. That relationship is visible directly from the table:

$80 + \frac{50}{100}r = \frac{70}{100}(100 + r)$

Step 7: Solve the Equation

Distribute the right side:

$80 + \frac{50}{100}r = 70 + \frac{70}{100}r$

Subtract 70 from both sides:

$10 + \frac{50}{100}r = \frac{70}{100}r$

Subtract $\frac{50}{100}r$ from both sides:

$10 = \frac{20}{100}r$

Reduce $\frac{20}{100}$ to $\frac{1}{5}$:

$10 = \frac{1}{5}r$

Multiply both sides by 5:

$r = 50$

Step 8: Answer the Question Asked

The question asks for the total number of games, not the remaining games. From the table, total games equals $100 + r$:

$100 + 50 = 150$

The answer is (D).

Why This Problem Matters

About 13% of test takers miss this problem. The wrong answers are evenly distributed across the other choices, which suggests that people who miss it are getting stuck rather than falling for a specific trap. They read the problem, don't know where to start, and end up guessing.

The organizational system is what separates people who solve it from people who get stuck. The table makes the relationship between the parts and the whole visible, and the equation emerges from the structure rather than from a flash of insight. Without the table, the problem has four or five pieces of information floating around with no clear connection. With the table, each piece has a specific cell, and the connection is the sum of the parts equals the total.

Percent word problems are some of the most common in the GMAT® quant section, and the part-to-whole structure shows up across many topic areas. Building a consistent table habit for any problem with comparisons or parts of a whole will pay off across dozens of questions.

Want the full strategy behind this problem? Read: GMAT® Word Translations: Three Systems for Setup and Organization

From Episode 34 of Real GMAT® Problems (The GMAT® Strategy Podcast).

Ready for the next one? "Jack Is Now 14 Years Older Than Bill. If in 10 Years Jack Will Be Twice as Old as Bill..." — GMAT® Worked Solution.