Unit 8 · Detecting Reasoning Errors

Kings County Volleyball — Qualification Overlap

Lesson 21 of 34

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About this lesson

Six groups, 15-point threshold, Fair Play Award — Lucy adds 12 + 14 + 1 = 27 finalist teams. But she’s making a classic counting mistake. Some of those teams qualify under MORE than one condition, and she’s counting them twice.

Chapters

0:00Introduction
0:21Question
1:24Strategy
2:29Step 1: Understand Lucy's calculation — and why it can go wrong
3:36Step 2: Test each option — eliminate the wrong ones
4:49Correct answer

Question

To qualify for the Kings’ County Volleyball Trophy finals, teams must meet at least one of three conditions:

  1. coming first or second in their qualifying group
  2. scoring 15 match points or more in the qualifying stages
  3. winning the ‘Fair Play Award’ in the qualifying stages

Lucy is looking at the qualifying results, and planning the final stage of the tournament.

Lucy said: “There were six groups, so twelve teams came first or second. Fourteen teams scored at least 15 match points. And of course one team won the Fair Play Award. So I should plan for 27 teams in the finals.”

Which one of the following sentences shows the mistake Lucy has made?

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