A shooting team of eight members had a competition. The top scorer got 85 points. If that person had scored 92 points, the team's…

Question

A shooting team of eight members had a competition. The top scorer got 85 points. If that person had scored 92 points, the team's average score would have been 84. What was the team's total score?

1. A. 679
2. B. 665 (Correct answer)
3. C. 666
4. D. 657

Correct Answer

Option B — 665

Detailed Solution & Explanation

The correct answer is 665.

Key Points

• This is an average and total problem.
• Use the relation Total = Average × Number of items.
• There are 8 team members.
• Suppose the top scorer had scored 92 instead of 85 — that is 7 points more (92 − 85 = 7).
• The problem says the team average would then have been 84, giving a hypothetical total of:
• 8 × 84 = 672.
• But that total includes the extra 7 points.
• The actual total (with the real score of 85) is therefore:
• 672 − 7 = 665.
• a change in one member's score changes the total by the same amount and the average by (change ÷ number of members).
• Working backwards from the hypothetical average recovers the real total.

Exam Tip

• whenever a question says 'if X had scored more/less, the average would be…', translate it into a hypothetical total and adjust by the difference.