JAMB 2021 Mathematics · Question 6

The mean of ten positive numbers is 16. When another number is added, the mean becomes 18. Find the eleventh number

Options

A.3
B.16
C.38
D.30

Answer: C. 38

Explanation written with AI and checked against the answer key

Analyze the question: We have 10 numbers with a mean of 16. After adding an 11th number, the mean of all 11 numbers becomes 18. We need to find that 11th number. Concept: Mean = (Sum of numbers) ÷ (Number of items), so Sum = Mean × Number of items. Solution: Step 1: Sum of the first 10 numbers = 10 × 16 = 160 Step 2: Sum of all 11 numbers = 11 × 18 = 198 Step 3: The eleventh number is the difference = 198 − 160 = 38 Check: (160 + 38) ÷ 11 = 198 ÷ 11 = 18 ✓ Answer: C. 38 Tip: For "a new number changes the mean" questions, always convert means to totals (mean × count), then subtract the old total from the new total. A quick shortcut is that the new number = old mean + (change in mean × new count) = 16 + (2 × 11) = 38.

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