1989 AMC 8 Problem 8

Attempt Problem 8 of the 1989 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1989 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

8.

What is the value of
(2×3×4)(12+13+14)?(2 \times 3 \times 4)\left(\frac{1}{2} + \frac{1}{3} + \frac{1}{4}\right)?
11
33
99
2424
2626
Answer: E
Concepts:distributive propertyfraction
Small hint:
2×3×4=24;2 \times 3 \times 4 = 24; distribute it across the three fractions
Big hint:
24⋅12+24⋅13+24⋅1424 \cdot \frac{1}{2} + 24 \cdot \frac{1}{3} + 24 \cdot \frac{1}{4}
Solution:
Since 2×3×4=24,2 \times 3 \times 4 = 24, distribute it over the sum: 24⋅12+24⋅13+24⋅14.24 \cdot \frac{1}{2} + 24 \cdot \frac{1}{3} + 24 \cdot \frac{1}{4}.
This equals 12+8+6=26.12 + 8 + 6 = 26.
Thus, the correct answer is E .
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