1992 AMC 8 Problem 2

Attempt Problem 2 of the 1992 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 1992 AMC 8 solutions, or check the answer key.

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

2.

Which of the following is not equal to 54?\dfrac54?
108\dfrac{10}{8}
1141\dfrac14
13121\dfrac{3}{12}
1151\dfrac15
110401\dfrac{10}{40}
Answer: D
Concepts:fraction
Small hint:
Rewrite 54\dfrac54 as the mixed number 1141\dfrac14
Big hint:
A mixed number 1ab1\dfrac{a}{b} equals 54\dfrac54 only when ab=14\dfrac{a}{b} = \dfrac14; check each choice
Solution:
Note 54=114.\dfrac54 = 1\dfrac14. Now check each choice: 108=54,\dfrac{10}{8} = \dfrac54, 114=54,1\dfrac14 = \dfrac54, 1312=114=54,1\dfrac{3}{12} = 1\dfrac14 = \dfrac54, and 11040=114=54.1\dfrac{10}{40} = 1\dfrac14 = \dfrac54.
But 115=65≠54.1\dfrac15 = \dfrac65 \neq \dfrac54.
Thus, the correct answer is D .
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