1989 AMC 8 Problem 21

Attempt Problem 21 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).

21.

Jack had a bag of 128128 apples. He sold 25%25\% of them to Jill. Next he sold 25%25\% of those remaining to June. Of those apples still in his bag, he gave the shiniest one to his teacher. How many apples did Jack have then?
77
6363
6565
7171
111111
Answer: D
Concepts:percentage
Small hint:
Selling 25%25\% leaves 75%=3475\% = \frac{3}{4} of the apples
Big hint:
Multiply 128128 by 34\frac{3}{4} twice, then subtract the one given to the teacher
Solution:
After selling 25%25\% to Jill, Jack keeps 34×128=96\frac{3}{4} \times 128 = 96 apples. After selling 25%25\% of those to June, he keeps 34×96=72\frac{3}{4} \times 96 = 72 apples.
He then gives 11 to his teacher, leaving 72−1=71.72 - 1 = 71.
Thus, the correct answer is D .
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