2008 AMC 8 Problem 24
Attempt Problem 24 of the 2008 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 2008 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
24.
Ten tiles numbered through are turned face down. One tile is turned up at random, and a die is rolled. What is the probability that the product of the numbers on the tile and the die will be a square?
Answer: C
Small hint:
There are equally likely tile-die pairs.
Big hint:
For each die roll, count tile numbers that make the product a square.
Solution:
If the rolled number was then the tile can be yielding combinations.
If the rolled number was then the tile can be yielding combinations.
If the rolled number was then the tile can be yielding combination.
If the rolled number was then the tile can be yielding combinations.
If the rolled number was then the tile can be yielding combination.
If the rolled number was then the tile can be yielding combination.
The total number of combinations is There are combinations each with equal likelihood, so the probability is
Thus, the answer is C .
Problem 24 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
- 1994 AMC 8
- 1995 AMC 8
- 1996 AMC 8
- 1997 AMC 8
- 1998 AMC 8
- 1999 AMC 8
- 2000 AMC 8
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