2006 AMC 8 Problem 25
Attempt Problem 25 of the 2006 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 2006 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
25.
Barry wrote different numbers, one on each side of cards, and laid the cards on a table, as shown. The sums of the two numbers on each of the three cards are equal. The three numbers on the hidden sides are prime numbers. What is the average of the hidden prime numbers?
Small hint:
The common card sum must have the same parity for all three visible numbers.
Big hint:
Use the fact that is the only even prime.
Solution:
The common sum must be odd. If the common sum were even, then the hidden numbers behind and would both have to be even primes, but there is only one even prime.
So the prime hidden behind the odd visible number must be , making the common sum .
The other two hidden primes are and .
The average of the hidden primes is .
Thus, B is the correct answer.
Problem 25 in other years
- 1985 AMC 8
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