Question

Barry wrote $6$ different numbers, one on each side of $3$ 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?

$13$

$14$

$15$

$16$

$17$

Solution:

The common sum must be odd. If the common sum were even, then the hidden numbers behind $44$ and $38$ would both have to be even primes, but there is only one even prime.

So the prime hidden behind the odd visible number $59$ must be $2$ , making the common sum $59+2=61$ .

The other two hidden primes are $61-44=17$ and $61-38=23$ .

The average of the hidden primes is $\dfrac{2+17+23}{3}=14$ .

Thus, B is the correct answer.

2006 AMC 8 Problem 25

Solution:

Problem 25 in Other Years