Question

Two integers have a sum of $26.$ When two more integers are added to the first two integers the sum is $41.$ Finally when two more integers are added to the sum of the previous four integers the sum is $57.$ What is the minimum number of even integers among the $6$ integers?

$1$

$2$

$3$

$4$

$5$

Answer: A

Concepts:parity

Difficulty rating: 960

Solution:

The first two integers have even sum $26$ , so they can both be odd. The next two integers have sum $41-26=15$ , which is odd, so one of them must be even and one odd.

The last two integers have sum $57-41=16$ , so they can both be odd. Therefore at least one integer must be even, and one is attainable.

Thus, A is the correct answer.

2012 AMC 10B Problem 9

Answer: A

Difficulty rating: 960

Solution:

Problem 9 in Other Years