Here is a simple test question:
The average of 5 different integers is 33. The smallest of the 5 integers is 30. The largest of the five integers is N. How many possible values of N are there?
A. 3
B. 6
C. 5
D. 4
E. 7
It seems pretty simple question, but I cannot get the right answer. Here is a solution.
Let the integers be $a_1, a_2, a_3, a_4, a_5$ and let $a_1=30$ be the smallest of 5. So, $a_2 + a_3 + a_4 + a_5 = 33*5-30=135$. If we brute-force the solution, we will have:
$31 + 32 + 33 + 39 = 135$
$32 + 33 + 34 + 36 = 135$
Which gives only $2$ possible solutions, but there is no choice of 2. What am I missing?
