2014-06-23 09:00:30

Kareem averaged scores of 88 on the first four tests of the school year. He has two more tests to take, each of which is worth the same number of points as each of the other four tests were. If Kareem hopes to average a 92 in the class, what must he average on the next two tests?

(A) 92
(B) 94
(C) 96
(D) 98
(E) 100

The correct answer is E
Explanation: Average is calculated by summing the individual numbers together and dividing by the number of numbers. Here, let's assume that Kareem has averaged 88 by getting 88 on each exam (it doesn't actually matter what is individual scores were, since we're going to sum them together anyway). Let x be the total points Kareem needs to average a 92 on 6 tests. That would mean that x/6 = 92. Multiply both sides by 6 to get x = 552.

That 552 is made up of 6 tests, four of which were 88 points each. Let the other two tests be scores of y.  Thus 4(88) + 2y = 552, or 352 + 2y = 552. Subtract 252 from both sides to get 2y = 200. By dividing both sides by 2, y = 100, so Kareem must average 100% on the next two exams.