Bunuel wrote:

The average of several test scores is 80. After that average was calculated, one make-up exam was given. After the make-up exam was included with the other scores, the new average was 83. Were more than 4 tests given total?

(1) The score on the make-up exam was 98.

(2) Two students scored an 82.

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTIONThe correct answer is (A).

It helps to know that the Average = Sum / # of Terms. Plugging in what we’re given:

80 = Sum / x

80x = Sum

83 = Sum + Make-up Score / x + 1

83x + 83 = Sum + Make-up Score

Let’s substitute “80x” for the “Sum”:

83x + 83 = 80x + Make-up Score

3x + 83 = Make-up Score

To know information about the number of tests given, we need to know more about the Make-up Score. Statement (1) tells us it was 98:

3x + 83 = 98

3x = 15

x = 5. Sufficient. The answer is Yes.

If you chose (B), Statement (2) tells us the scores of two students, but it’s possible to get both a yes and a no with these numbers. We also need to know the make-up students’ score to find the total number of given tests.

If you chose (C), Statement (1) alone is sufficient. We can solve by setting up two equations with the same two variables and substituting.

If you chose (E), Statement (1) is sufficient. You may want to review the formula for mathematical mean, as well as the “n equations with n variables” concept.

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