The average of several test scores is 80. After that average was calcu

VERITAS PREP OFFICIAL SOLUTION

The 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.

Given: Say total test=x
Avg of x test scores=80
So, Sum of x test scores=80x

1 make-up test is given and avg becomes 83
New sum of test scores=83(x+1)

a. make-up test score=98
So, 8ox+98=83(x+1)

we can solve & get value of x
Sufficient

b. 2 students scored 82 would not help to get an info from avg.
Insufficient

Hence A

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