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Moussaillon
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Moussaillon
On a certain quiz with 25 questions, each correct answer is scored 4 points and each incorrect answer is scored –1 point. Questions not answered receive no points. A student who answered 23 questions and had a total score of 82 points answered how many questions correctly?

A - 18
B - 19
C - 20
D - 21
E - 22

Solution:

Let n be the number of questions he answered correctly, and thus (23 - n) is the number of questions he answered incorrectly. We can create the equation:

4n - 1(23 - n) = 82

4n - 23 + n = 82

5n = 105

n = 21

Answer: D
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Trying each answer choice is a waste of time. Let us make a system of equations :)

C = number of correct answers
I = number of incorrect answers
C + I = 23

We know that each correct answer is +4 and each incorrect answer is -1... we also know that the total earned points is 82
4C - I = 82

Now, add both sides of both equations:
C + I + 4C - I = 82 + 23

5C = 105

C = 21 (we know 100/5 = 20 and we have 5 left over and 5/5 = 1... 20 + 1 = 21)
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Automated notice from GMAT Club BumpBot:

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