An instructor scored a student's test of 50 questions by

AAPL wrote:An instructor scored a student’s test of 50 questions by subtracting 2 times the number of incorrect answers from the number of correct answers. If the student answered all of the questions and received a score of 38, how many questions did that student answer correctly?

A. 19
B. 38
C. 41
D. 44
E. 46

Letting C = the number of correct answers and W = the number of incorrect answers, we can create the equations:

C + W = 50

W = 50 - C

and

C - 2W = 38

Substituting, we have:

C - 2(50 - C) = 38

C - 100 + 2C = 38

3C = 138

C = 46

Alternate Solution:

Let’s test each answer choice. Notice that the number of questions answered correctly cannot be less than or equal to the final score, thus we can immediately eliminate answer choices A and B (the number of correct answers is equal to the final score only if a student answer all questions correctly).

Answer Choice C: 41 correct answers, 9 false answers

Since 41 - 2*9 = 23, C is not the correct choice.

Answer Choice D: 44 correct answers, 6 false answers

Since 44 - 2*6 = 32, D is not the correct choice.

At this point, we know the answer must be E since we eliminated every other possibility, but let’s verify it anyway.

Answer Choice E: 46 correct answers, 4 false answers

Since 46 - 2*4 = 38, E is the correct choice.

Answer: E

If we let X equal the number of answers that are correct and W equal the number of answers that are incorrect, then we can create the following equations:
X + W = 50
basket random
W = 50 - X

and X - 2W = 38

When we make this exchange, we get:

X - 2(50 - X) = 38

X - 100 + 2X = 38

3X = 138

X = 46

scotchsure wrote: ↑

Thu Jan 12, 2023 6:17 pm

If we let X equal the number of answers that are correct and W equal the number of answers that are incorrect, then we can create the following equations:
X + W = 50

W = 50 - X

and X - 2W = 38

When we make this exchange, we get:

X - 2(50 - X) = 38

X - 100 + 2X = 38

3X = 138

X = 46

Great setup! Just to double-check: when you solve, you get X = 46 correct and W = 4 incorrect — did I follow that right? Could you walk through how you interpret “-2W” from the scoring rules?

That's a neat algebraic solution! It's definitely the most straightforward way to tackle this kind of problem. Thinking about it, you could also work backwards from the answer choices. Start with option C, for example: If 41 were correct, then 9 would be wrong, and the score would be 41 - (2 * 9) = 23. Too low! Then, try the next highest choice and repeat. Sometimes, that guess-and-check approach can be quicker.