A teacher grades students' tests by subtracting twice the

Hi All,

This question can be solved by TESTing THE ANSWERS.

We're given a few facts about a particular test and a student who took that test:
1) The score on the test is generated by subtracting TWICE the number of incorrect responses from the number of correct responses.
2) A student answered ALL 100 questions.
3) That student earned a score of 73.

We're asked for the number of questions that the student answered correctly.

Since the number of incorrect answers is DOUBLED before that number is subtracted, it would clearly take MORE than 73 correct answers to get a score of 73 (since 27 wrong answers would end up leading to a score of 73 - 2(27) = 19).

Let's TEST Answer D: 82 correct

With 82 correct answers, we would have a score of 82- 2(18) = 46. This is TOO SMALL (it's supposed to be a score of 73). The only way to score HIGHER than 46 is with MORE correct answers. There's only one answer left...

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

BTGmoderatorLU wrote:A teacher grades students’ tests by subtracting twice the number of incorrect responses from the number of correct responses. If Student A answers each of the 100 questions on her test and receives a score of 73, how many questions did Student A answer correctly?

A. 55
B. 60
C. 73
D. 82
E. 91

We can create the following equations, in which c = the number of correct responses and w = the number of incorrect responses:

c + w = 100

w = 100 - c

and

c - 2w = 73

Substituting, we have:

c - 2(100 - c) = 73

c - 200 + 2c = 73

3c = 273

c = 91

Answer: E