Acer86 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
STRATEGY: As with all GMAT Problem Solving questions, we should immediately ask ourselves, Can I use the answer choices to my advantage?
In this case, we can easily test the answer choices.
At this point, we should typically give ourselves 15 to 20 seconds to identify a faster approach, but testing the answer choices will be incredibly easy, and I'm pretty sure I'll need to test 2 answer choices at most. So, I'll start testing the answer choices immediately.We'll start with answer choice C -
41There are 50 questions and total.
If the student
correctly answered
41 questions, we know that the student
incorrectly answered
9 questions.
Total score =
41 - (
2)(
9) = 41 - 18 =
23Since we're told the students received a score of
38, we know that answer choice C is incorrect.
It's also clear that, in order to achieve a score of
38, the student must get
more than 41 questions right, which means we can also eliminate answer choices A and B.
MORE STRATEGY: At this point, I need only test ONE answer choice. For example, if I test answer choice D and it works, then I know the correct answer is D. Alternatively, if I test answer choice D and it doesn't work, then I know the correct answer is E. Let's test choice D -
44So, if the student
correctly answered
44 questions, we know that the student
incorrectly answered
6 questions.
Total score =
44 - (
2)(
6) = 44 - 12 =
32Since we're told the students received a score of
38, we know that answer choice D is incorrect.
By the process of elimination, the correct answer must be E.