el1981 wrote:
A student responded to all of the 22 questions on a test and received a score of 63.5. If the scores were derived by adding 3.5 points for each correct answer and deducting 1 point for each incorrect answer, how many questions did the student answer incorrectly?
A. 3
B. 4
C. 15
D. 18
E. 20
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 -
15There are 22 questions and total.
If the student
incorrectly answered
15 questions, we know that the student
correctly answered
7 questions.
Total score = (
7)(
3.5) - (
15)(
1) = 25.5 - 15 =
10.5Since we're told the students received a score of
63.5, we know that answer choice C is incorrect.
It's also clear that, in order to achieve a score of
63.5, the student must get
fewer than 15 questions wrong, which means we can also eliminate answer choices D and E.
MORE STRATEGY: At this point, I need only test ONE answer choice. For example, if I test answer choice A and it works, then I know the correct answer is A. Alternatively, if I test answer choice A and it doesn't work, then I know the correct answer is B. Let's test choice B -
4So, if the student
incorrectly answered
4 questions, we know that the student
correctly answered
18 questions.
Total score = (
18)(
3.5) - (
4)(
1) = 63.5 - 4 =
58.5Since we're told the students received a score of
63.5, we know that answer choice B is incorrect.
By the process of elimination, the correct answer must be A.
_________________
Brent Hanneson – Creator of gmatprepnow.com
I’ve spent the last 20 years helping students overcome their difficulties with GMAT math, and the biggest thing I’ve learned is…
Students often get questions wrong NOT because they lack the skills to solve the question, but because they don’t understand what the GMAT is testing Learn more