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50 students took a quiz with two questions A, B and each que

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by Max@Math Revolution » Tue Sep 24, 2019 11:57 pm
[GMAT math practice question]

50 students took a quiz with two questions A, B and each question has 10 points. 35 students solved question A correctly and 20 students solve both questions correctly. If the total average is 13 points, then how many students solved only question B correctly?

A. 4
B. 6
C. 8
D. 10
E. 12
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by Max@Math Revolution » Thu Sep 26, 2019 11:48 pm
=>

Assume x is the number of students who solved only question B correctly.
Then we have the total average (10*35 + 10x)/50 = 13 which is equivalent to
350 + 10x = 650.
=> 10x = 300
=> x = 30.

Then the number of students who solved only question B correctly is
x - 20 = 30 - 20 = 10.

Therefore, D is the answer.
Answer: D
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by deloitte247 » Fri Sep 27, 2019 10:01 pm
Let the total number of students who solved question B correctly = x
Total average = B points
Question A = 10 points * 35 students
Question B = 10 points * x
$$Total\ average=\frac{\left(10\cdot35\right)+10x}{50}=13$$
$$350+10x=650$$
$$10x=650-350=300$$
$$x=\frac{300}{10}=30$$
Given that 20 students score both questions correctly, students who solved ONLY question B correctly = x-20
=30-20
=10 (Answer = option D)
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