On a particular exam, the boys in a history class averaged 86 points and the girls in the class averaged 80 points...

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Wed Mar 17, 2021 7:38 am

Manhattan Prep

On a particular exam, the boys in a history class averaged 86 points and the girls in the class averaged 80 points. If the overall class average was 82 points, what was the ratio of boys to girls in the class?

A. 1:4
B. 1:3
C. 1:2
D. 2:1
E. 3:1

OA C

Solution:

We can use the following fact:

If two groups of people, A and B, have an overall average when the two groups’ scores are combined, if the positive difference between group A’s average and the overall average is assigned the value a and the positive difference between group B’s average and the overall average is assigned the value b, then the ratio between the number of people of group A to that of group B is b to a.

We see that the boys’ average of 86 points is 4 points away from the overall class average of 82 points, whereas the girls’ average of 80 points is only 2 points away from the overall class average. Therefore, the ratio of boys to girls is 2 to 4, or 1 to 2.

Answer: C