In a high school class, the average score on a test among girls was 92

Question

In a high school class, the average score on a test among girls was 92.6, while the average score among boys was 83.0. The average score for the class was 89. If there are 16 students in the class, which of the following represents the relationship between the number of girls (g) and boys (b) in the class?

A. g+4=b

B. g+2=b

C. g=b

D. g - 2=b

E. g - 4=b

A. g+4=b
B. g+2=b
C. g=b
D. g - 2=b
E. g - 4=b

vishalkazone · Accepted Answer

G/B = Avg score of class- Avg of boy score/ avg score of girl - Avg score of class
 = 89-83/ 92.6-89
 = 6/3.6
 = 5/3
Total 16 student so 10 girl and 6 boys.

G-4= B
Option E

GMATinsight · Answer

Average of Girls = 92.6
Number of girls = g
i.e. Total score of all girls = 92.6*g

Average of Boys = 83
Number of girls = b
i.e. Total score of all girls = 83*b

Also, b+g = 16

And, total of entire class = 89*(b+g) = 92.6g + 83b

i.e. 6b = 3.6g
i.e. b = (3/5)g

b+g = 16
i.e. (3/5)g + g = 16
i.e. g = 10
and b = 6

i.e. b = g-4

Answer: Option E

ScottTargetTestPrep · Answer

Since the overall class average (89) is closer to the girls’ average (92.6) than it’s to the boys’ average (83), there must be more girls than boys. This narrows to choice D or E as the correct answer. If choice D is the correct answer, then we have:

b + g = 16

g - 2 + g = 16

2g = 18

g = 9

So b = 16 - 9 = 7. Now let’s check the overall class average by calculating the weighted average:

Average = (9 x 92.6 + 7 x 83)/16 = 1414.4/16 = 88.4

Answer choice D does not yield the given overall class average of 89. So the correct answer must be E.

Answer: E

RushGum · Answer

Given the fact that we can narrow the answers down to D and E based on the overall average being closer to the girls average (requiring g>b), can you simply take that fact that, given the restriction of 16 students, girls will be 10 in order to get an integer sum of 16*89?

Bunuel · Answer

Yes, that shortcut works.

Since the overall average is closer to the girls’ average, we know g > b, so the only possibilities are:

g = 9, b = 7
or
g = 10, b = 6.

The total class score is 16 * 89, which is an integer. The boys’ total score, 83b, is also an integer whether b = 7 or b = 6.

Therefore, the girls’ total score, 92.6g, must also be an integer.

92.6 * 9 is not an integer, while 92.6 * 10 is.

So g = 10 and b = 6.

Answer: E.

IshmaelJN · Answer

Boys = B // Girls =g

b+g=16--> b=16-g

92.6g+83b=89g+89b

3.6g=6b-->3.6g=6(16-g)--> 3.6g=96-6g--> 9.6g=96 --> g=10

b=16-g--> b=16-10--> b=6

Then try all the answers.

Answer E) g-4=b--> 10-4=6 CORRECT

In a high school class, the average score on a test among girls was 92

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