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

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards