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A group of 4 boys and 5 girls take a test. What is the average (arithmetic mean) score of the group in the test?

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by BTGmoderatorDC » Mon Aug 16, 2021 5:27 pm

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A group of 4 boys and 5 girls take a test. What is the average (arithmetic mean) score of the group in the test?
1. The average score of the boys is 23 points while the average score of the girls is 20 points
2. If one of the girls had scored 6 points more, the average score of the group would have been 22


OA D

Source: e-GMAT
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Source: — Data Sufficiency |
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Re: A group of 4 boys and 5 girls take a test. What is the average (arithmetic mean) score of the group in the test?

by swerve » Tue Aug 17, 2021 4:23 am
BTGmoderatorDC wrote: ↑
Mon Aug 16, 2021 5:27 pm
 A group of 4 boys and 5 girls take a test. What is the average (arithmetic mean) score of the group in the test?
1. The average score of the boys is 23 points while the average score of the girls is 20 points
2. If one of the girls had scored 6 points more, the average score of the group would have been 22


OA D

Source: e-GMAT
Let B represent Boys average \(= 4B\)
G represent Girls average \(= 5G\)

Statement 1: The average score of the boys is \(23\) points while the average score of the girls is \(20\) points
\(\Rightarrow 23(4)+\dfrac{20(5)}{9} = \dfrac{192}{9} \Rightarrow 21.3333.\) Sufficient \(\Large{\color{green}\checkmark}\)

Statement 2: If one of the girls had scored \(6\) points more, the average score of the group would have been \(22\)
Let \(X\) be the total of marks of Boys and Girls.
Such that \(X+\dfrac{6}{9}=22\)
\(X+6 = 198\)
\(X = 192\)
Average \(= \dfrac{\text{Total}}{\text{no. Of students}}\)
\(\dfrac{192}{9} = 21.3333\) Sufficient \(\Large{\color{green}\checkmark}\)

Therefore, D
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