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A group of 4 boys and 5 girls take a test. What is the avera

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A group of 4 boys and 5 girls take a test. What is the avera [#permalink] New post   06 Jun 2020, 19:13
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GMATBusters’ Quant Quiz Question -6

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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
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D
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Raxit85
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Re: A group of 4 boys and 5 girls take a test. What is the avera [#permalink] New post   06 Jun 2020, 19:45
Suppose, the scores of the 4 boys be B1, B2, B3, B4
And, the scores of the 5 girls be G1, G2, G3, G4, G5
So, the Average score of the group =B1+B2+B3+B4+G1+G2+G3+G4+G5/9
We need to find the value of the sum (B1 + B2 + . . . + G4 + G5)
1) The average score of the boys is 23 points while the average score of the girls is 20 points means the average score of the boys is 23 points while the average score of the girls is 20 points
B1+B2+B3+B4/4=23, So, B1+B2+B3+B4=23*4
And G1+G2+G3+G4+G5/5=20, So, G1+G2+G3+G4+G5=20*5
So, B1+B2+B3+B4+G1+G2+G3+G4+G5=23*4+20*5
Therefore, we can find the value of the Average Score of the group. So sufficient.
2) If one of the girls had scored 6 points more, the average score of the group would have been 22 means if one of the girls had scored 6 points more, the average score of the group would have been 22.
Let the girl who scored 6 points be the first girl. So, her new score = G1 + 6
The new total score of the group = B1+B2+B3+B4+(G1+6)+G2+G3+G4+G5
As per Statement, B1+B2+B3+B4+(G1+6)+G2+G3+G4+G5/9=22
So, B1+B2+B3+B4+G1+G2+G3+G4+G5/9+6/9=22
Now, we can easily find the value of B1+B2+B3+B4+G1+G2+G3+G4+G5/9
So, sufficient.
Imo. D
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Re: A group of 4 boys and 5 girls take a test. What is the avera [#permalink] New post   06 Jun 2020, 20:08
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Answer:D
Let b be average score by boy and g be average score by girl
Hence Average score of the group= (4 b+5 g)/9
State:1 sufficient
given b=23,g=20
Average score of the group= (4x 23+ 5x20)/9=192/9
State:2 sufficient
One of the girl has 6 more mark means total scores increase to 4b+5g+6
22=(4b+5g+6)/9
4b+5g=22x9-6=198-6=192
(4b+5g)/9=192/9
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Re: A group of 4 boys and 5 girls take a test. What is the avera [#permalink] New post   06 Jun 2020, 20:25
Average of the group= 4* Average of Girls + 5* Average of Boys / 4+5
So we need the average of girls and the average of boys.

1) Provides the exact needed information. Sufficient.
2) Since we don't have information on the average of boys, we cannot find the answer. Not sufficient.

Answer: A
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Re: A group of 4 boys and 5 girls take a test. What is the avera [#permalink] New post   06 Jun 2020, 21:22
IMO D

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
=> 23(4)+20(5)/9 = 192/9
=> 21.33333
(Sufficient)

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+6/9=22
X+6 = 198
X = 192
Average = Total/no. Of students
192/9 = 21.3333

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Re: A group of 4 boys and 5 girls take a test. What is the avera [#permalink] New post   06 Jun 2020, 21:36
target find avg of score of group of boys & girls
#1
The average score of the boys is 23 points while the average score of the girls is 20 points
sum of score of boys = 23*4 ; 92
sum of score of girls = 20*5 ; 100
total score of group = 192 and avg ; 192/9 ; 21.3
sufficient
#2
If one of the girls had scored 6 points more, the average score of the group would have been 22
sum of score of boys + sum of score of girls +6 = 22 *9
sum of score of boys + sum of score of girls = 192
avg ; 192/6 ; 21.3
sufficient
OPTION D


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
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Re: A group of 4 boys and 5 girls take a test. What is the avera [#permalink] New post   06 Jun 2020, 21:56
D.
From 1 we get 192/3
From 2 we get 64/3

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Re: A group of 4 boys and 5 girls take a test. What is the avera [#permalink] New post   06 Jun 2020, 22:20
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

1. 4 boys avg is 23, 5 girls avg is 20. The average of the entire group can be calculated. Hence sufficient.

2. No info is given about the boys, Hence, not sufficient.

So, Option A is the correct answer
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Re: A group of 4 boys and 5 girls take a test. What is the avera [#permalink] New post   06 Jun 2020, 23:15
each statement alone is sufficient
1. 4xaverage score of boys +5x average score of girls)/9
2. (average score of group*9-6)/9
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Re: A group of 4 boys and 5 girls take a test. What is the avera [#permalink] New post   07 Jun 2020, 00:57
Given: A group of 4 boys and 5 girls take a test.
Asked: 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
Sum of scores = 4*23 + 5*20 = 92 + 100 = 192
Average score = 192/9 = 21 3/9 = 21 1/3 = 21.33
SUFFICIENT

2. If one of the girls had scored 6 points more, the average score of the group would have been 22
Sum increases by 6 points - > Average increases by 6/9 points = 2/3 points
Average score = 22 - 2/3 = 21 1/3 = 21.33
SUFFICIENT

IMO D
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Re: A group of 4 boys and 5 girls take a test. What is the avera [#permalink] New post   07 Jun 2020, 01:02
Quote:
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


D,imo

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

-- We can find the total score by boys , by girls so can find the mean of entire group .. sufficient .
2. If one of the girls had scored 6 points more, the average score of the group would have been 22

if T is the total score of the group
T+6= 22*9
we can find T . and mean score of the group . Sufficient
Hence D is my ans .
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Re: A group of 4 boys and 5 girls take a test. What is the avera [#permalink] New post   07 Jun 2020, 02:52
Let B be the Sum of Boy's Score.
G be the Sum of Girl's Score.

\(Average =\frac{ B+G}{9}\)

1. The average score of the boys is 23 points while the average score of the girls is 20 points

Sum of Boys' Score B = Average * Number of Boys.
\(\therefore Sum = 23*4 = 92\)

Sum of Girls' Score G = Average * Number of Girls.
\(\therefore Sum = 20*5 = 100\)

\(Average = \frac{92+100}{9\\
}\\
\)
Show Spoiler
(A) is Sufficient


2. If one of the girls had scored 6 points more, the average score of the group would have been 22

Thus,
\(22 = \frac{B+G+6}{9}\)

\(\therefore B+G=192\)
Show Spoiler
(B) is Sufficient
(A) & (B) is Sufficient. Thus, (D) is the answer
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Re: A group of 4 boys and 5 girls take a test. What is the avera [#permalink] New post   25 Oct 2023, 08:53
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Re: A group of 4 boys and 5 girls take a test. What is the avera [#permalink]
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