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

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Director
Joined: 18 Feb 2019
Posts: 608
Location: India
GMAT 1: 460 Q42 V13
GPA: 3.6
A group of 4 boys and 5 girls take a test. What is the average  [#permalink]

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23 Mar 2019, 00:25
00:00

Difficulty:

45% (medium)

Question Stats:

45% (00:43) correct 55% (00:49) wrong based on 11 sessions

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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?

I. The average score of the boys is 23 points while the average score of the girls is 20 points
II. If one of the girls had scored 6 points more, the average score of the group would have been 22
Manager
Joined: 11 Feb 2013
Posts: 230
Location: United States (TX)
GMAT 1: 490 Q44 V15
GMAT 2: 690 Q47 V38
GPA: 3.05
WE: Analyst (Commercial Banking)
Re: A group of 4 boys and 5 girls take a test. What is the average  [#permalink]

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23 Mar 2019, 04:50
1
Statement 2: Sufficient
If a girl scored 6 more points, average score of the group (9 members i.e. 4 boys & 5 girls) is 22. That means total score of the group would be 22*9=198.

What's the existing situation if a single girl don't score 6 more points?
Total present score would be 6 less than the situation in which a single girl with 6 more scores.
Thus, present total= 198-6= 192.
Now, total (192) is available & number of students is also available. So, Average is definitely possible.

Statement 1: SUFFICIENT
Weighted average = {(number of girls*score of each girl)+ (number of boys*score of each boy)}/(number of girls + number of boys)

Everything needed to calculated WEIGHTED AVERAGE is readily available in Statement 1.

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Manager
Joined: 11 Feb 2013
Posts: 230
Location: United States (TX)
GMAT 1: 490 Q44 V15
GMAT 2: 690 Q47 V38
GPA: 3.05
WE: Analyst (Commercial Banking)
Re: A group of 4 boys and 5 girls take a test. What is the average  [#permalink]

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23 Mar 2019, 04:58
What we cacultate in the numerator of WEIGHTED AVERAGE formula is TOTAL in the form of {(number of girls*score of each girl)+ (number of boys*score of each boy)}.
In statement 2, total can easily be calculated from the mentioned hypothetical situation. And DENOMINATOR of weighted average has already given in the main question.

So, everything for WEIGHTED average can be found from statement 2. Thus, statement is Sufficient even without calculation.

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Re: A group of 4 boys and 5 girls take a test. What is the average   [#permalink] 23 Mar 2019, 04:58
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