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# If the average (arithmetic mean) of the scores of x students of class

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Math Expert
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If the average (arithmetic mean) of the scores of x students of class  [#permalink]

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25 Oct 2018, 01:26
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Difficulty:

35% (medium)

Question Stats:

67% (01:03) correct 33% (01:23) wrong based on 24 sessions

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If the average (arithmetic mean) of the scores of x students of class X is 40 and the average of the scores of y students of class Y is 30, what is the average of the scores of the students of both the classes?

(1) x + y = 60
(2) x = 3y

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Re: If the average (arithmetic mean) of the scores of x students of class  [#permalink]

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25 Oct 2018, 03:22

What we are looking for here is a weighted average: we need to take into account both of the averages (which we have), and the relative size of each group (which we don't).
1) doesn't give us this - the total number of students gives us no info about the relative die of each group.
2) does - if x is 3 times the size of y, then we will give it 3 times the weight. This is all we need! Answer B.

(Just to show the calculation: the weighted average = (40*3+30)/4 = 150/4=37.5.)
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Re: If the average (arithmetic mean) of the scores of x students of class  [#permalink]

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25 Oct 2018, 05:25

Solution

Given:
• The average of the scores of x students of Class X = 40
• The average of the scores of y students of Class Y = 30
To find:
• The average of the scores of the students of both the classes
Approach and Working:
• Average of the scores of both classes = Sum of the scores of all students/total number of students = $$\frac{(40x + 30y)}{(x + y)}$$

Analysing Statement 1
• Given, x + y = 60
• Thus, average of all scores = $$\frac{[10x + 30(x + y)]}{(x + y)} = \frac{(10x + 30*60)}{60}=\frac{(x + 180)}{6}$$

We do not have any further information about x

Therefore, Statement 1 alone is not sufficient to answer this question

Analysing Statement 2
• Given, x = 3y
• Substituting x = 3y, we get,
o Average of the scores of both the classes =$$\frac{[40(3y) + 30y]}{(3y + y)} = \frac{150y}{4y} = 37.5$$

Therefore, Statement 2 alone is sufficient to answer this question

Hence, the correct answer is Option B

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Re: If the average (arithmetic mean) of the scores of x students of class &nbs [#permalink] 25 Oct 2018, 05:25
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