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# Three math classes: X, Y, and Z, take an algebra test.

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Math Expert
Joined: 02 Sep 2009
Posts: 55681
Three math classes: X, Y, and Z, take an algebra test.  [#permalink]

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28 Jan 2019, 06:05
00:00

Difficulty:

45% (medium)

Question Stats:

64% (02:09) correct 36% (02:53) wrong based on 24 sessions

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Three math classes: X, Y, and Z, take an algebra test.
The average score in class X is 83.
The average score in class Y is 76.
The average score in class Z is 85.
The average score of all students in classes X and Y together is 79.
The average score of all students in classes Y and Z together is 81.
What is the average score for all the three classes, taken together?

A. 81
B. 81.5
C. 82
D. 82.5
E. 84.5

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Three math classes: X, Y, and Z, take an algebra test.  [#permalink]

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28 Jan 2019, 06:43
1
By using alligation, we can find that the ratio of students in each class x:y:z is 3:4:5

and the average = $$\frac{(3*83)+(4*76)+(5*85)}{3+4+5} = \frac{978}{12} = 81.5$$

B
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Joined: 04 Jan 2015
Posts: 2888
Re: Three math classes: X, Y, and Z, take an algebra test.  [#permalink]

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29 Jan 2019, 04:50

Solution

Given:
• The average score of class X = 83
• The average score of class Y = 76
• The average score of class Z = 85
• The average score of all students in X and Y together = 79
• The average score of all students in Y and Z together = 81

To find:
• The average score of all the three classes

Approach and Working:
• $$\frac{S_1}{X} = 83$$
o Implies, $$S_1 = 83X$$

• $$\frac{S_2}{Y} = 76$$
o Implies, $$S_2 = 76Y$$

• $$\frac{S_3}{Z} = 85$$
o Implies, $$S_3 = 85Z$$

$$\frac{(S_1 + S_2)}{(X + Y)} = 79$$
• Implies, $$S_1 + S_2 = 79X + 79Y$$
• Thus, 83X + 76Y = 79X + 79Y
• 4X = 3Y

$$\frac{(S_2 + S_3)}{(Y + Z)} = 81$$
• Implies, $$S_2 + S_3 = 81Y + 81Z$$
• Thus, 85Z + 76Y = 81Y + 81Z
• 4Z = 5Y

The average score of all the three classes = $$S_1 +S_2 + S_3/X + Y + Z = \frac{83X + 76Y + 85Z}{X + Y + Z}$$

• Therefore, total average score = ($$83 * \frac{3}{4} + 76 + 85 * \frac{5}{4})/ (\frac{3}{4}+ 1 + \frac{5}{4}) = \frac{163}{2} = 81.5$$

Hence, the correct answer is Option B

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Re: Three math classes: X, Y, and Z, take an algebra test.   [#permalink] 29 Jan 2019, 04:50
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