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# An instructor gave the same test to three groups: P, Q, and R. The ave

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Math Expert
Joined: 02 Sep 2009
Posts: 58434
An instructor gave the same test to three groups: P, Q, and R. The ave  [#permalink]

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25 Sep 2018, 04:57
00:00

Difficulty:

15% (low)

Question Stats:

83% (02:10) correct 17% (03:14) wrong based on 34 sessions

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An instructor gave the same test to three groups: P, Q, and R. The average (arithmetic mean) scores for the three groups were 64, 84, and 72, respectively. The ratio of the numbers of candidates in each class who took the test was 3 : 5 : 4, respectively. What was the average score for the three groups combined?

(A) 72
(B) 75
(C) 77
(D) 78
(E) 80

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An instructor gave the same test to three groups: P, Q, and R. The ave  [#permalink]

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29 Sep 2018, 22:52
Sum=N*Mean

Sum of P=3x*64
Sum of Q=5x*84
Sum of R=4x*72

If you keep calculations till the end for sum problems you could save time

Sum of all three groups = $$3x*64+5x*84+4x*72$$
Total members in all three group=$$n = 3x+5x+4x = 12x$$

Mean of all three group = Sum/n = $$3x/12x*64+5x/12x*84+4x/12x*72 = 16+35+24$$ = 75 = Answer B
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Joined: 20 Feb 2015
Posts: 762
Concentration: Strategy, General Management
Re: An instructor gave the same test to three groups: P, Q, and R. The ave  [#permalink]

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29 Sep 2018, 23:30
Bunuel wrote:
An instructor gave the same test to three groups: P, Q, and R. The average (arithmetic mean) scores for the three groups were 64, 84, and 72, respectively. The ratio of the numbers of candidates in each class who took the test was 3 : 5 : 4, respectively. What was the average score for the three groups combined?

(A) 72
(B) 75
(C) 77
(D) 78
(E) 80

$$\frac{(3*64 + 5*84 + 4*72)}{12}$$ = (16 + 7*5 + 4*6) = 75
B
Re: An instructor gave the same test to three groups: P, Q, and R. The ave   [#permalink] 29 Sep 2018, 23:30
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