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# A cookery course is divided into two groups. In group X, the average

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Math Expert
Joined: 02 Sep 2009
Posts: 52902
A cookery course is divided into two groups. In group X, the average  [#permalink]

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25 Sep 2018, 03:49
00:00

Difficulty:

15% (low)

Question Stats:

79% (01:43) correct 21% (02:07) wrong based on 32 sessions

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A cookery course is divided into two groups. In group X, the average score in the test was 76. In group Y, the average score in the test was 70. If the average score of all 30 trainees in the course was 74, how many trainees are in group X?

(A) 10
(B) 17
(C) 20
(D) 25
(E) 28

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Re: A cookery course is divided into two groups. In group X, the average  [#permalink]

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28 Sep 2018, 14:38
Let a be the number of trainees in group X

76*a + 70 (30 - a) = 30*74

76a + 2,100 - 70a = 2,220

6a = 120
a = 20

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Joined: 04 Jan 2015
Posts: 2568
Re: A cookery course is divided into two groups. In group X, the average  [#permalink]

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29 Sep 2018, 04:47

Solution

Given:
• A cookery course is divided into two groups – X and Y.
• Total trainees in two groups combined: 30.
• In group X, the average score is 76.
• In group Y, the average score is 70.
• Overall average score of two groups combined: 74.

To find:
• Number of trainees in group X.

Approach and Working:
If group X has n trainees, then group Y has (30 – n) trainees.
• Total score of group X = n x 76 = 76n
• Total score of group Y = (30 – n) x 70 = 2100 – 70n
• Total score of both groups combined = 30 x 74 = 2220

Therefore, we can write,
• 76n + 2100 – 70n = 2220
Or, 6n = 120
Or, n = 20

Hence, the correct answer is option C.

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Re: A cookery course is divided into two groups. In group X, the average   [#permalink] 29 Sep 2018, 04:47
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