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23 students appeared for the Geography paper. What is the sum of marks

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Math Expert
Joined: 02 Sep 2009
Posts: 59622
23 students appeared for the Geography paper. What is the sum of marks  [#permalink]

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21 Nov 2019, 03:28
00:00

Difficulty:

45% (medium)

Question Stats:

56% (01:30) correct 44% (01:31) wrong based on 24 sessions

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23 students appeared for the Geography paper. What is the sum of marks obtained by them?

(1) The average mark obtained by the students equals the median mark obtained by the students

(2) The top 12 students have an average of 84 marks and the bottom 12 students have an average of 62 marks

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Intern
Joined: 29 May 2019
Posts: 6
23 students appeared for the Geography paper. What is the sum of marks  [#permalink]

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21 Nov 2019, 04:38
Need to find:
$$S_1$$ + ... + $$S_2_3$$ = ?
Assuming $$S_1$$... $$S_2_3$$ to be in ascending order.

Statement 1:
$$S_1$$ + ... + $$S_2_3$$ = $$23S_1_2$$ ->(1)
Not sufficient

Statement 2:
$$S_1$$ + ... + $$S_1_2$$ = 744 -> (2)
$$S_2_3$$ + ... + $$S_1_2$$ = 1008 ->(3)

$$S_1$$ + .. + 2$$S_1_2$$ .. + $$S_2_3$$ = 1752
Not sufficient

From (1)
$$(24)S_1_2$$ = 1752
$$S_1_2$$ = 73
Therefore, $$S_1$$ + ... + $$S_2_3$$ = 1679

Ans: C
Director
Joined: 24 Nov 2016
Posts: 935
Location: United States
Re: 23 students appeared for the Geography paper. What is the sum of marks  [#permalink]

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22 Nov 2019, 07:26
Bunuel wrote:
23 students appeared for the Geography paper. What is the sum of marks obtained by them?

(1) The average mark obtained by the students equals the median mark obtained by the students

(2) The top 12 students have an average of 84 marks and the bottom 12 students have an average of 62 marks

average=sum/n

(1) The average mark obtained by the students equals the median mark obtained by the students insufic

average=median; median = 12th highest mark

(2) The top 12 students have an average of 84 marks and the bottom 12 students have an average of 62 marks insufic

average of marks from 1 to 12 = 62; sum without median = 12(62)-m
average of marks from 12 to 23 = 84; sum without median = 12(84)-m

(1&2) sufic

average=sum/n
m=[12(62)-m+12(84)-m+m]/23
23m=12(62+84)-m
24m=12(146)
m=12(146)/24=146/2=73
sum=average•n=73•23=1679

Ans (C)
Re: 23 students appeared for the Geography paper. What is the sum of marks   [#permalink] 22 Nov 2019, 07:26
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