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10 Nov 2022, 07:41
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List L consists of 11 different positive numbers. The sum of the 6 smallest numbers in L is 35, and the sum of the 6 greatest numbers in L is 125. If the sum of all the numbers in L is 142, what is the median of the numbers in L?
A. 17
B. 18
C. 19
D. 20
E. 21
A. 17
B. 18
C. 19
D. 20
E. 21
10 Nov 2022, 08:19
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Bunuel
List L consists of 11 different positive numbers. The sum of the 6 smallest numbers in L is 35, and the sum of the 6 greatest numbers in L is 125. If the sum of all the numbers in L is 142, what is the median of the numbers in L?
A. 17
B. 18
C. 19
D. 20
E. 21
A. 17
B. 18
C. 19
D. 20
E. 21
We know there are 11 numbers in the list.
Let's list these down
A B C D E F G H I J K
Median = F
Given
A + B + ..+ F = 35 --- (1)
K + J + .. + G + F = 125 --- (2)
A + B + .. + J + K = 142
Note, the median F gets counted in the sum of both the equations (1) and (2)
Hence when we add 1 and 2, basically we are adding all the numbers + K
142 + K = 160
K = 18
IMO B
13 Feb 2025, 09:28
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Good sets problem. Look at the overlap between bottom 6 and top 6:
