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20%
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x, x, x, x, 8, 8, 8, 8, 12, 12, 11,y
The twelve numbers shown represent, the ages, in years, of the twelve children in a school bus. What is the median age, in years, of the twelve children in the bus?
(1) x = 10
(2) y = 13
M36-112
The twelve numbers shown represent, the ages, in years, of the twelve children in a school bus. What is the median age, in years, of the twelve children in the bus?
(1) x = 10
(2) y = 13
M36-112
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15 Nov 2021, 08:28
Kudos
Bookmarks
Bunuel
Official Solution:
\(\{x, x, x, x, 8, 8, 8, 8, 12, 12, 11,y\}\)
The twelve numbers shown represent, the ages, in years, of the twelve children in a school bus. What is the median age, in years, of the twelve children in the bus?
The median of a list with even number of terms is the average of the two middle terms (after the numbers have been arranged in ascending/descending order).
(1) \(x = 10\)
The list in ascending order is \(\{8, 8, 8, 8, 10, 10, 10, 10, 11, 12, 12, y\}\).
Notice that irrespective the value of \(y\), the two middle terms will always be 10 and 10, making the median 10. For example, if \(y < 10\), then the list is {8, 8, 8, 8, \(y\), 10, 10, 10, 10, 11, 12, 12} (the two middle terms are 10 and 10) and if \(y \geq 10\), then the list is {8, 8, 8, 8, 10, 10, 10, 10, \(y\), 11, 12, 12} (the two middle terms are 10 and 10). Sufficient.
(2) \(y = 13\)
The list in ascending order is \(\{x, x, x, x, 8, 8, 8, 8, 11, 12, 12, 13\}\). The median can take more than one value. For example:
If \(x=10\), then the list would be \(\{8, 8, 8, 8, 10, 10, 10, 10, 11, 12, 12, 13\}\), making the median equal to 10.
If \(x=12\), then the list would be \(\{8, 8, 8, 8, 12, 12, 12, 12, 12, 12, 12, 13\}\), making the median equal to 12.
Not sufficient.
Answer: A
General Discussion
20 May 2019, 21:32
Kudos
Bookmarks
Bunuel
Median is the middlemost number when a list is arranged in ascending order, for even number of elements the median is the mean of two middlemost numbers/
Statement 1:
Y 8 8 8 8 Y 10 10 10 10 Y 11 Y 12 Y; Y represent the positions where we can put y (Y age in years so integer)
When Y<8 median is 10
When Y >12 median is 10
When y=10/11 median is still 10
When y= 9, median still 10. So sufficient.
Statement 2.
y=13
x, x, x, x, 8, 8, 8, 8, 11, 12, 12, 13; median= 8.5 for x<=8
But for x=10 we saw that median is 10. So B statement is insufficient. Only A.
