Bunuel
FRESH GMAT CLUB TESTS QUESTION
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
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