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15 Nov 2021, 08:27
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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) \(y = 13\)
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) \(y = 13\)
15 Nov 2021, 08:27
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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
\(\{x, x, x, x, 8, 8, 8, 8, 12, 12, 11,y\}\)
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
Apoorv0194
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Schools: NUS '26 (WL) ISB '26 (D) Emory Goizueta (D) Jones '26 (A$$) UNC '26 (D) Kelley '26 (D) IESE '26 (D) Fischer'26 (D) Ross '26 (D)
GMAT Focus 1: 655 Q85 V82 DI81
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24 Oct 2025, 23:26
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I like the solution - it’s helpful. Hi, it's not mentioned that ages are integer values - what if x is 10.3/ 10.5 etc?
