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children in the crèche

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children in the crèche

by sanju09 » Thu Feb 09, 2012 4:46 am
Is the median age of all 65 children in a certain crèche more than 5?
I. 40 percent of all children in the crèche are more than 5.
II. 40 percent of all children in the crèche are 5.





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by MBACenter » Thu Feb 09, 2012 7:28 am
sanju09 wrote:Is the median age of all 65 children in a certain crèche more than 5?
I. 40 percent of all children in the crèche are more than 5.
II. 40 percent of all children in the crèche are 5.





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The median is defined as the 50th percentile: the term for which there is an equal number of elements in the set both less than or equal to and greater than or equal to that term.

Statement 1 is sufficient. If only 40 percent of the children are above age 5, then the 50th percentile will be at age 5 or below.

Statement 2 is not sufficient. We don't know how many of the children are younger than 5 or older than 5. If more than 10 percent are younger than 5, then the 50th percentile will be 5 or younger. If fewer than 10 percent are younger than 5, then the 50th percentile will by default be older than 5.
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by Brent@GMATPrepNow » Thu Feb 09, 2012 8:16 am
sanju09 wrote:Is the median age of all 65 children in a certain crèche more than 5?
I. 40 percent of all children in the crèche are more than 5.
II. 40 percent of all children in the crèche are 5.

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Nice question.

Target question: Is the median age of all 65 children in a certain crèche more than 5
To find the median age, we arrange all 65 children in ascending order (by age), and the median age will be the age of the middlemost (33rd) child.

Rephrase target question: Is the 33rd child older than 5?

Statement 1: 40 percent of all children in the crèche are more than 5.
In other words 26 children are older than 5.
This means that 39 children are 5 years old or younger.
So, if we arrange all 65 children in ascending order (by age), the first 39 children will be 5 years old or younger. As such, the 33rd child will not be older than 5.
Since we can definitively answer the target question, statement 1 is SUFFICIENT

Statement 2: 40 percent of all children in the crèche are 5.
In other words 26 children are 5 years old.
So, if we arrange all 65 children in ascending order (by age), there are several outcomes.
case a: 39 children are 4 years old, and 26 children are 5 years old. Median age = 4, which means the answer to the target question is no
case b: 39 children are 6 years old, and 26 children are 5 years old. Median age = 6, which means the answer to the target question is yes
Since we cannot definitively answer the target question, statement 2 is INSUFFICIENT

So, the answer is A.

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