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need expert help - fastest way to solve this problem

by voodoo_child » Sun May 06, 2012 5:35 am
Table shows average age of students with the number of students.

Age of student - 11 10 8 7
# of students - 4 5 n 3

If average of the students' ages was greater than the median age, what is the smallest possible value of n?

a-2
b-3
c-4
d-5
e-6

OA - e

Any help?
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by aneesh.kg » Sun May 06, 2012 6:51 am
For the options given,
As n increases from 2(option A) to 5(option D), the median is 10 but the mean increases.

for n = 2 (Option A), Average = (44 + 50 + 16 +21)/14 = 131/14 (which is smaller than 10)
Now as increase n by 1, we're adding a 8 to the Sum and thus the average will only decrease below the value above.

So, options (A) to (D) are ruled out.
We don't need to verify option (E) as there is just one correct answer.

[spoiler](E)[/spoiler] is the answer.

By the way, when n = 6 the median drops to 9. So, it's possible that average is above 9 in this case. But there is no point calculating it because it doesn't matter.
Aneesh Bangia
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