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Source: — Data Sufficiency |
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by ankur.agrawal » Tue Feb 15, 2011 9:26 am
[spoiler]IMO 'C'[/spoiler]

gmatapril wrote:Given the ascending set of positive integers {a, b, c, d, e, f}, is the median greater than the mean?

(1) a + e = (3/4)(c + d)

(2) b + f = (4/3)(c + d)
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by gmatapril » Tue Feb 15, 2011 11:23 am
can you please explain your answer


ankur.agrawal wrote:[spoiler]IMO 'C'[/spoiler]

gmatapril wrote:Given the ascending set of positive integers {a, b, c, d, e, f}, is the median greater than the mean?

(1) a + e = (3/4)(c + d)

(2) b + f = (4/3)(c + d)
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by GMATGuruNY » Tue Feb 15, 2011 12:10 pm
gmatapril wrote:Given the ascending set of positive integers {a, b, c, d, e, f}, is the median greater than the mean?

(1) a + e = (3/4)(c + d)

(2) b + f = (4/3)(c + d)
Median = (c+d)/2
Average = (a+b+c+d+e+f)/6

Median > Average
(c+d)/2 > (a+b+c+d+e+f)/6
3c + 3d > a+b+c+d+e+f
2c + 2d > a+b+e+f
2(c+d) > a+b+e+f

Thus, the question can be rephrased:

Is 2(c+d) > a+b+e+f?

Statement 1: a + e = (3/4)(c + d)
No information about b+f.
Insufficient.

Statement 2: b + f = (4/3)(c + d)
No information about a+e.
Insufficient.

Statement 1 and 2 together:
Adding the equations, we get:
a+b+e+f = (3/4)(c+d) + (4/3)(c+d)
a+b+e+f = (3/4 + 4/3)(c+d)
a+b+e+f = (25/12)(c+d)
Sufficient.

The correct answer is C.
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