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If a, b, c, d, e are integers such that a<b<c<d<

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If a, b, c, d, e are integers such that a<b<c<d<

by GMATinsight » Sat Sep 29, 2018 10:20 pm

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If a, b, c, d, e are integers such that a<b<c<d<e, then what is the positive difference between averages of Sets (b, c, d, e) and (a, b, c, d)

1) a, b, c, d, e are consecutive integers
2) a = 5

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by GMATGuruNY » Sun Sep 30, 2018 3:13 am

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GMATinsight wrote:If a, b, c, d, e are integers such that a < b < c < d < e, then what is the positive difference between averages of Sets (b, c, d, e) and (a, b, c, d)

1) a, b, c, d, e are consecutive integers
2) a = 5
Statement 1:
For any set of consecutive integers, average = median.

Case 1: 1, 2, 3, 4, 5
Average of 2, 3, 4 and 5 = 3.5.
Average of 1, 2, 3, and 4 = 2.5.
Difference between the averages = 3.5 - 2.5 = 1.

Case 2: 2, 3, 4, 5, 6
Average of 3, 4, 5, and 6 = 4.5.
Average of 2, 3, 4 and 5 = 3.5.
Difference between the averages = 4.5 - 3.5 = 1.

As the two cases above illustrate -- if a, b, c, d and e are consecutive integers -- the difference between the 4 greatest integers and the 4 smallest integers = 1.
SUFFICIENT.

Statement 2:
No info about b, c, d and e.
INSUFFICIENT.

The correct answer is A.

Proof for Statement 1:
Let the 5 integers be as follows:
x, x+1, x+2, x+3, x+4.
Average of the 4 greatest integers = median of the 4 greatest integers = x + 2.5.
Average of the 4 smallest integers = median of the 4 greatest integers = x + 1.5.
Difference between the averages = (x + 2.5) - (x + 1.5) = 1.
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