Bunuel wrote:
If set S consists of the numbers n, -2, and 4, is the mean of set S greater than the median of set S ?
(1) n > 2
(2) n < 3
First we need to know how to get the Mean = Median condition, it happens when the set is evenly spaced. Hence n = 1 is right between -2 and 4 so -2, 1, 4 would allow Mean = Median. We can also have n = -8 in order to get -8, -2, 4 which also satisfies Mean = Median.
Statement 1:n is greater than 2 so we can confirm -2 is the smallest integer in the set. Then either n or 4 is the median, depending on which is smaller. A good reference here is the evenly spaced set -2, 4, 10. When 4 < n < 10 the mean is smaller than 4 (the median), and when n > 10 the mean is bigger than 4 (the median). Since we have both cases this is insufficient.
Statement 2:Again let us find an evenly spaced set, -8, -2, 4 for example. When n < -8 we have mean < median. Also when -8 < n < -2 we have mean > median. Then statement 2 is still insufficient.
Combined:Combined we have 2 < n < 3, so we must have the ordering -2, n, 4. The mean is (-2 + n + 4) / 3 and the median is n. We can find they are equal when n = 1, which makes sense as -2. 1. 4 is an evenly spaced set. Thus that is the equilibrium, and when n > 1 we will have mean > median or the other way around. Since we can confirm only one case this is sufficient.
Ans: C
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