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Bunuel
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

Hello nick1816,

Why option B is not sufficient here ?

Mean of Set S is \(\frac{N+2}{3}\)
As per option B, N<3 i.e. 2.9,2,-10 etc.

If we put these values in mean we will get that Mean is less than median.

What I am missing here ?
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Bunuel
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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Case 1 If -2<n<3, median is n

\(\frac{n+2}{3} > n\)

n+2 > 3n

n< 1

If -2<n<1, Mean > Median (Yes)

If 1<n<3, Median > Mean (No)

Hence, statement 2 is insufficient. (no need to analyze the case when n<-2)


ammuseeru
Bunuel
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

Hello nick1816,

Why option B is not sufficient here ?

Mean of Set S is \(\frac{N+2}{3}\)
As per option B, N<3 i.e. 2.9,2,-10 etc.

If we put these values in mean we will get that Mean is less than median.

What I am missing here ?
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