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If set S consists of the numbers n, -2, and 4, is the mean of set S gr

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If set S consists of the numbers n, -2, and 4, is the mean of set S gr [#permalink]

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New post 10 Jun 2018, 04:27
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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
Spoiler: OA

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If set S consists of the numbers n, -2, and 4, is the mean of set S gr [#permalink]

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New post 10 Jun 2018, 05:49
Testing numbers smartly:

For (1), if n = 2 (it can't be technically, but we are figuring out the boundary), then mean = 4/3 and median = 2, so the median > mean. The reason why I tested 2 is because we can imagine our number to actually be 2 and an infinity number of 0s after the decimal point, then 1 at the very end. The result of plugging in such a number (which we can't) would be close enough to plugging a 2 in for this type of question specifically, so we can test 2. So anyways, let's try a much larger n. Much, much larger. Say 100. In that case, the mean is (-2 + 4 + 100)/3 = 102/3, or 34. In this case, our median is 4 (the moment n is greater than or equal to 4, the median will always be 4). Thus the mean here is greater than the median. Hence not sufficient.

(2) would be tested in a similar way. What if we use 3? Then we'd get mean = 5/3, and median = 3. So median > mean. What if n = -2? Mean = (-2 + -2 +4)/3 = 0. Median is -2, so mean > median. So not sufficient.

Together, we know that values between 2 and 3 would result in a mean < median. So, both (1) and (2) together are sufficient. So C is the answer.

I think the proper math calculations for it involves assuming n < -2, -2 < n < 4, and n > 4 or something, and so combining (1) and (2) gives you 2 < n < 3 which is between -2 and 4 so it can be figured out, but I a.) I don't remember all the proper math stuff because it's too long ago, and b.) am doing all this off the top of my head.
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If set S consists of the numbers n, -2, and 4, is the mean of set S gr [#permalink]

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New post 11 Jun 2018, 18:21
1) not sufficient


If n>2 and <4

then it means the set is -2,n,4 and median is n.

so, median - 2<n<4.

mean is (2+n)/3
so, largest value of mean is slightly less than 2 since largest value of n is slightly less than 4.

so, mean < median

If n>4 say 20

then median = 4
and mean = -2+4+20/3=7.something
so, mean > median

NS

2)n<3

n can be anywhere. no sufficient

1+2
n is between 2 and 3.
so the set is 2,n,4 - 1st check of 1st condn
so, mean < median

answer C
If set S consists of the numbers n, -2, and 4, is the mean of set S gr   [#permalink] 11 Jun 2018, 18:21
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