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If the mean of set S is 20, what is the median of set S ?

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If the mean of set S is 20, what is the median of set S ?  [#permalink]

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New post 24 Feb 2017, 10:03
10
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A
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D
E

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  95% (hard)

Question Stats:

37% (02:00) correct 63% (01:53) wrong based on 132 sessions

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If the mean of set S is 20, what is the median of set S ?

1. In set S there are as many numbers larger than 20 as there are numbers smaller than 20.
2. All numbers in set S are even integers.
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Re: If the mean of set S is 20, what is the median of set S ?  [#permalink]

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New post 24 Feb 2017, 16:01
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1
Well, they don't tell us how many numbers there are in set S, so let's keep it as simple as possible. It's easier to find the median with an odd number of numbers, so we'll start with sets that have 3 elements (although we might have to try even-numbered sets, too, if we can't find good cases.)

(1)

Let's say the set is (10, 20, 30). The mean is 20. The median is also 20.
Next, try (19, 20, 21). The mean is 20. The median is also 20.

It seems like whenever we have one element larger than 20, and one element smaller than 20, the median is 20. That makes sense, because the third number in the set would have to be equal to 20. That number would be in the middle, so it would be the median.

What if we try some sets of four numbers, then? There could be two numbers smaller than 20, and two numbers bigger than 20.

(0, 0, 40, 40) - the mean is 20, and the median is 20 again (average of 0 and 20, the two middle numbers).

BUT, how about (0, 19, 30, 31)? The mean is 20 (I figured this out by making sure the sum was 80) but the median definitely isn't 20.

Insufficient.

(2) This is definitely insufficient on its own, since we could test almost any set.

(1+2) It's pretty easy to find a case where the median is equal to 20, and that fits both statements: (10,20,30) would work. What we need, then, is to find a case where the median isn't equal to 20. That is, we want a case similar to the one that worked for statement (1), above, except where all of the numbers are even.

Let's use the same idea - a set that sums to 80 and has 4 elements, but that isn't 'evenly spaced'. One set that works here is (0, 18, 30, 32), which has a mean of 20 but a median of 24.

Insufficient.

The correct answer is E.
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If the mean of set S is 20, what is the median of set S ?  [#permalink]

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New post 27 Feb 2017, 07:34
the trick of this question is not to assume that 20 is one of the numbers in the set

( 0, 19, 30, 31), average of 04 numbers is 20 and median is now 20 now

( 0,19, 20, 30, 31) average is 20 and median is 20


choice 1


0, 18, 30,32 , average is 20 and median is 24

0, 18, 20, 30, 32 average of 05 numbers is 20 and median is now 20

choice 2
all even, above all numbers are even

combined both we don't get the definite answer

so choice E is the correct answer
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Re: If the mean of set S is 20, what is the median of set S ?  [#permalink]

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New post 22 Mar 2018, 21:29
If the mean of set S is 20, what is the median of set S ?

1. In set S there are as many numbers larger than 20 as there are numbers smaller than 20.
2. All numbers in set S are even integers.

Option 1
Consider set1 - 16, 18, 20, 22,24 - Mean=20, Median=20
Set2 - 0,21,23,36 - mean=20, Median=22 - INSUFF

Option 2
Consider set1 - 16, 18, 20, 22,24 - Mean=20, Median=20
Set2 - 2,4,6,68 = Mean=20, Median=5 - INSUFF

Both -(the key here is 0 is an even no, and not necessarily 20 be there in the list)
Consider set1 - 16, 18, 20, 22,24 - Mean=20, Median=20
Set2 - 0,2,20,58 - mean=20, Median=11 - INSUFF
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Re: If the mean of set S is 20, what is the median of set S ? &nbs [#permalink] 22 Mar 2018, 21:29
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