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# Set A consists of a series of unique numbers. When added together, the

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Set A consists of a series of unique numbers. When added together, the [#permalink]

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25 Nov 2014, 20:44
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Difficulty:

95% (hard)

Question Stats:

41% (01:11) correct 59% (01:26) wrong based on 145 sessions

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Set A consists of a series of unique numbers. When added together, the numbers of Set A total 140. How many of the numbers within the set are above the median?

(1) The average of the set of numbers is equal to its median.
(2) The average of the set of numbers is equal to 28.

try to get the twist
[Reveal] Spoiler: OA

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Re: Set A consists of a series of unique numbers. When added together, the [#permalink]

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25 Nov 2014, 21:40
anceer wrote:
Set A consists of a series of unique numbers. When added together, the numbers of Set A total 140. How many of the numbers within the set are above the median?

1. The average of the set of numbers is equal to its median.
2. The average of the set of numbers is equal to 28.

try to get the twist

Statement 1: We don't know much about the average. So not sufficient to solve.

Statement 2: If Average=28. Let n be the total number in the set.

We are given the sum of numbers, we know that sum divided by total number(n) will equal average.

So $$\frac{140}{n}= 28$$ ,

Now,

$$\frac{140}{28}= n$$ => $$n=5$$.

We now know the total number of numbers in the set.

let x be the median. And,

x-2, x-1, x, x+1, x+2 be the numbers.

We are given

$$(x-2) +(x-1)+x +(x+1) + (x+2)= 140$$.---> $$5x=140$$

x=28. So median is 28. Then the numbers above the median in 29 and 30.

So there are 2 numbers above median.

Statement 2 is sufficient.

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Re: Set A consists of a series of unique numbers. When added together, the [#permalink]

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26 Nov 2014, 04:58
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Expert's post
Gnpth wrote:
anceer wrote:
Set A consists of a series of unique numbers. When added together, the numbers of Set A total 140. How many of the numbers within the set are above the median?

1. The average of the set of numbers is equal to its median.
2. The average of the set of numbers is equal to 28.

try to get the twist

Statement 1: We don't know much about the average. So not sufficient to solve.

Statement 2: If Average=28. Let n be the total number in the set.

We are given the sum of numbers, we know that sum divided by total number(n) will equal average.

So $$\frac{140}{n}= 28$$ ,

Now,

$$\frac{140}{28}= n$$ => $$n=5$$.

We now know the total number of numbers in the set.

let x be the median. And,

x-2, x-1, x, x+1, x+2 be the numbers.

We are given

$$(x-2) +(x-1)+x +(x+1) + (x+2)= 140$$.---> $$5x=140$$

x=28. So median is 28. Then the numbers above the median in 29 and 30.

So there are 2 numbers above median.

Statement 2 is sufficient.

Comment for (2):

We have that the median of 5 distinct numbers is 28: {a, b, 28, c, d}. Thus two numbers must be greater than the median.
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Set A consists of a series of unique numbers. When added together, the [#permalink]

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26 Nov 2014, 09:39
Hi Gnpth

How did you come up with the following assumption?

let x be the median. And,

x-2, x-1, x, x+1, x+2 be the numbers.

Since we are given in the question that Set A consists of a series of unique numbers, but we are not given that those unique numbers are consecutive numbers, if they are not consecutive numbers, the series might be different

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Re: Set A consists of a series of unique numbers. When added together, the [#permalink]

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26 Nov 2014, 23:57
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Expert's post
You don't need to assume that the numbers are consecutive. If you know there are 5 numbers and they're all different ("unique"), by definition two of them will be greater than the median.

In addition to the consecutive set, we could have any of these:

0, 5, 28, 50, 57
1, 2, 3, 4, 130
-1,000,000; -100; 0, 100; 1,000,140

You get the idea . . .
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Re: Set A consists of a series of unique numbers. When added together, the [#permalink]

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03 Nov 2016, 17:51
Looked at this problem again and realized OA is wrong.

Please look at the following set:

27 27 27 27 32

Adds up to 140, has mean: 28 median:27.
Only 1 number is more than the median.

Same assumption (II) we can create set 26 27 28 29 30 which has median 28 and 2 numbers more than the median.

Someone please confirm and correct the OA.

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Re: Set A consists of a series of unique numbers. When added together, the [#permalink]

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03 Nov 2016, 18:08
Watch out for those constraints! "Set A consists of a series of unique numbers."
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Re: Set A consists of a series of unique numbers. When added together, the [#permalink]

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04 Nov 2016, 00:49
r0ckst4r wrote:
Looked at this problem again and realized OA is wrong.

Please look at the following set:

27 27 27 27 32

Adds up to 140, has mean: 28 median:27.
Only 1 number is more than the median.

Same assumption (II) we can create set 26 27 28 29 30 which has median 28 and 2 numbers more than the median.

Someone please confirm and correct the OA.

Stem says Set of Unique Numbers.. so not all can be same

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Re: Set A consists of a series of unique numbers. When added together, the [#permalink]

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16 Nov 2017, 10:13
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Re: Set A consists of a series of unique numbers. When added together, the   [#permalink] 16 Nov 2017, 10:13
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