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# If the median of the 5 numbers is 20, is the range of the 5 numbers

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Joined: 29 Jan 2017
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If the median of the 5 numbers is 20, is the range of the 5 numbers  [#permalink]

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02 Apr 2018, 05:57
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65% (hard)

Question Stats:

49% (01:37) correct 51% (02:12) wrong based on 54 sessions

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If the median of the 5 numbers is 20, is the range of the 5 numbers greater than 8?

(1) The average (arithmetic mean) of the 5 numbers is 24.

(2) Three of the 5 numbers have the same value
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Re: If the median of the 5 numbers is 20, is the range of the 5 numbers  [#permalink]

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02 Apr 2018, 06:35
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1) The average (arithmetic mean) of the 5 numbers is 24.
The sum of 5 numbers = 5*24 = 120
To find the least range, let all the numbers lower than median be 20.
(20,20,20,x,y)
Now 20+20+20+x+y=120
x+y= 60
for range to be lowest , x=y, hence x=y=30
range = 10
Hence range is always greater than 8.
It is sufficient.

2) Three of the 5 numbers have the same value
the numbers can be (20,20,20, 21, 21) range = 1
or numbers can be (20,20,20, 21, 30) range = 10

Not sufficient.

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If the median of the 5 numbers is 20, is the range of the 5 numbers  [#permalink]

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02 Apr 2018, 07:02
fah_shoumo wrote:
If the median of the 5 numbers is 20, is the range of the 5 numbers greater than 8?

1) The average (arithmetic mean) of the 5 numbers is 24.

2) Three of the 5 numbers have the same value

The set has a median of 20 and there are 5 numbers in the set.
Since the set has an odd number of elements, the middle term is 20.

1. Since the average of 5 numbers is 24, their sum must be 120.
The elements in the set smaller than the median can be 20 at most.
The two numbers greater than the median must have a sum of 60.
The range is greater than 8 since the lowest possible value is 30, making range 10 (Sufficient)

2. 3 of 5 numbers have the same value
Case 1: 20,20,20,25,25 (Range is 5, less than 8)
Case 2: 20,20,20,30,30 (Range is 10, more than 8) (Insufficient) (Option A)
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Re: If the median of the 5 numbers is 20, is the range of the 5 numbers  [#permalink]

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02 Apr 2018, 08:34
fah_shoumo wrote:
If the median of the 5 numbers is 20, is the range of the 5 numbers greater than 8?

(1) The average (arithmetic mean) of the 5 numbers is 24.

(2) Three of the 5 numbers have the same value

Similar question to practice: https://gmatclub.com/forum/if-the-media ... 37064.html
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Re: If the median of the 5 numbers is 20, is the range of the 5 numbers   [#permalink] 02 Apr 2018, 08:34
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