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{3, 5, 8, x} For the above mentioned Set, Mean of the set is equal to

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{3, 5, 8, x} For the above mentioned Set, Mean of the set is equal to [#permalink] New post   21 Dec 2015, 11:42
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{3, 5, 8, x}
For the above mentioned Set, Mean of the set is equal to Range of the set then find out possible values of x

A) 16/5, 28/3
B) 4, 16/5
C) 4, 16/5, 28/3
D) 4, 28/3
E) 3, 4, 5

Source:https://www.GMATinsight.com
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{3, 5, 8, x} For the above mentioned Set, Mean of the set is equal to [#permalink] New post   21 Dec 2015, 11:50
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GMATinsight wrote:
{3, 5, 8, x}
For the above mentioned Set, Mean of the set is equal to Range of the set then find out possible values of x

A) 16/5, 28/3
B) 4, 16/5
C) 4, 16/5, 28/3
D) 4, 28/3
E) 3, 4, 5

Source:https://www.GMATinsight.com


Good question.

The set can have the following forms:

1. {3,5,8,x} , range = x-3 and mean = 4+x/4, x = 28/3
2. {3,5,x,8} , range = 5 and mean = 4+x/4, x=4
3. {3,x,5,8} , range = 5 and mean = 4+x/4, x=4
4. {x,3,5,8} , range = 8-x and mean = 4+x/4, x=16/5. But as x<3 (assumed here), x=3.2 can not be true. Hence reject this case.

Thus the possible values are 4 and 28/3.

D is the correct answer.
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Re: {3, 5, 8, x} For the above mentioned Set, Mean of the set is equal to [#permalink] New post   21 Dec 2015, 11:52
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Engr2012 wrote:
GMATinsight wrote:
{3, 5, 8, x}
For the above mentioned Set, Mean of the set is equal to Range of the set then find out possible values of x

A) 16/5, 28/3
B) 4, 16/5
C) 4, 16/5, 28/3
D) 4, 28/3
E) 3, 4, 5

Source:https://www.GMATinsight.com


GMATinsight, IMO, the OA should be C and not D. Please check.

The set can have the following forms:

1. {3,5,8,x} , range = x-3 and mean = 4+x/4, x = 28/3
2. {3,5,x,8} , range = 5 and mean = 4+x/4, x=4
3. {3,x,5,8} , range = 5 and mean = 4+x/4, x=4
4. {x,3,5,8} , range = 8-x and mean = 4+x/4, x=16/5

Thus the possible values are 4,16/5 and 28/3.


The highlighted 4th case is the TRAP :P

That case is valid only for x to be smaller than 3 whereas the value obtained of x is 16/5 i.e. 3.2 i.e. Inconsistent solution so we need to reject it.

I hope this helps! :)
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{3, 5, 8, x} For the above mentioned Set, Mean of the set is equal to [#permalink] New post   22 Dec 2015, 01:10
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GMATinsight wrote:
{3, 5, 8, x}
For the above mentioned Set, Mean of the set is equal to Range of the set then find out possible values of x

A) 16/5, 28/3
B) 4, 16/5
C) 4, 16/5, 28/3
D) 4, 28/3
E) 3, 4, 5

Source:https://www.GMATinsight.com


My Solution:

mean = (3+5+8+x)/4 = (16+x/4)

Case 1: x>8 - {3,5,8,x} , range = x-3 = (16+x)/4 i.e. x = 28/3
Case 2: 3<x<8 - {3,5,x,8} , range = 8-3 = 5 = (16+x)/4 i.e. x=4
Case 3: x < 3 - {x, 3,5,8} , range = 8-x = (16+x)/4, x=16/5 = 3.2 Which is greater than 3 hence violates the assumption of Case 3 Therefore rejected

Answer: Option D
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Re: {3, 5, 8, x} For the above mentioned Set, Mean of the set is equal to [#permalink] New post   19 Aug 2023, 06:18
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Re: {3, 5, 8, x} For the above mentioned Set, Mean of the set is equal to [#permalink]
19 Aug 2023, 06:18
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