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What is the average (arithmetic mean) of 25, 21, 16, 17, and x?

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What is the average (arithmetic mean) of 25, 21, 16, 17, and x?  [#permalink]

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Updated on: 25 Sep 2016, 03:20
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What is the average (arithmetic mean) of 25, 21, 16, 17, and x?

(1) The range of these 5 numbers is 9
(2) The median of these 5 numbers is 21

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Originally posted by MathRevolution on 24 Sep 2016, 06:12.
Last edited by Bunuel on 25 Sep 2016, 03:20, edited 1 time in total.
Renamed the topic and edited the question.
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Re: What is the average (arithmetic mean) of 25, 21, 16, 17, and x?  [#permalink]

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24 Sep 2016, 06:24
MathRevolution wrote:
(ex 18) *(statistics) What is the average (arithmetic mean) of 25, 21, 16, 17, and x?
1) The range of these 5 numbers is 9
2) The median of these 5 numbers is 21

Statement 1 : Range is 9. So, x could vbe 25 or any number less than 25 and greater than 16. hence, Insufficient.

Statement 2 : Median is 21. So, no clue on the value of x. hence, Insufficient.

Combining, again x could be anything between 9 and 25. hence, Insufficient.
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Re: What is the average (arithmetic mean) of 25, 21, 16, 17, and x?  [#permalink]

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24 Sep 2016, 11:08
MathRevolution wrote:
(ex 18) *(statistics) What is the average (arithmetic mean) of 25, 21, 16, 17, and x?
1) The range of these 5 numbers is 9
2) The median of these 5 numbers is 21

(1) Range can be defined as Greatest no. - Smallest no.
so X could be 25....as 25-16(listed)=9
or 16.........as 25(listed)-16=9
Not suff...

(2) 21 is median then x can be any number on either side of 21....Not suff..

Combining x again can be 16 (left side of 21) or could be 25(right side of 21).......Not suff...

Ans E
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Re: What is the average (arithmetic mean) of 25, 21, 16, 17, and x?  [#permalink]

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24 Sep 2016, 22:43

From first,we can have two possible values for X i.e 16 or 25, since 25 can be the last no so 25-9 will be 16, or 16 can be the smallest no i.e 16+9=25==>Insuff

From second, Median is 21==> Insuff

Combining both will give the answer.

By combining both ,we have two series

16,16,17,21,25=>median 17
16,17,21,25,25=> median 21

As we have given in the second statement that median is 21, the second series will be considered for calculating the average.
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Re: What is the average (arithmetic mean) of 25, 21, 16, 17, and x?  [#permalink]

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24 Sep 2016, 22:51
varundixitmro2512 wrote:

From first,we can have two possible values for X i.e 16 or 25, since 25 can be the last no so 25-9 will be 16, or 16 can be the smallest no i.e 16+9=25==>Insuff

From second, Median is 21==> Insuff

Combining both will give the answer.

By combining both ,we have two series

16,16,17,21,25=>median 17
16,17,21,25,25=> median 21

As we have given in the second statement that median is 21, the second series will be considered for calculating the average.

How can you say X could be only 16 or 25. It may happen that X is anything less than 25 but greater than 16. In that case also, Range will remain 9.

I think you MUST revisit the question.
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Re: What is the average (arithmetic mean) of 25, 21, 16, 17, and x?  [#permalink]

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26 Sep 2016, 05:26
==> In the original condition, the variable is 1(x), and in order for it to match the number of equations, the equation also need one as well. One 1)equation and one 2)equation, the answer is D with high chance.
In the case of 1), x=21,22 is possible, so it is not unique, thus not suffi. In the case of 2), x=21,22 is possible, hence not suffi. In the case of 1)&2) you get x=21,22 and it’s also possible, thus not unique, hence not suffi. So the answer is E.
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Re: What is the average (arithmetic mean) of 25, 21, 16, 17, and x?  [#permalink]

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08 Oct 2016, 02:07
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Please remove Mixtures tag and move to Statistics
Thank you
MathRevolution wrote:
What is the average (arithmetic mean) of 25, 21, 16, 17, and x?

(1) The range of these 5 numbers is 9
(2) The median of these 5 numbers is 21

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Re: What is the average (arithmetic mean) of 25, 21, 16, 17, and x?  [#permalink]

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08 Oct 2016, 02:46
BrushMyQuant wrote:
Please remove Mixtures tag and move to Statistics
Thank you
MathRevolution wrote:
What is the average (arithmetic mean) of 25, 21, 16, 17, and x?

(1) The range of these 5 numbers is 9
(2) The median of these 5 numbers is 21

Done. Thank you for noticing.
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Re: What is the average (arithmetic mean) of 25, 21, 16, 17, and x?  [#permalink]

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23 Feb 2017, 05:42
PROMPT ANALYSIS

Five numbers are given: 25,21,16,17,x. Average will be (79+x)/5. X is a positive integer

Superset
The value of average will be greater than 15.8.

Translation
In order to find x we need:
1# exact value of x
2# any relation or equation to determine x.

STATEMENT ANALYSIS

St 1: range = 9. Lowest of the known is 16 and highest is 29. Range is 9. So x will lie in between 16 and 25.INSUFFICIENT
St 2: median =21. So 2 numbers should below and two numbers should be above 21. Hence x>21. INSUFFICIENT

St 1& St 2: we can say that x can be 22, 23, 24. INSUFFICIENT

Option E.
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Re: What is the average (arithmetic mean) of 25, 21, 16, 17, and x? &nbs [#permalink] 23 Feb 2017, 05:42
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