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There is a set of numbers 2, 4, 6, 8,10 and x. What is the value of x?

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Manager
Joined: 06 Jul 2014
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There is a set of numbers 2, 4, 6, 8,10 and x. What is the value of x? [#permalink]

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15 Sep 2017, 15:12
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There is a set of numbers 2, 4, 6, 8,10 and x. What is the value of x?

(1) x is a 2-digit positive integer.
(2) The average of these integers is equal to the median of these integers.
Intern
Joined: 15 Jul 2017
Posts: 7
Re: There is a set of numbers 2, 4, 6, 8,10 and x. What is the value of x? [#permalink]

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15 Sep 2017, 16:22
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A. This can not determine the value of x. In other word, the value can be 20 or 11. So insufficient.

B. If value of x is lower than 10, it would be necessary to be determined. But if the value of x is equals or higher than 10, it would be determinable. So insufficient.

(1) & (2) says that x is higher than 9. So the value of x is:
(2+4+6+8+10+x)/6=7
X=12

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Re: There is a set of numbers 2, 4, 6, 8,10 and x. What is the value of x? [#permalink]

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15 Sep 2017, 20:57
Ans is C.. But a slight trap here in Statement A is: its given two digit integer and with the sequence given in the question, it might lead us to think that x is 12 after 10.
Just highlighting a possible trap.
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Re: There is a set of numbers 2, 4, 6, 8,10 and x. What is the value of x? [#permalink]

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15 Sep 2017, 21:05
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Bounce1987 wrote:
There is a set of numbers 2, 4, 6, 8,10 and x. What is the value of x?

(1) x is a 2-digit positive integer.
(2) The average of these integers is equal to the median of these integers.

Statement 1: $$x$$ can be any two digit no 10,20,30.... etc. Hence Insufficient

Statement 2: Average of the set $$=\frac{(2+4+6+8+10+x)}{6}=\frac{(30+x)}{6}=5+\frac{x}{6}$$

Median, if $$6<x<8$$, then the Median would be $$\frac{6+x}{2}$$ but if $$x>8$$, then the Median would be $$\frac{6+8}{2} = 7$$

Now the two values of median when equated against the average will give two different values of $$x$$. Hence Insufficient

Combining 1 & 2, we know for sure that $$x>8$$
.
Therefore $$5+\frac{x}{6}=7$$ or $$x =12$$

Option C
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Re: There is a set of numbers 2, 4, 6, 8,10 and x. What is the value of x? [#permalink]

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30 Sep 2017, 04:16
Bounce1987 wrote:
There is a set of numbers 2, 4, 6, 8,10 and x. What is the value of x?

(1) x is a 2-digit positive integer.
(2) The average of these integers is equal to the median of these integers.

Value base Qs, x=? in set ={2,4,6..x}

St-1 x is 2 digit positive integer- x can be any 2 digit integer insufficient
St-2 the average is equal to median then consecutive integers x can be 0 or 12,insufficient

Combine- x can be only 12 sufficient
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Joined: 10 May 2017
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Re: There is a set of numbers 2, 4, 6, 8,10 and x. What is the value of x? [#permalink]

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18 Oct 2017, 00:08
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I went through with a little easier approach. Please let me know if I am on the right track though.
There is a set of numbers 2, 4, 6, 8,10 and x. What is the value of x?

(1) x is a 2-digit positive integer.
(2) The average of these integers is equal to the median of these integers.

1) According to the first statement, x=11,12,13 or any number.
Hence insufficient
2)According to this statement, Average of these integers(mean)=Median
The above Statement is possible when the set of integers are consecutive integers
x=0,12
Not sufficient
1+2=x=12
Senior Manager
Joined: 27 May 2012
Posts: 473
Re: There is a set of numbers 2, 4, 6, 8,10 and x. What is the value of x? [#permalink]

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30 Jan 2018, 09:07
niks18 wrote:
Bounce1987 wrote:
There is a set of numbers 2, 4, 6, 8,10 and x. What is the value of x?

(1) x is a 2-digit positive integer.
(2) The average of these integers is equal to the median of these integers.

Statement 1: $$x$$ can be any two digit no 10,20,30.... etc. Hence Insufficient

Statement 2: Average of the set $$=\frac{(2+4+6+8+10+x)}{6}=\frac{(30+x)}{6}=5+\frac{x}{6}$$

Median, if $$6<x<8$$, then the Median would be $$\frac{6+x}{2}$$ but if $$x>8$$, then the Median would be $$\frac{6+8}{2} = 7$$

Now the two values of median when equated against the average will give two different values of $$x$$. Hence Insufficient

Combining 1 & 2, we know for sure that $$x>8$$
.
Therefore $$5+\frac{x}{6}=7$$ or $$x =12$$

Option C

Actually if x is 8 then median is 7 and and average is 6.66.. hence x= 8 does not satisfy the condition , only x= 0, or 6 or 12 satisfy statement 2, since there are 3 values hence insufficient .

1 and 2 combined
we have only one two digit integer, 12 hence sufficient.
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Joined: 14 Dec 2016
Posts: 12
Re: There is a set of numbers 2, 4, 6, 8,10 and x. What is the value of x? [#permalink]

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12 Feb 2018, 10:28
Bounce1987 wrote:
There is a set of numbers 2, 4, 6, 8,10 and x. What is the value of x?

(1) x is a 2-digit positive integer.
(2) The average of these integers is equal to the median of these integers.

A quick way to solve would be:
#1 in itself is insufficient.
#2 this statement tells us the set is evenly spaced, so x must either be zero or 12.

Now considering statement 1, we can conclude x=12.
Re: There is a set of numbers 2, 4, 6, 8,10 and x. What is the value of x?   [#permalink] 12 Feb 2018, 10:28
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