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Math Expert V
Joined: 02 Sep 2009
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In the set of data above, is x>10?  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 64% (01:37) correct 36% (01:39) wrong based on 183 sessions

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10,17,5,23,x
In the set of data above, is x>10?

(1) x is the median of the set

(2) x is 3 less than the mean of the set

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Re: In the set of data above, is x>10?  [#permalink]

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1
1
5,10,17,23,x.
St. 1- x is the median; so x=10 or 10<x<17----- hence insufficient
St. 2- Let mean = y; x=y-3
Mean= (55+x)/5 =y
55+x=5y
55+y-3=5y
y=13
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In the set of data above, is x>10?  [#permalink]

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1
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Bunuel wrote:
10,17,5,23,x
In the set of data above, is x>10?

(1) x is the median of the set

(2) x is 3 less than the mean of the set

Arranging terms in increasing order {5, 10, 17, 23, x}

Statement (1): x is the median of the set
i.e. {5, 10, x, 17, 23} but according to this condition x may be anything from 10 to 17 inclusive
hence x may be equal to 10 or greater than 10
NOT SUFFICIENT

Statement (2): x is 3 less than the mean of the set
i.e. x+3 = (55+x)/4
We get exact value of x hence
SUFFICIENT

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Re: In the set of data above, is x>10?  [#permalink]

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GMATinsight wrote:
Bunuel wrote:
10,17,5,23,x
In the set of data above, is x>10?

(1) x is the median of the set

(2) x is 3 less than the mean of the set

Arranging terms in increasing order {5, 10, 17, 23, x}

Statement (1): x is the median of the set
i.e. {5, 10, x, 17, 23} but according to this condition x may be anything from 10 to 17 inclusive
hence x may be equal to 10 or greater than 10
NOT SUFFICIENT

Statement (2): x is 3 less than the mean of the set
i.e. x+3 = (55+x)/4
We get exact value of x hence
SUFFICIENT

I would like to draw your attention that the number of numbers are 5.
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Re: In the set of data above, is x>10?  [#permalink]

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It is B
A says that x is median so X can be 10, 11 12 or anything so not sufficient
however B says that 5+10+17+23+x/5 = x-3-----solving this we get the value of x which is 12
thus x > 10
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Re: In the set of data above, is x>10?  [#permalink]

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Bunuel wrote:
10,17,5,23,x
In the set of data above, is x>10?

(1) x is the median of the set

(2) x is 3 less than the mean of the set

Statement 1- actually x could be exactly 10. insuff

Statement 2-

x-3 = 55 +x /5
15x -15= 55 + x
15x = 70 +x
14x= 70

x=5

Suff

B
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Re: In the set of data above, is x>10?  [#permalink]

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Nunuboy1994 wrote:
Bunuel wrote:
10,17,5,23,x
In the set of data above, is x>10?

(1) x is the median of the set

(2) x is 3 less than the mean of the set

Statement 1- actually x could be exactly 10. insuff

Statement 2-

x-3 = 55 +x /5
15x -15= 55 + x
15x = 70 +x
14x= 70

x=5

Suff

B

It should be the other way around

x=(55+x-3)/5
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Re: In the set of data above, is x>10?  [#permalink]

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10,17,5,23,x
In the set of data above, is x>10?

(1) x is the median of the set

(2) x is 3 less than the mean of the set

Bunuel Could you explain, where I am getting wrong. My choice is D. Both should suffice. 1) x is the median. Median No means Middle No of a set of numbers. Arranging the nos, we get : 5, 10, 17, 23

(x-5) + (x-10) = (17-x) + (23-x)
=> 2x-15 = 40-2x => 4x=55 => x=13.75≈14. Thus x>10

2) x = ((5+10+17+23+x)/5) - 3. From this we can deduce the value of x
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Re: In the set of data above, is x>10?  [#permalink]

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There are few errors in above post except for the one.
10,17,5,23,x
In the set of data above, is x>10?

(1) x is the median of the set
Statement 1 says only the median. Arranging in asecending order we have, 5,10,x,17,23 ( Since x is the median , so kept in the middle) : Now x could be either 10 or more than 10 but less than equal 17( So mathematically, 10<=x<=17) . Not sufficient

(2) x is 3 less than the mean of the set
Statement 2 :Now we know that mean = (5+10+17+23+x)/5 = (55+x)/5 = 11+x/5
Now this expression(which is Mean) is equal to 3 more than x
Hence we have the equation as :
x+3 = 11+x/5
A simple linear equation for which x has a unique value.
Hence SUFFICIENT

Hope that helps!
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Re: In the set of data above, is x>10?  [#permalink]

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Statement 1: X can b 10 or 11. Not sufficient.
Statement 2: 55+ m-3 = 5m
So m is 13 and X is 10.
Thus, X has a unique value of 10 and the answer is NO. X is 10 , not bigger than 10

Posted from my mobile device Re: In the set of data above, is x>10?   [#permalink] 02 Jul 2020, 06:22

# In the set of data above, is x>10?  