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Is the median of the 3 different integers equal to the average (arithm

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Is the median of the 3 different integers equal to the average (arithm [#permalink]

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New post 27 Jun 2017, 16:51
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Difficulty:

  95% (hard)

Question Stats:

28% (01:02) correct 72% (01:27) wrong based on 135 sessions

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Is the median of the 3 different integers equal to the average (arithmetic mean) of them?

1) The median of the 3 integers is 19.

2) The range of the 3 integers is 19.
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Re: Is the median of the 3 different integers equal to the average (arithm [#permalink]

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New post 27 Jun 2017, 19:22
1
aazt wrote:
Is the median of the 3 different integers equal to the average (arithmetic mean) of them?

1) The median of the 3 integers is 19.

2) The range of the 3 integers is 19.



let three integers be (a,b,c)
is a+c =2b

(1) b=19
a,c can be any integers
not suff

(2) c-a = 19--(a)
let b be any odd integer = 19
then if a+c =2b then it must satisfy a+c =38--(b)

solving (a) and (b)
c = 57/2 = not integer

similarly if b =even let =10
then if a+c =2b then it must satisfy a+c =20--(c)
then solving (a) and (c)
c =39/2 --not an integer

thus both cases are not giving any integer value (ie odd + even /2 =not integer)

thus suff

Ans B
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Re: Is the median of the 3 integers equal to the average (arithmetic mean) [#permalink]

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New post 06 Jul 2017, 08:53
Is the median of the 3 integers equal to the average (arithmetic mean) of them?
Statement 1) The median of the 3 integers is 19

Yes, if the three numbers are 19,19,19.
No, if the three numbers are 2,19,21.

This statement is not sufficient.

2) The range of the 3 integers is 19

If the first number is integer x, the third number will be integer (x+19). Let the second number be the median and also the mean of the three numbers = m

So,
x+x+19+m = 3m
2x+19 = 2m
m = x+9.5
As we know m should be an integer, but above we see m is not. Hence the answer is No to the original question stem. This statement is sufficient.

Answer is B
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Is the median of the 3 different integers equal to the average (arithm [#permalink]

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New post 06 Sep 2017, 13:04
rohit8865 wrote:
aazt wrote:
Is the median of the 3 different integers equal to the average (arithmetic mean) of them?

1) The median of the 3 integers is 19.

2) The range of the 3 integers is 19.



let three integers be (a,b,c)
is a+c =2b

(1) b=19
a,c can be any integers
not suff

(2) c-a = 19--(a)
let b be any odd integer = 19
then if a+c =2b then it must satisfy a+c =38--(b)

solving (a) and (b)
c = 57/2 = not integer

similarly if b =even let =10
then if a+c =2b then it must satisfy a+c =20--(c)
then solving (a) and (c)
c =39/2 --not an integer

thus both cases are not giving any integer value (ie odd + even /2 =not integer)

thus suff

Ans B


Can any one help me understand why have we taken even and odd numbers to test the second statement? abhimahna
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Re: Is the median of the 3 different integers equal to the average (arithm [#permalink]

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New post 13 Sep 2017, 03:50
TheMastermind wrote:
Can any one help me understand why have we taken even and odd numbers to test the second statement? abhimahna


Hi TheMastermind ,

Personally, I would never prefer to solve in this way.

I think a very well explanation has bee given here.

Feel free to ask if you have any questions.
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Re: Is the median of the 3 different integers equal to the average (arithm   [#permalink] 13 Sep 2017, 03:50
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Is the median of the 3 different integers equal to the average (arithm

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