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Set A = {a, b, c} and has a median of b. Is the average of a and c gre

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Set A = {a, b, c} and has a median of b. Is the average of a and c gre  [#permalink]

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New post 10 Aug 2018, 03:43
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Difficulty:

  25% (medium)

Question Stats:

82% (01:31) correct 18% (00:51) wrong based on 44 sessions

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VP
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Set A = {a, b, c} and has a median of b. Is the average of a and c gre  [#permalink]

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New post 10 Aug 2018, 08:17
1
Bunuel wrote:
Set A = {a, b, c} and has a median of b. Is the average of a and c greater than b?

(1) The average of Set A is b
.

(2) c = 2a


Given A = {a, b, c} and has a median of b, implies that the elements of set A are either in the ascending order or in the descending order.
And 'b' is the median.

Question stem:- Is the average of a and c greater than b
Or, Is \(\frac{a+c}{2}>b\) ?
Or, Is \((a+c)>2b\) ?

St1:- The average of Set A is b
Note:-
1)The average value of a series of terms is equal to the median value when the terms are in A.P.(Arithmetic progression).
2) When all the terms in a series are equal, they are also in A.P. with common difference zero.
So, a, b, and c are in A.P.
Or, c+a=2b.

Answer to the question stem is No.
Sufficient.

St2:- c = 2a

1) If A={4,5,8}, then (a+c)>2b. Answer to question stem is Yes.
2) If A={4,7,8}, then (a+c)<2b. Answer to question stem is No.

Insufficient.

Ans. (A)
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Re: Set A = {a, b, c} and has a median of b. Is the average of a and c gre  [#permalink]

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New post 10 Aug 2018, 09:52
+ 1 for A

According to 1st stmt mean =median that means set is in AP that is sufficient .
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Re: Set A = {a, b, c} and has a median of b. Is the average of a and c gre  [#permalink]

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New post 10 Aug 2018, 11:04
PKN wrote:
Bunuel wrote:
Set A = {a, b, c} and has a median of b. Is the average of a and c greater than b?

(1) The average of Set A is b
.

(2) c = 2a


Given A = {a, b, c} and has a median of b, implies that the elements of set A are either in the ascending order or in the descending order.
And 'b' is the median.

Question stem:- Is the average of a and c greater than b
Or, Is \(\frac{a+c}{2}>b\) ?
Or, Is \((a+c)>2b\) ?

St1:- The average of Set A is b
Note:-
1)The average value of a series of terms is equal to the median value when the terms are in A.P.(Arithmetic progression).
2) When all the terms in a series are equal, they are also in A.P. with common difference zero.
So, a, b, and c are in A.P.
Or, c+a=2b.

Answer to the question stem is No.
Sufficient.

St2:- c = 2a

1) If A={4,5,8}, then (a+c)>2b. Answer to question stem is Yes.
2) If A={4,7,8}, then (a+c)<2b. Answer to question stem is No.

Insufficient.

Ans. (A)


Hi PKN

I do not agree with the highlighted part above. Take the example below:

7,7,10,12,16..............Median= Mean=10..........it is not AP.
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Re: Set A = {a, b, c} and has a median of b. Is the average of a and c gre  [#permalink]

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New post 10 Aug 2018, 12:31
Mo2men wrote:
PKN wrote:
Bunuel wrote:
Set A = {a, b, c} and has a median of b. Is the average of a and c greater than b?

(1) The average of Set A is b
.

(2) c = 2a


Given A = {a, b, c} and has a median of b, implies that the elements of set A are either in the ascending order or in the descending order.
And 'b' is the median.

Question stem:- Is the average of a and c greater than b
Or, Is \(\frac{a+c}{2}>b\) ?
Or, Is \((a+c)>2b\) ?

St1:- The average of Set A is b
Note:-
1)The average value of a series of terms is equal to the median value when the terms are in A.P.(Arithmetic progression).
2) When all the terms in a series are equal, they are also in A.P. with common difference zero.
So, a, b, and c are in A.P.
Or, c+a=2b.

Answer to the question stem is No.
Sufficient.

St2:- c = 2a

1) If A={4,5,8}, then (a+c)>2b. Answer to question stem is Yes.
2) If A={4,7,8}, then (a+c)<2b. Answer to question stem is No.

Insufficient.

Ans. (A)


Hi PKN

I do not agree with the highlighted part above. Take the example below:

7,7,10,12,16..............Median= Mean=10..........it is not AP.


My point is when the series is in AP , then mean=median. But vice-versa is not true.
_________________
Regards,

PKN

Rise above the storm, you will find the sunshine
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Re: Set A = {a, b, c} and has a median of b. Is the average of a and c gre  [#permalink]

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New post 10 Aug 2018, 13:14
PKN wrote:
Mo2men wrote:

Hi PKN

I do not agree with the highlighted part above. Take the example below:

7,7,10,12,16..............Median= Mean=10..........it is not AP.


My point is when the series is in AP , then mean=median. But vice-versa is not true.


Actually, there is one exception to the highlighted part. When you have a set of 3 numbers only (as in the question) and mean equal to Median, then you conclude directly that it is AP. If the set has more than 3 numbers, then it true that it is not vice verse.
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Re: Set A = {a, b, c} and has a median of b. Is the average of a and c gre  [#permalink]

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New post 10 Aug 2018, 13:20
Mo2men wrote:
PKN wrote:
Mo2men wrote:

Hi PKN

I do not agree with the highlighted part above. Take the example below:

7,7,10,12,16..............Median= Mean=10..........it is not AP.


My point is when the series is in AP , then mean=median. But vice-versa is not true.


Actually, there is one exception to the highlighted part. When you have a set of 3 numbers only (as in the question) and mean equal to Median, then you conclude directly that it is AP. If the set has more than 3 numbers, then it true that it is not vice verse.


Thank you. I am aware of the exception. ☺️
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Regards,

PKN

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Re: Set A = {a, b, c} and has a median of b. Is the average of a and c gre   [#permalink] 10 Aug 2018, 13:20
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