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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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Math Expert
Joined: 02 Sep 2009
Posts: 51035
Set A = {a, b, c} and has a median of b. Is the average of a and c gre  [#permalink]

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10 Aug 2018, 02:43
00:00

Difficulty:

15% (low)

Question Stats:

83% (01:10) correct 18% (01:40) wrong based on 40 sessions

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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

_________________
Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 931
WE: Supply Chain Management (Energy and Utilities)
Set A = {a, b, c} and has a median of b. Is the average of a and c gre  [#permalink]

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10 Aug 2018, 07:17
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)
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

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Joined: 02 May 2015
Posts: 24
Location: United States (NJ)
Schools: Wharton Exec '19
GMAT 1: 720 Q48 V41
GPA: 3.4
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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10 Aug 2018, 08:52
+ 1 for A

According to 1st stmt mean =median that means set is in AP that is sufficient .
SVP
Joined: 26 Mar 2013
Posts: 1904
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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10 Aug 2018, 10:04
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.
Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 931
WE: Supply Chain Management (Energy and Utilities)
Re: Set A = {a, b, c} and has a median of b. Is the average of a and c gre  [#permalink]

### Show Tags

10 Aug 2018, 11:31
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

SVP
Joined: 26 Mar 2013
Posts: 1904
Re: Set A = {a, b, c} and has a median of b. Is the average of a and c gre  [#permalink]

### Show Tags

10 Aug 2018, 12:14
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.
Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 931
WE: Supply Chain Management (Energy and Utilities)
Re: Set A = {a, b, c} and has a median of b. Is the average of a and c gre  [#permalink]

### Show Tags

10 Aug 2018, 12:20
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. ☺️
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

Re: Set A = {a, b, c} and has a median of b. Is the average of a and c gre &nbs [#permalink] 10 Aug 2018, 12:20
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