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

Question

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

PKN · Answer

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)

rachitbechem · Answer

+ 1 for A

According to 1st stmt mean =median that means set is in AP that is sufficient .

Mo2men · Answer

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.

PKN · Answer

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

Mo2men · Answer

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.

PKN · Answer

Thank you. I am aware of the exception. ☺️

AliciaSierra · Answer

Hello  Mo2men

Can you explain below ?

Why--> 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.

HoneyLemon · Answer

Given a 3-term set, one of the terms must always be the median. In this case, the median is b
 this means that a
 and c
 are on either side of b
 and that either a<b<c
 or that c<b<a
. You are then asked whether the average of a
 and c
 is greater than b
.

Statement (1) gives that b
 is the average of Set A as well as its median. Sets with the same median as average are always going to equally spaced sets around the median. And for any equally spaced set, the average of the two extremes (in this case a
 and c
) will be the same as the average of the set as a whole. This means that the average of the set is b
 and the answer to the question posed is a definitive "no".

If the rule described above wasn't immediately apparent, consider a set of three numbers 1, 2, and 3. The average of the three numbers will be 2, as will the median. Similarly, the average of the first and third terms will be 2.

Statement (2) gives you that c=2a
. While this gives you information about the relative values of c
 and a
 and would allow you to calculate the average of the terms in terms of a
, it does not give you any information about how these two numbers would relate to b
, so it is impossible to answer the question posed with the information given in statement (2). Statement (2) is therefore insufficient.

If you wanted to prove that with numbers, note that you can just place the median immediately adjacent to either a
 or c
 to move the average in either direction. For example, given that c=2a
, you could use 4 and 8. If you make the median 5, then the average of a
 and c
, 6, is greater than the median (giving the answer "yes"); if you make the median 7, it's less than the median ("no"). Since you can answer the question either way, this proves that statement (2) is insufficient.

The correct answer is (A).

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards