Last visit was: 09 Jul 2025, 12:59 It is currently 09 Jul 2025, 12:59
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
655-705 Level|   Statistics and Sets Problems|                           
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 9 July 2025
Posts: 102,609
Own Kudos:
739,888
 [1]
Given Kudos: 97,813
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,609
Kudos: 739,888
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
avatar
BeepBoop
Joined: 30 Dec 2020
Last visit: 12 Jun 2022
Posts: 5
Given Kudos: 3
Location: Romania
Posts: 5
Kudos: 0
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
Kimberly77
Joined: 16 Nov 2021
Last visit: 07 Sep 2024
Posts: 440
Own Kudos:
Given Kudos: 5,899
Location: United Kingdom
GMAT 1: 450 Q42 V34
Products:
GMAT 1: 450 Q42 V34
Posts: 440
Kudos: 42
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
BrentGMATPrepNow
User avatar
Major Poster
Joined: 12 Sep 2015
Last visit: 13 May 2024
Posts: 6,756
Own Kudos:
Given Kudos: 799
Location: Canada
Expert
Expert reply
Posts: 6,756
Kudos: 34,041
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Kimberly77
karovd
A certain list consists of 3 different numbers. Does the median of the 3 numbers equal the average (arithmetic mean) of the 3 numbers?

(1) The range of the 3 numbers is equal to twice the difference between the greatest number and the median.
(2) The sum of the 3 numbers is equal to 3 times one of the numbers.

Hi BrentGMATPrepNow, question asked Does the median of the 3 numbers equal the average (arithmetic mean) of the 3 numbers? So it means are these numbers evenly spaced set?
Does this mean we should only assing even numbers here e.g 8 ,10 ,12 if number testing? Thought assign 1,2,3 work too but is this still correct though? Thanks Brent

Since we know a list consists of three different numbers, then we can reward the target question as "Are the three numbers equally spaced?"
Don't forget that, when testing numbers for each statement, the values must satisfy the information in each statement.
User avatar
Kavicogsci
Joined: 13 Jul 2024
Last visit: 09 Feb 2025
Posts: 173
Own Kudos:
Given Kudos: 154
GMAT 1: 710 Q48 V40
GMAT 1: 710 Q48 V40
Posts: 173
Kudos: 68
Kudos
Add Kudos
Bookmarks
Bookmark this Post
1. Median = Mean if the set is symmterical around median. Symmetrical means lets say for a set a,b,c where b is median if a-b=c-b then Median = Mean
A-b = c-b
2b-c-a......(1)

Once we solve Statement A we get to the exact same equation so A is sufficient and quite direct

2. B is what seems indirect and requires 2 layers of thinking and has two methods to solve

a)Translation Method
What is mean?
Avg = Sum of 3 values in set/3
What is statement Telling us?
The sum of three values in set is = 3 times the value of one number in set

Avg = Sum of 3 values / 3
3*Avg = Sum of 3 values

Now interpret slowly Sum of 3 values which is our RHS (Right hand side of equation ) IS 3 times value of one number in set
Hence Avg = One number in set
Avg cannot be lowest or highest value and has to be middle number in an odd set (odd number of terms)

b)Logical Method
Lets say we couldn't translate properly. What do we now? The obvious doubt is Sum is 3 times of which number - smallest, middle or largest

Lets say three nos are a,b,c and a<b<c

Can sum be 3a??
Sum = a+b+c >3a Why??? Because we know that the three nos. are different and the two numbers are BIGGER than a so there is no way that the sum of 3 nos could be equal to three times the smallest number. [In which case would the sum be 3a? If all nos were same which violates our given info]

Can sum be 3c??
Sum = a+b+c <3c Why??? Because we know that the three nos. are different and the two numbers are SMALLER than c so there is no way that the sum of 3 nos could be equal to three times the largest number. [In which case would the sum be 3c? If all nos were same which violates our given info]

Hence only one option remains sum is equal to 3 times median. Once you transform this equation we get back to 2b = a+c which is exactly what we had to prove!
   1   2 
Moderator:
Math Expert
102609 posts