GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Jun 2019, 08:50

### 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

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

# For a list of positive numbers, if the median is greater

Author Message
TAGS:

### Hide Tags

General GMAT Forum Moderator
Joined: 29 Jan 2015
Posts: 1271
Location: India
WE: General Management (Non-Profit and Government)
For a list of positive numbers, if the median is greater  [#permalink]

### Show Tags

26 Dec 2018, 08:45
2
00:00

Difficulty:

75% (hard)

Question Stats:

33% (01:49) correct 67% (02:16) wrong based on 29 sessions

### HideShow timer Statistics

For a list of positive numbers, if the median is greater than the average, which of the following must be true?

I. At least 50% of the numbers are smaller than the median.

II. Less than 50% of the numbers are greater than the median.

III. Median is greater than the average of the largest number and smallest number.

(A) I only

(B) II only

(C) III only

(D) I and III only

(E) None

_________________
If you liked my post, kindly give me a Kudos. Thanks.
Math Expert
Joined: 02 Aug 2009
Posts: 7750
Re: For a list of positive numbers, if the median is greater  [#permalink]

### Show Tags

27 Dec 2018, 08:46
1
1
For a list of positive numbers, if the median is greater than the average, which of the following must be true?

Be careful with numbers you choose

I. At least 50% of the numbers are smaller than the median.
If there are odd numbers in the list, it is not necessary that 50% are smaller than the median
Say there are five numbers...1,1,3,3,3....average is 2.2 and median is 3, so median>average...
But there are only 2 numbers less than the median ..
2 out of 5 means just 40%.. thus not ATLEAST 50%

II. Less than 50% of the numbers are greater than the median.
If there are even numbers, it is not necessary
Take 6 numbers 1, 1, 3, 4, 4, 5....median is 3.5 and average is 3..
50% are above the median..
Therefore not necessarily true

III. Median is greater than the average of the largest number and smallest number.
Not necessarily true ..
Say the numbers are...
1,1,1,2,2,2,3...
Average is 12/7 so less than 2... Median is 2..
The average of the last number and the first number is (3+1)/2=2..
Thus median is equal to the average of the first and the last number.
Again not necessarily true.

All three are not necessarily true..

E
_________________
Re: For a list of positive numbers, if the median is greater   [#permalink] 27 Dec 2018, 08:46
Display posts from previous: Sort by