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

 It is currently 11 Dec 2019, 22:28

### 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

# In the data set, {a, 0, 1, 6, 9, 10, 11}, consisting of seven distinct

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Manager
Joined: 18 Jul 2019
Posts: 54
In the data set, {a, 0, 1, 6, 9, 10, 11}, consisting of seven distinct  [#permalink]

### Show Tags

25 Nov 2019, 06:23
00:00

Difficulty:

55% (hard)

Question Stats:

43% (01:51) correct 57% (01:50) wrong based on 21 sessions

### HideShow timer Statistics

In the data set, {a, 0, 1, 6, 9, 10, 11}, consisting of seven distinct integers, one of the numbers is the mean as well as the median. How many values of ‘a’ are possible?

a) 1
b) 2
c) 3
d) 4
e) 5
Director
Joined: 27 May 2012
Posts: 947
In the data set, {a, 0, 1, 6, 9, 10, 11}, consisting of seven distinct  [#permalink]

### Show Tags

25 Nov 2019, 12:04
CaptainLevi wrote:
In the data set, {a, 0, 1, 6, 9, 10, 11}, consisting of seven distinct integers, one of the numbers is the mean as well as the median. How many values of ‘a’ are possible?

a) 1
b) 2
c) 3
d) 4
e) 5

Total of the data set is $$= 37+a$$

One of the numbers is the mean as well as the median so:

If mean is 0 as then total of Data set would be 7*0= 0 which implies $$37+a=0$$ which implies $$a=$$ -37
So set looks like { -37,0, 1, 6, 9,10,11} is this NOT valid as mean $$\neq$$ median , mean=0 and median =6

If mean is 1 as then total of the data set would be 7*1=7 which implies $$37+a=7$$ which implies $$a=$$ -30
So set looks like { -30,0, 1, 6, 9,10,11} is this NOT valid as mean $$\neq$$ median , mean=7 and median =6

If mean is 6 then total of data set is 7*6= 42 which implies $$37+a=42$$ which implies $$a=$$ 5
So set looks like { 0, 1, 5, 6, 9,10,11} is this valid as mean = median = 6

If mean is 9 then total of data set is 7*9= 63 which implies $$37+a=63$$ which implies $$a=$$ 26
So set looks like { 0, 1, 6, 9,10,11,26} is this also valid as mean = median = 9

If mean is 10 then total of data set is 7*10=70 which implies $$37+a=70$$ which implies $$a=$$33
So set would look like { 0, 1, 6, 9,10,11,33} this is NOT valid as mean $$\neq$$median , mean is 10 and median is 9

Hence among the elements of the data set mean cannot be 0,1, 10,11 and 13 as then mean $$\neq$$median.

Thus we can have only two values of mean 6 and 10 such that mean= median, leading to two values for $$a$$ (5 and 26)

Ans-B
_________________
- Stne
In the data set, {a, 0, 1, 6, 9, 10, 11}, consisting of seven distinct   [#permalink] 25 Nov 2019, 12:04
Display posts from previous: Sort by

# In the data set, {a, 0, 1, 6, 9, 10, 11}, consisting of seven distinct

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne