The arithmetic mean (average) of a set of 10 numbers is 10. : DS Archive
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 17 Jan 2017, 01:34

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# The arithmetic mean (average) of a set of 10 numbers is 10.

Author Message
Intern
Joined: 15 Sep 2007
Posts: 26
Followers: 0

Kudos [?]: 1 [0], given: 0

The arithmetic mean (average) of a set of 10 numbers is 10. [#permalink]

### Show Tags

26 Sep 2007, 07:07
1
This post was
BOOKMARKED
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 5 sessions

### HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

The arithmetic mean (average) of a set of 10 numbers is 10. Is the median value of the same set also equal to 10?

1) Exactly half of the numbers are less than 10.
2) The mode of the set of numbers is 10.
Intern
Joined: 15 Sep 2007
Posts: 26
Followers: 0

Kudos [?]: 1 [0], given: 0

### Show Tags

26 Sep 2007, 07:16
I am sure that it can't be (A). Here is why :

Median = (5th + 6th)/2

From (1), we know that 5th < 10, but we know nothing about 6th.

Case 1 : 5th = 9, 6th = 10, median = 19/2
Case 2 : 5th = 9, 6th = 11, median = 10

Therefore (1) is insufficient.
VP
Joined: 09 Jul 2007
Posts: 1104
Location: London
Followers: 6

Kudos [?]: 103 [0], given: 0

### Show Tags

26 Sep 2007, 09:31
E

Although half of the numbers are less than 10 in wht order are they placed. it can be 1-5 or 2-6 so on.
mode 10 still not suff.
Director
Joined: 09 Aug 2006
Posts: 763
Followers: 1

Kudos [?]: 192 [0], given: 0

### Show Tags

26 Sep 2007, 11:04
coldweather999 wrote:
The arithmetic mean (average) of a set of 10 numbers is 10. Is the median value of the same set also equal to 10?

1) Exactly half of the numbers are less than 10.
2) The mode of the set of numbers is 10.

I'm getting C. Knowing both Stat 1 and Stat 2, we can say that the median value will never be 10.

Median = (5th term + 6th term)/2

Stat 1:
set = 5, 5, 5, 5, 5, 15, 15, 15, 15, 15
In this case median = 10.

set = 4, 4, 4, 4, 9, 15, 15, 15, 15, 15
median is not equal to 10.

Insuff

Stat 2:
set = 10 times 10.
Median = 10

set = 3, 4, 4, 5, 9, 10, 10, 10, 20, 25
median is not equal to 10

Insuff.

Stat 1 & 2:

Since exactly half the values are under 10 then the 5th term has to be less than 10. Since the mode is 10, the 6th term has to be 10.
(10+number less than 10)/2 has to be less than 10.

Suff.
Manager
Joined: 18 Apr 2007
Posts: 120
Followers: 1

Kudos [?]: 5 [0], given: 0

### Show Tags

26 Sep 2007, 11:21
I get the same - C - using the same rationale as GK_GMAT. What's the OA?
Intern
Joined: 15 Sep 2007
Posts: 26
Followers: 0

Kudos [?]: 1 [0], given: 0

### Show Tags

26 Sep 2007, 12:07
Bluebird wrote:
I get the same - C - using the same rationale as GK_GMAT. What's the OA?

I also got (C) using the same logic as GK_GMAT...(i didn't assume the numbers to be whole numbers since it's not mentioned anywhere)...but the OA is (E)
VP
Joined: 10 Jun 2007
Posts: 1459
Followers: 7

Kudos [?]: 255 [0], given: 0

### Show Tags

26 Sep 2007, 13:02
coldweather999 wrote:
The arithmetic mean (average) of a set of 10 numbers is 10. Is the median value of the same set also equal to 10?

1) Exactly half of the numbers are less than 10.
2) The mode of the set of numbers is 10.

C for me.

(1)
1,2,3,4,5,15,16,17,18,19 gives you median of 10
1,2,3,4,8,15,16,17,18,22 gives you median more than 10
INSUFFICIENT

(2)
If all numbers are 10, then median =10
1,2,3,4,5,6,10,10, large, large gives median not equal to 10
INSUFFICIENT

Together, you can have
1,2,3,4,5,10,10,20,22,23
gives you median of not 10

Say a<10
You know that median = (10+a)/2
Since a is always less than 10, the median will never equals to 10.
SUFFICIENT
SVP
Joined: 28 Dec 2005
Posts: 1575
Followers: 3

Kudos [?]: 147 [0], given: 2

### Show Tags

26 Sep 2007, 16:15
why does the 6th term have to be 10 ?

It could be 11, and the 5th term could be 9, which give median of 10

Or, the 6th term could be 25, and the 5th term could be 3, therefore giving a median of 15

Just because the mode is 10, I dont think it means that the 6th term has to be 10
VP
Joined: 10 Jun 2007
Posts: 1459
Followers: 7

Kudos [?]: 255 [0], given: 0

### Show Tags

26 Sep 2007, 16:24
pmenon wrote:
why does the 6th term have to be 10 ?

It could be 11, and the 5th term could be 9, which give median of 10

Or, the 6th term could be 25, and the 5th term could be 3, therefore giving a median of 15

Just because the mode is 10, I dont think it means that the 6th term has to be 10

The question said exactly half the terms (5 terms) are less than 10. The mode is 10. This means the sixth term must be 10.
SVP
Joined: 28 Dec 2005
Posts: 1575
Followers: 3

Kudos [?]: 147 [0], given: 2

### Show Tags

26 Sep 2007, 17:02
bkk145 wrote:
pmenon wrote:
why does the 6th term have to be 10 ?

It could be 11, and the 5th term could be 9, which give median of 10

Or, the 6th term could be 25, and the 5th term could be 3, therefore giving a median of 15

Just because the mode is 10, I dont think it means that the 6th term has to be 10

The question said exactly half the terms (5 terms) are less than 10. The mode is 10. This means the sixth term must be 10.

Mode refers to the value in a set that is most repeated, right ? If that is the case, how does it mean that the sixth term has to be 10 ?

As long as 10 is the most repeated number in the set, thats all that matters right ?

Forgive me ! lol
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5062
Location: Singapore
Followers: 30

Kudos [?]: 355 [0], given: 0

### Show Tags

26 Sep 2007, 17:59
St1:
The set could be {0,0,0,0,1,10,10,10,10,59}. Mean = 10, Median = 5.5
The set could be {0,0,0,0,0,20,20,20,20,20}. Mean = 10, Median = 10.
Insufficient.

St2:
The set could be {10,10,10,10,10,10,10,10,10,10}. Mode = Mean = Median = 10
The set could be {1,2,3,4,5,6,10,10,10,49}. Mode = 10. Mean = 10. Median = 5.5
Insufficient.

St1 and St2:
The set could be {1,2,3,4,5,10,10,10,10,45}. Mode = Mean = 10. Median = 7.5
The set could eb {0,0,0,0,0,10,10,10,10,60}. Mode = Mean = 10. Median = 5.
Insufficient.

Ans E
Senior Manager
Joined: 18 Jun 2007
Posts: 294
Followers: 2

Kudos [?]: 56 [0], given: 0

### Show Tags

26 Sep 2007, 18:32
ywilfred wrote:
St1:
The set could be {0,0,0,0,1,10,10,10,10,59}. Mean = 10, Median = 5.5
The set could be {0,0,0,0,0,20,20,20,20,20}. Mean = 10, Median = 10.
Insufficient.

St2:
The set could be {10,10,10,10,10,10,10,10,10,10}. Mode = Mean = Median = 10
The set could be {1,2,3,4,5,6,10,10,10,49}. Mode = 10. Mean = 10. Median = 5.5
Insufficient.

St1 and St2:
The set could be {1,2,3,4,5,10,10,10,10,45}. Mode = Mean = 10. Median = 7.5
m
The set could eb {0,0,0,0,0,10,10,10,10,60}. Mode = Mean = 10. Median = 5.
Insufficient.

Ans E

how does it make C insufficient?
If we take both sets together 10 can never be median..question solved.
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5062
Location: Singapore
Followers: 30

Kudos [?]: 355 [0], given: 0

### Show Tags

26 Sep 2007, 18:36
rishi2377 wrote:
ywilfred wrote:
St1:
The set could be {0,0,0,0,1,10,10,10,10,59}. Mean = 10, Median = 5.5
The set could be {0,0,0,0,0,20,20,20,20,20}. Mean = 10, Median = 10.
Insufficient.

St2:
The set could be {10,10,10,10,10,10,10,10,10,10}. Mode = Mean = Median = 10
The set could be {1,2,3,4,5,6,10,10,10,49}. Mode = 10. Mean = 10. Median = 5.5
Insufficient.

St1 and St2:
The set could be {1,2,3,4,5,10,10,10,10,45}. Mode = Mean = 10. Median = 7.5
m
The set could eb {0,0,0,0,0,10,10,10,10,60}. Mode = Mean = 10. Median = 5.
Insufficient.

Ans E

how does it make C insufficient?
If we take both sets together 10 can never be median..question solved.

my bad.... it should be C. I thought the question was asking for the value of the median in which case the answer would be E.
Director
Joined: 14 Jan 2007
Posts: 777
Followers: 2

Kudos [?]: 136 [0], given: 0

### Show Tags

10 May 2008, 23:09
****makes no sense so Deleted*****

Last edited by vshaunak@gmail.com on 11 May 2008, 05:54, edited 1 time in total.
Intern
Joined: 29 Apr 2008
Posts: 21
Followers: 0

Kudos [?]: 0 [0], given: 0

### Show Tags

11 May 2008, 05:43
vshaunak@gmail.com wrote:
Should be 'E'.

S1 + S2 not suff

case1 - set = {7,8,9,10,10,16} mean=median=mode=10 and 3 elements are smaller than 10.
case2- set={1,2,3,4,10,10,10,40} mean=10, mode=10, median=7 and 4 elements and smaller than 10.

C)
case1 - median will be (9 + 10)/2 = 9.5 <10
Director
Joined: 14 Jan 2007
Posts: 777
Followers: 2

Kudos [?]: 136 [0], given: 0

### Show Tags

11 May 2008, 05:52
tarkumar wrote:
vshaunak@gmail.com wrote:
Should be 'E'.

S1 + S2 not suff

case1 - set = {7,8,9,10,10,16} mean=median=mode=10 and 3 elements are smaller than 10.
case2- set={1,2,3,4,10,10,10,40} mean=10, mode=10, median=7 and 4 elements and smaller than 10.

C)
case1 - median will be (9 + 10)/2 = 9.5 <10

Oops..wrong numbers....
yes it should be 'C'
Director
Joined: 26 Jul 2007
Posts: 541
Schools: Stern, McCombs, Marshall, Wharton
Followers: 7

Kudos [?]: 158 [0], given: 0

### Show Tags

12 May 2008, 12:05
ywilfred wrote:
St1:
The set could be {0,0,0,0,1,10,10,10,10,59}. Mean = 10, Median = 5.5
The set could be {0,0,0,0,0,20,20,20,20,20}. Mean = 10, Median = 10.
Insufficient.

St2:
The set could be {10,10,10,10,10,10,10,10,10,10}. Mode = Mean = Median = 10
The set could be {1,2,3,4,5,6,10,10,10,49}. Mode = 10. Mean = 10. Median = 5.5
Insufficient.

St1 and St2:
The set could be {1,2,3,4,5,10,10,10,10,45}. Mode = Mean = 10. Median = 7.5
The set could eb {0,0,0,0,0,10,10,10,10,60}. Mode = Mean = 10. Median = 5.
Insufficient.

Ans E

Quick question.

In you example St1 and St2. Wouldn't the mode be 0 as it's used 5 times and 10 is used 4 times.
Re:   [#permalink] 12 May 2008, 12:05
Display posts from previous: Sort by

# The arithmetic mean (average) of a set of 10 numbers is 10.

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.