If the average of four distinct positive integers is 60, how : DS Archive
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 24 Jan 2017, 01:51

### 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

# If the average of four distinct positive integers is 60, how

Author Message
Manager
Joined: 05 Dec 2009
Posts: 127
Followers: 2

Kudos [?]: 87 [0], given: 0

If the average of four distinct positive integers is 60, how [#permalink]

### Show Tags

02 Jan 2010, 08:13
4
This post was
BOOKMARKED
00:00

Difficulty:

(N/A)

Question Stats:

82% (01:59) correct 18% (03:33) wrong based on 65 sessions

### HideShow timer Statistics

If the average of four distinct positive integers is 60, how many integers of these four are smaller than 50?

1)One of the integers is 200.
2)The median of the four integers is 50.

Statements (1) and (2) TOGETHER are NOT sufficient
Statement (1) by itself is sufficient. The sum of the 4 integers equals . If one of the integers is 200 then the sum of the other three has to be 40. It is clear that each of these three integers is less than 50.

Statement (2) by itself is sufficient. From S2 it follows that two of the integers are less than 50 and two of the integers are more than 50. If the integers are arranged in ascending order, then the . As all the integers are different, no number can equal 50.

I am not convinced with the Stmt 2's conclusion since we can have a set (20,50,70,100)...so only 1 number is less than 50.
While in (20, 40, 60, 120) we have 2 numbers less than 50. in both the sets all the 4 numbers are less than 50.
Math Expert
Joined: 02 Sep 2009
Posts: 36625
Followers: 7103

Kudos [?]: 93607 [0], given: 10583

Re: Q#28 of GMATclub test # 8 [#permalink]

### Show Tags

02 Jan 2010, 09:26
xyztroy wrote:
If the average of four distinct positive integers is 60, how many integers of these four are smaller than 50?

1)One of the integers is 200.
2)The median of the four integers is 50.
Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient

Statements (1) and (2) TOGETHER are NOT sufficient
Statement (1) by itself is sufficient. The sum of the 4 integers equals . If one of the integers is 200 then the sum of the other three has to be 40. It is clear that each of these three integers is less than 50.

Statement (2) by itself is sufficient. From S2 it follows that two of the integers are less than 50 and two of the integers are more than 50. If the integers are arranged in ascending order, then the . As all the integers are different, no number can equal 50.

I am not convinced with the Stmt 2's conclusion since we can have a set (20,50,70,100)...so only 1 number is less than 50.
While in (20, 40, 60, 120) we have 2 numbers less than 50. in both the sets all the 4 numbers are less than 50.

Note: we have four distinct positive integers and x1+x2+x3+x4=240.

(1) x1+x2+x3+200=240 --> x1+x2+x3=40, hence three integers are less than 50. Sufficient.

(2) Median of this set would be the average of middle numbers: x2+x3=100 --> x2<50 (as integers are distinct). x1<x2, hence we have two integers less than 50. Sufficient.

In your example {20,50,70,100} median is (50+70)/2=60 and not 50.

BUT there is another problem with this question: from (1) we got that there are 3 integers less than 50 and from (2) we got that there are 2 integers less than 50. In DS statements never contradict so either of the statement should be changed.
_________________
Manager
Joined: 09 May 2009
Posts: 203
Followers: 1

Kudos [?]: 226 [0], given: 13

Re: Q#28 of GMATclub test # 8 [#permalink]

### Show Tags

02 Jan 2010, 09:32
xyztroy wrote:
If the average of four distinct positive integers is 60, how many integers of these four are smaller than 50?

1)One of the integers is 200.
2)The median of the four integers is 50.
Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient

Statements (1) and (2) TOGETHER are NOT sufficient
Statement (1) by itself is sufficient. The sum of the 4 integers equals . If one of the integers is 200 then the sum of the other three has to be 40. It is clear that each of these three integers is less than 50.

Statement (2) by itself is sufficient. From S2 it follows that two of the integers are less than 50 and two of the integers are more than 50. If the integers are arranged in ascending order, then the . As all the integers are different, no number can equal 50.

I am not convinced with the Stmt 2's conclusion since we can have a set (20,50,70,100)...so only 1 number is less than 50.
While in (20, 40, 60, 120) we have 2 numbers less than 50. in both the sets all the 4 numbers are less than 50.

SETS CHOSEN DOESN'T SATISFY s2) CONDITION

if we select a set as per 2 then its 2nd and 3rd element must be equidistant from 50 and therfore we have exactly two no's less than 50
_________________

GMAT is not a game for losers , and the moment u decide to appear for it u are no more a loser........ITS A BRAIN GAME

Manager
Joined: 05 Dec 2009
Posts: 127
Followers: 2

Kudos [?]: 87 [0], given: 0

Re: Q#28 of GMATclub test # 8 [#permalink]

### Show Tags

02 Jan 2010, 09:54
Sorry, I was not thinking in the right direction

Bunuel wrote:
xyztroy wrote:
If the average of four distinct positive integers is 60, how many integers of these four are smaller than 50?

1)One of the integers is 200.
2)The median of the four integers is 50.
Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient

Statements (1) and (2) TOGETHER are NOT sufficient
Statement (1) by itself is sufficient. The sum of the 4 integers equals . If one of the integers is 200 then the sum of the other three has to be 40. It is clear that each of these three integers is less than 50.

Statement (2) by itself is sufficient. From S2 it follows that two of the integers are less than 50 and two of the integers are more than 50. If the integers are arranged in ascending order, then the . As all the integers are different, no number can equal 50.

I am not convinced with the Stmt 2's conclusion since we can have a set (20,50,70,100)...so only 1 number is less than 50.
While in (20, 40, 60, 120) we have 2 numbers less than 50. in both the sets all the 4 numbers are less than 50.

Note: we have four distinct positive integers and x1+x2+x3+x4=240.

(1) x1+x2+x3+200=240 --> x1+x2+x3=40, hence three integers are less than 50. Sufficient.

(2) Median of this set would be the average of middle numbers: x2+x3=100 --> x2<50 (as integers are distinct). x1<x2, hence we have two integers less than 50. Sufficient.

In your example {20,50,70,100} median is (50+70)/2=60 and not 50.

BUT there is another problem with this question: from (1) we got that there are 3 integers less than 50 and from (2) we got that there are 2 integers less than 50. In DS statements never contradict so either of the statement should be changed.
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13536
Followers: 577

Kudos [?]: 163 [0], given: 0

Re: If the average of four distinct positive integers is 60, how [#permalink]

### Show Tags

29 Nov 2014, 08:52
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Director
Status: Tutor - BrushMyQuant
Joined: 05 Apr 2011
Posts: 583
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 570 Q49 V19
GMAT 2: 700 Q51 V31
GPA: 3
WE: Information Technology (Computer Software)
Followers: 101

Kudos [?]: 572 [0], given: 55

Re: If the average of four distinct positive integers is 60, how [#permalink]

### Show Tags

21 Nov 2015, 07:54
Please move this problem to DS
Thank you
xyztroy wrote:
If the average of four distinct positive integers is 60, how many integers of these four are smaller than 50?

1)One of the integers is 200.
2)The median of the four integers is 50.

Statements (1) and (2) TOGETHER are NOT sufficient
Statement (1) by itself is sufficient. The sum of the 4 integers equals . If one of the integers is 200 then the sum of the other three has to be 40. It is clear that each of these three integers is less than 50.

Statement (2) by itself is sufficient. From S2 it follows that two of the integers are less than 50 and two of the integers are more than 50. If the integers are arranged in ascending order, then the . As all the integers are different, no number can equal 50.

I am not convinced with the Stmt 2's conclusion since we can have a set (20,50,70,100)...so only 1 number is less than 50.
While in (20, 40, 60, 120) we have 2 numbers less than 50. in both the sets all the 4 numbers are less than 50.

_________________

Ankit

Check my Tutoring Site -> Brush My Quant

GMAT Quant Tutor
How to start GMAT preparations?
How to Improve Quant Score?
Gmatclub Topic Tags
Check out my GMAT debrief

How to Solve :
Statistics || Reflection of a line || Remainder Problems || Inequalities

Re: If the average of four distinct positive integers is 60, how   [#permalink] 21 Nov 2015, 07:54
Display posts from previous: Sort by