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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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

Show Tags

02 Jan 2010, 09:13

4

This post was BOOKMARKED

00:00

A

B

C

D

E

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.

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.

Answer: D.

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. _________________

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

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.

Answer: D.

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.

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

Show Tags

29 Nov 2014, 09:52

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.
_________________

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

Show Tags

21 Nov 2015, 08:54

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.

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

Show Tags

16 Apr 2017, 04:06

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.
_________________