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 range of the set containing the numbers x, y, and z [#permalink]

Show Tags

05 Feb 2012, 16:31

4

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

65% (hard)

Question Stats:

62% (02:03) correct
38% (02:26) wrong based on 244 sessions

HideShow timer Statistics

If the range of the set containing the numbers x, y, and z is 8, what is the value of the smallest number in the set?

(1) The average of the set containing the numbers x, y, z, and 8 is 12.5. (2) The mean and the median of the set containing the numbers x, y, and z are equal.

If the range of the set containing the numbers x, y, and z is 8, what is the value of the smallest number in the set?

Let the numbers in ascending order be {x, y, z} (it really doesn't matter how we group them).

The range of a set is the difference between the largest and smallest elements in the set. Given: \(z-x=8\). Question: \(x=?\)

(1) The average of the set containing the numbers x, y, z, and 8 is 12.5 --> \(x+y+z+8=4*12.5=50\) --> \(x+y+z=42\): 2 distinct linear equations 3 with unknowns. Not sufficient.

(2) The mean and the median of the set containing the numbers x, y, and z are equal --> \(mean=\frac{x+y+z}{3}=y=median\) --> \(x+z=2y\): 2 distinct linear equations with 3 unknowns. Not sufficient.

(1)+(2) 3 distinct linear equations with 3 unknowns --> we can solve for \(x\). Sufficient.

here when you have calculated the mean .. as per the data in 1st option mean should include 8 in the set and its value is 12.5

but you have excluded it... can you just let me know where i am goin wrong

please explain me about the relation between mean and median.....

I don't understand what you mean.

(1) says: The average of the set containing the numbers x, y, z, and 8 is 12.5. So, \(\frac{x+y+z+8}{4}=12.5\) --> \(x+y+z+8=4*12.5=50\) --> \(x+y+z=42\).
_________________

if the range of the set containing the numbers x, y, and z [#permalink]

Show Tags

15 Sep 2012, 07:47

if the range of the set containing the numbers x, y, and z is 8, what is the value of the smallest number in the set?

(1) The average of the set containing the numbers x, y, z, and 8 is 12.5. (2) The mean and the median of the set containing the numbers x, y, and z are equal.

if the range of the set containing the numbers x, y, and z is 8, what is the value of the smallest number in the set?

(1) The average of the set containing the numbers x, y, z, and 8 is 12.5. (2) The mean and the median of the set containing the numbers x, y, and z are equal.

Merging similar topics. Please refer to the solution above.
_________________

Re: If the range of the set containing the numbers x, y, and z [#permalink]

Show Tags

15 Sep 2012, 08:10

I had a doubt regarding option A:

In that we are given that x + y+ z = 42 and also that range is 8.

Now lets say smallest number is x and largest is z then equation is (x) + (x+n) + (x+8). Where 0<n<8 .

isnt this constraint enough to give us the required answer? Since we are just looking for the smallest number, for finding the middle number we will need another equation.

In that we are given that x + y+ z = 42 and also that range is 8.

Now lets say smallest number is x and largest is z then equation is (x) + (x+n) + (x+8). Where 0<n<8 .

isnt this constraint enough to give us the required answer? Since we are just looking for the smallest number, for finding the middle number we will need another equation.

From (1) we can have many options, for example: {10, 14, 18} or {11, 12, 19}, therefore this statement is not sufficient.

Re: If the range of the set containing the numbers x, y, and z [#permalink]

Show Tags

21 Sep 2014, 18:41

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.
_________________

If the range of the set containing the numbers x, y, and z [#permalink]

Show Tags

22 Sep 2014, 09:26

calreg11 wrote:

If the range of the set containing the numbers x, y, and z is 8, what is the value of the smallest number in the set?

(1) The average of the set containing the numbers x, y, z, and 8 is 12.5. (2) The mean and the median of the set containing the numbers x, y, and z are equal.

C.

did it like this

1) x+y+z+8 = 50 => x+y+z = 42 and |x-z| = 8 so, sets can be: {8,16,16}, {9,15,17}, {10,14,18}, {11,13,19}, and {12,12,20} A is insufficient.

2) (x+y+z)/3 = y => x+z = 2y and |x-z| = 8 B is insufficient.

(1)+(2) among the sets in (1) the sets which have x+z = 2y is {10,14,18} hence C.
_________________

Re: If the range of the set containing the numbers x, y, and z [#permalink]

Show Tags

17 May 2016, 06:05

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 range of the set containing the numbers x, y, and z [#permalink]

Show Tags

29 Jul 2017, 07:45

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 range of the set containing the numbers x, y, and z [#permalink]

Show Tags

04 Aug 2017, 18:38

Bunuel wrote:

If the range of the set containing the numbers x, y, and z is 8, what is the value of the smallest number in the set?

Let the numbers in ascending order be {x, y, z} (it really doesn't matter how we group them).

The range of a set is the difference between the largest and smallest elements in the set. Given: \(z-x=8\). Question: \(x=?\)

(1) The average of the set containing the numbers x, y, z, and 8 is 12.5 --> \(x+y+z+8=4*12.5=50\) --> \(x+y+z=42\): 2 distinct linear equations 3 with unknowns. Not sufficient.

(2) The mean and the median of the set containing the numbers x, y, and z are equal --> \(mean=\frac{x+y+z}{3}=y=median\) --> \(x+z=2y\): 2 distinct linear equations with 3 unknowns. Not sufficient.

(1)+(2) 3 distinct linear equations with 3 unknowns --> we can solve for \(x\). Sufficient.

Answer: C.

Hey Bunuel , It doesn't say that x,y,z are the ONLY numbers in the set, right? I found this question quite ambiguous. Please help .
_________________

Version 8.1 of the WordPress for Android app is now available, with some great enhancements to publishing: background media uploading. Adding images to a post or page? Now...

“Keep your head down, and work hard. Don’t attract any attention. You should be grateful to be here.” Why do we keep quiet? Being an immigrant is a constant...

“Keep your head down, and work hard. Don’t attract any attention. You should be grateful to be here.” Why do we keep quiet? Being an immigrant is a constant...