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:

Re: For a set of 3 numbers, assuming there is only one mode, [#permalink]

Show Tags

17 Dec 2009, 01:17

1

This post was BOOKMARKED

xcusemeplz2009 wrote:

For a set of 3 numbers, assuming there is only one mode, does the mode equal the range? 1 The median equals the range 2 The largest number is twice the value of the smallest number

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D) EACH statement ALONE is sufficient. E) Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

The question stem says " assuming there is only one mode" so we need to consider sets where Mode is well defined [ I hope my understanding is correct] A stmnt 1 - median is equal to range lets consider a set { 0,2,2}. here we have median is equal to range. mode[2] is also equal to range lets consider the set { 2,2,4} here we median is equal to range but mode is equal to range. hence suff

stmnt2 - lets consider a set { 2,2,4}. here 4 = 2* 2(smallest number) and mode[2] is equal to range[2]. lets consider a set { 5,10,10} here 10 = 2* 5(smallest number) but mode[10] is not equal to range[5]. hence insuff

Re: For a set of 3 numbers, assuming there is only one mode, [#permalink]

Show Tags

17 Dec 2009, 02:05

Expert's post

kp1811 wrote:

The question stem says " assuming there is only one mode" so we need to consider sets where Mode is well defined [ I hope my understanding is correct] A stmnt 1 - median is equal to range lets consider a set { 0,2,2}. here we have median is equal to range. mode[2] is also equal to range lets consider the set { 2,2,4} here we median is equal to range but mode is equal to range. hence suff

stmnt2 - lets consider a set { 2,2,4}. here 4 = 2* 2(smallest number) and mode[2] is equal to range[2]. lets consider a set { 5,10,10} here 10 = 2* 5(smallest number) but mode[10] is not equal to range[5]. hence insuff

PS: What is the source of this question?

I think that above solution is correct and the answer is A, though there is one case missing.

Set can be of a form: A. {X,Y,Y} B. {X,X,Y} OR C. {XXX}

Basically telling us that there is only one mode, stem is saying that we do not have three distinct numbers in the set.

(2) The largest number is twice the value of the smallest number:

A. {X,Y,Y} --> Y=2X --> Set: {X,2X,2X}. Mode=2X, Range=2X-X=X, --> 2X equals to X only if X=0 (set: {0,0,0}), but we don't know that. Not always true. For example we can have set: {1,2,2} Mode=2, but range=1, 2#1. B. {X,X,Y} --> Y=2X --> Set: {X,X,2X}. Mode=X, Range=2X-X=X --> X=X. True. C. {XXX} --> X=2X --> X=0 --> Set: {0,0,0}. Mode=0, Range=0 --> 0=0. True.

Two different answers (cases B and C always true, A not always).

Re: For a set of 3 numbers, assuming there is only one mode, [#permalink]

Show Tags

17 Dec 2009, 02:25

kp1811 wrote:

xcusemeplz2009 wrote:

For a set of 3 numbers, assuming there is only one mode, does the mode equal the range? 1 The median equals the range 2 The largest number is twice the value of the smallest number

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D) EACH statement ALONE is sufficient. E) Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

The question stem says " assuming there is only one mode" so we need to consider sets where Mode is well defined [ I hope my understanding is correct] A stmnt 1 - median is equal to range lets consider a set { 0,2,2}. here we have median is equal to range. mode[2] is also equal to range lets consider the set { 2,2,4} here we median is equal to range but mode is equal to range. hence suff

stmnt2 - lets consider a set { 2,2,4}. here 4 = 2* 2(smallest number) and mode[2] is equal to range[2]. lets consider a set { 5,10,10} here 10 = 2* 5(smallest number) but mode[10] is not equal to range[5]. hence insuff

Re: For a set of 3 numbers, assuming there is only one mode, [#permalink]

Show Tags

26 Aug 2010, 12:17

Bunuel Can you please explain this about mode? I believe it is the number that occurs most frequently in the set? So in this case if all 3 numbers were different then would the mode be 0? Mode 1 means a number repeats more than once? Can there be mode 2 or 3?

Re: For a set of 3 numbers, assuming there is only one mode, [#permalink]

Show Tags

26 Aug 2010, 13:18

Expert's post

mainhoon wrote:

Bunuel Can you please explain this about mode? I believe it is the number that occurs most frequently in the set? So in this case if all 3 numbers were different then would the mode be 0? Mode 1 means a number repeats more than once? Can there be mode 2 or 3?

Posted from my mobile device

The mode is the number that occurs the most frequently in a data set. For example mode of the set {2, 3, 4, 4} is 4.

Set can have more than one mode, for example set {2, 2, 3, 3, 5} has 2 modes 2 and 3.

If every number in the set occurs an equal number of times, then the set has no mode. For example set {1, 2, 3} has no mode. _________________

Re: For a set of 3 numbers, assuming there is only one mode, [#permalink]

Show Tags

26 Aug 2010, 14:26

Expert's post

xcusemeplz2009 wrote:

For a set of 3 numbers, assuming there is only one mode, does the mode equal the range? 1 The median equals the range 2 The largest number is twice the value of the smallest number

We don't really need to consider cases for Statement 1. We have one mode, so at least two of our elements are equal. So our set is {a, a, b}, where b could be anything. Whether b is greater than, equal to, or less than a, a is going to be the median, so median=mode. If from S1, median=range, then mode=range.

S2 is not sufficient, as seen above; your set can be {a, a, 2a} or {a, 2a, 2a}, and the answer might be yes or no respectively. _________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

For a set of 3 numbers, assuming there is only one mode, does the mode equal the range?

1>The median equals the range

2>The largest number is twice the value of the smallest number

mode is the number which occurs most frequently in a set of numbers.

lets say mode is x. there have to be at least two instances of x. set can be x, x, y or z,x,x median equals range:Range= y - x = x --> y = 2x. Mode x is equal to range y-x which is equal to x or x - z = x --> z--> 0 thus range is x which is equal to the median/mode if all three numbers are same : set is x,x,x range is zero; but it can be equal to median only if x is zero, or the set is 0,0,0 here range= median = mode =0 1 is sufficient

2. largest number is twice smallest number. For there to be a single mode either the largest number comes twice, or the smallest number. n,n,2n ---> Range=n, median is n and so is mode hence satsified n,2n,2n ---> Range is n , median is 2n so is mode but mode is not equal to median or range. thus this is not giving one result.. not sufficient.

Let a,b,c is 2,2,4. As per statement 1which is true. then mode(2) equals to range 4-2=2.sufficient.

statement 2 is also implies same meaning but with different wording. By taking 2,2,4 as a,,b,c values , we can conclude that mode equals to range. Sufficient. The answer is D

Re: For a set of 3 numbers, assuming there is only one mode, [#permalink]

Show Tags

14 Jul 2015, 10:50

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. _________________

Excellent posts dLo saw your blog too..!! Man .. you have got some writing skills. And Just to make an argument = You had such an amazing resume ; i am glad...

So Much $$$ Business school costs a lot. This is obvious, whether you are a full-ride scholarship student or are paying fully out-of-pocket. Aside from the (constantly rising)...

London is the best kept secret of the corporate world. It is English speaking and time delayed by only 5 hours. That means when London goes home at 5...