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Re: For a set of 3 numbers, assuming there is only one mode, [#permalink]
17 Dec 2009, 00:17

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]
17 Dec 2009, 01:05

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]
17 Dec 2009, 01:25

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]
26 Aug 2010, 11:17

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]
26 Aug 2010, 12:18

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]
26 Aug 2010, 13:26

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. _________________

Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.

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Re: For a set of 3 numbers, assuming there is only one mode,
[#permalink]
26 Aug 2010, 13:26