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For a set of 3 numbers, assuming there is only one mode,

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For a set of 3 numbers, assuming there is only one mode, [#permalink] New post 16 Dec 2009, 21:36
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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
[Reveal] Spoiler: OA

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

PS: What is the source of this question?
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Re: For a set of 3 numbers, assuming there is only one mode, [#permalink] New post 17 Dec 2009, 01:05
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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.

(1) The median equals the range:

A. {X,Y,Y} --> Y=Y-X --> X=0 --> Set: {0,Y,Y}. Mode=Y, Range=Y-0=Y, --> Y=Y. True.
B. {X,X,Y} --> X=Y-X --> 2X=Y --> Set: {X,X,2X}. Mode=X, Range=2X-X=X --> X=X. True.
C. {XXX} --> X=X-X --> X=0 --> Set: {0,0,0}. Mode=0, Range=0 --> 0=0. True.

Sufficient.

(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).

Not sufficient.

Answer: A.
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Re: For a set of 3 numbers, assuming there is only one mode, [#permalink] New post 17 Dec 2009, 01:21
thanks bunuel for the soln..
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Re: For a set of 3 numbers, assuming there is only one mode, [#permalink] New post 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

PS: What is the source of this question?

thanks for the expln
OA is
[Reveal] Spoiler:
A


source-http://www.takegmat.com/
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Re: For a set of 3 numbers, assuming there is only one mode, [#permalink] New post 26 Aug 2010, 06:04
For a set of 3 numbers, assuming there is only one mode, does the mode equal the range?


s1 The median equals the range

s2 The largest number is twice the value of the smallest number


can some one list all the properties of range / SD / median

for EG: SD can never be negative or SD = 0 if all memberes of sets are =

thanks
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Re: For a set of 3 numbers, assuming there is only one mode, [#permalink] New post 26 Aug 2010, 06:35
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Re: For a set of 3 numbers, assuming there is only one mode, [#permalink] New post 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?

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Re: For a set of 3 numbers, assuming there is only one mode, [#permalink] New post 26 Aug 2010, 12:18
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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?

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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.
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Re: For a set of 3 numbers, assuming there is only one mode, [#permalink] New post 26 Aug 2010, 13:26
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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.
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For a set of 3 numbers, assuming there is only one mode, [#permalink] New post 23 Jul 2011, 01:29
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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
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Re: mode ,median! [#permalink] New post 23 Jul 2011, 01:45
Very nice question. I did it wrong and understood and very important concept. Thanks

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Re: mode ,median! [#permalink] New post 23 Jul 2011, 05:14
AnkitK 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


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.
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Re: mode ,median! [#permalink] New post 24 Jul 2011, 07:36
I got D as answer.

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
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Re: For a set of 3 numbers, assuming there is only one mode, [#permalink] New post 14 Jul 2015, 09:50
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Re: For a set of 3 numbers, assuming there is only one mode,   [#permalink] 14 Jul 2015, 09:50
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