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Set X consists of at least 2 members and is a set of consecutive odd i

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Director
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Set X consists of at least 2 members and is a set of consecutive odd i  [#permalink]

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28 May 2018, 09:23
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5
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Difficulty:

85% (hard)

Question Stats:

45% (02:13) correct 55% (02:31) wrong based on 72 sessions

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Set X consists of at least 2 members and is a set of consecutive odd integers with an average (arithmetic mean) of 37.
Set Y consists of at least 10 members and is also a set of consecutive odd integers with an average (arithmetic mean) of 37.
Set Z consists of all of the members of both set X and set Y.

Which of the following statements must be true?

I. The standard deviation of set Z is not equal to the standard deviation of set X.
II. The standard deviation of set Z is equal to the standard deviation of set Y.
III. The average (arithmetic mean) of set Z is 37.

A) I only
B) II only
C) III only
D) I and III
E) II and III

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Status: Learning stage
Joined: 01 Oct 2017
Posts: 931
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Re: Set X consists of at least 2 members and is a set of consecutive odd i  [#permalink]

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04 Jun 2018, 04:21
CAMANISHPARMAR wrote:
Set X consists of at least 2 members and is a set of consecutive odd integers with an average (arithmetic mean) of 37.
Set Y consists of at least 10 members and is also a set of consecutive odd integers with an average (arithmetic mean) of 37.
Set Z consists of all of the members of both set X and set Y.

Which of the following statements must be true?

I. The standard deviation of set Z is not equal to the standard deviation of set X.
II. The standard deviation of set Z is equal to the standard deviation of set Y.
III. The average (arithmetic mean) of set Z is 37.

A) I only
B) II only
C) III only
D) I and III
E) II and III

Set X:-

#elements=2n+1, where $$n\geq{1}$$ (since set X contains consecutive odd integers with mean as an odd integer)

Since 37 is the mean, hence set X contains odd numbers of elements with at least 37 as one of the member.

Set Y:-

#elements=2n+1, where $$n\geq{5}$$
Since 37 is the mean, hence set Y contains odd numbers of elements with at least 37 as one of the member.

Set Z:-

Z=X U Y

Now let's evaluate each statement:-

I. SD of set Z will be same as SD of set X when set X and set Y are equal. In all other cases, SD of Z will be different from SD of X. Hence this statement is not true.
II.SD of set Z will be same as SD of set Y when set X and set Y are equal. In all other cases, SD of Z will be different from SD of Y. Hence this statement is not true.
Note:- 2 sets equally spaced , there SD depend on #elements they possess. Greater the no of elements in the set, greater is the SD.
III. Here there are 3 cases, viz,
1. Set Z=Set X=Set Y
2. Set Z= Set X or Set Y
3. Set Z= Set X and Set Y
In the above cases, since both Set X and Y have mean 37. Hence, set Z will always has a mean of 37. hence this statement is correct.

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Joined: 04 Apr 2017
Posts: 20
Re: Set X consists of at least 2 members and is a set of consecutive odd i  [#permalink]

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29 Jun 2018, 06:51
PKN wrote:
CAMANISHPARMAR wrote:
Set X consists of at least 2 members and is a set of consecutive odd integers with an average (arithmetic mean) of 37.
Set Y consists of at least 10 members and is also a set of consecutive odd integers with an average (arithmetic mean) of 37.
Set Z consists of all of the members of both set X and set Y.

Which of the following statements must be true?

I. The standard deviation of set Z is not equal to the standard deviation of set X.
II. The standard deviation of set Z is equal to the standard deviation of set Y.
III. The average (arithmetic mean) of set Z is 37.

A) I only
B) II only
C) III only
D) I and III
E) II and III

Set X:-

#elements=2n+1, where $$n\geq{1}$$ (since set X contains consecutive odd integers with mean as an odd integer)

Since 37 is the mean, hence set X contains odd numbers of elements with at least 37 as one of the member.

Set Y:-

#elements=2n+1, where $$n\geq{5}$$
Since 37 is the mean, hence set Y contains odd numbers of elements with at least 37 as one of the member.

Set Z:-

Z=X U Y

Now let's evaluate each statement:-

I. SD of set Z will be same as SD of set X when set X and set Y are equal. In all other cases, SD of Z will be different from SD of X. Hence this statement is not true.
II.SD of set Z will be same as SD of set Y when set X and set Y are equal. In all other cases, SD of Z will be different from SD of Y. Hence this statement is not true.
Note:- 2 sets equally spaced , there SD depend on #elements they possess. Greater the no of elements in the set, greater is the SD.
III. Here there are 3 cases, viz,
1. Set Z=Set X=Set Y
2. Set Z= Set X or Set Y
3. Set Z= Set X and Set Y
In the above cases, since both Set X and Y have mean 37. Hence, set Z will always has a mean of 37. hence this statement is correct.

PKN
The Q says that "Set Z consists of all of the members of both set X and set Y". Nothing mentioned here that no repeated members in set Z. So I thought if X =Y, then Z should equals 2X equals 2Y, then statement 2 should be true. Isn't it?
Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 931
WE: Supply Chain Management (Energy and Utilities)
Set X consists of at least 2 members and is a set of consecutive odd i  [#permalink]

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29 Jun 2018, 07:05
HisHo wrote:
PKN wrote:
CAMANISHPARMAR wrote:
Set X consists of at least 2 members and is a set of consecutive odd integers with an average (arithmetic mean) of 37.
Set Y consists of at least 10 members and is also a set of consecutive odd integers with an average (arithmetic mean) of 37.
Set Z consists of all of the members of both set X and set Y.

Which of the following statements must be true?

I. The standard deviation of set Z is not equal to the standard deviation of set X.
II. The standard deviation of set Z is equal to the standard deviation of set Y.
III. The average (arithmetic mean) of set Z is 37.

A) I only
B) II only
C) III only
D) I and III
E) II and III

Set X:-

#elements=2n+1, where $$n\geq{1}$$ (since set X contains consecutive odd integers with mean as an odd integer)

Since 37 is the mean, hence set X contains odd numbers of elements with at least 37 as one of the member.

Set Y:-

#elements=2n+1, where $$n\geq{5}$$
Since 37 is the mean, hence set Y contains odd numbers of elements with at least 37 as one of the member.

Set Z:-

Z=X U Y

Now let's evaluate each statement:-

I. SD of set Z will be same as SD of set X when set X and set Y are equal. In all other cases, SD of Z will be different from SD of X. Hence this statement is not true.
II.SD of set Z will be same as SD of set Y when set X and set Y are equal. In all other cases, SD of Z will be different from SD of Y. Hence this statement is not true.
Note:- 2 sets equally spaced , there SD depend on #elements they possess. Greater the no of elements in the set, greater is the SD.
III. Here there are 3 cases, viz,
1. Set Z=Set X=Set Y
2. Set Z= Set X or Set Y
3. Set Z= Set X and Set Y
In the above cases, since both Set X and Y have mean 37. Hence, set Z will always has a mean of 37. hence this statement is correct.

PKN
The Q says that "Set Z consists of all of the members of both set X and set Y". Nothing mentioned here that no repeated members in set Z. So I thought if X =Y, then Z should equals 2X equals 2Y, then statement 2 should be true. Isn't it?

Hi HisHo,

First of all, please notice that the question stem is a "MUST BE TRUE". In these type of questions, you need to validate the data at all possible circumstances.

You have found out one possible case where (II) is valid. But there are many cases as highlighted in the explanation where (II) is not valid( When set X and Y are not equal).
Hope it helps.
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

Senior Manager
Joined: 04 Aug 2010
Posts: 310
Schools: Dartmouth College
Set X consists of at least 2 members and is a set of consecutive odd i  [#permalink]

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29 Jun 2018, 10:35
2
CAMANISHPARMAR wrote:
Set X consists of at least 2 members and is a set of consecutive odd integers with an average (arithmetic mean) of 37.
Set Y consists of at least 10 members and is also a set of consecutive odd integers with an average (arithmetic mean) of 37.
Set Z consists of all of the members of both set X and set Y.

Which of the following statements must be true?

I. The standard deviation of set Z is not equal to the standard deviation of set X.
II. The standard deviation of set Z is equal to the standard deviation of set Y.
III. The average (arithmetic mean) of set Z is 37.

A) I only
B) II only
C) III only
D) I and III
E) II and III

Not a precise definition of SD, but close enough for the GMAT:
SD = average distance from the mean.

The prompt indicates that X and Y are each composed of consecutive odd integers.
They have the SAME MEAN but could have the SAME NUMBER of terms or a DIFFERENT NUMBER of terms.

Consider an easy case in which X and Y have the same mean and the SAME number of terms:
X = 1, 3, 5
Y = 1, 3, 5
Z = 1, 1, 3, 3, 5, 5
In this case, the average distance from the mean in Z is equal to the average distance from the mean in X, implying that the two sets have the same SD.
The case above illustrates the following:
If X and Y have the same number of terms, then Z and X will have the same SD.
Since Statement I does not have to be true, eliminate A and D.

Consider an easy case in which X and Y have the same mean but a DIFFERENT number of terms:
X = 1, 3, 5, 7, 9
Y = 3, 5, 7
Z = 1, 3, 3, 5, 5, 7, 7, 9
In this case, the values in Z deviate more from the mean than do the values in Y, implying that the two sets do NOT have the same SD.
The case above illustrates the following:
If X and Y have a DIFFERENT number of terms, then Z and Y will NOT have the same SD.
Since Statement II does not have to be true, eliminate B and E.

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Set X consists of at least 2 members and is a set of consecutive odd i &nbs [#permalink] 29 Jun 2018, 10:35
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