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CAMANISHPARMAR
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Set X consists of at least 2 members and is a set of consecutive odd i 28 May 2018, 10:23
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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95% (hard)

Question Stats:

48% (02:07) correct 52% (02:34) wrong based on 305 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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C
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Set X consists of at least 2 members and is a set of consecutive odd i 04 Jun 2018, 05:21
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CAMANISHPARMAR
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.

Answer Option. C
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Set X consists of at least 2 members and is a set of consecutive odd i 29 Jun 2018, 07:51
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CAMANISHPARMAR
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.

Answer Option. C
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?
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Set X consists of at least 2 members and is a set of consecutive odd i 29 Jun 2018, 08:05
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HisHo
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CAMANISHPARMAR
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.

Answer Option. C
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.
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Set X consists of at least 2 members and is a set of consecutive odd i 29 Jun 2018, 11:35
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CAMANISHPARMAR
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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C
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Set X consists of at least 2 members and is a set of consecutive odd i 22 Jun 2025, 09:19
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We need to recognise few things here before we move on to the Statements.
X >=2. But, for two consecutive odd integers, mean will be even integer. Eg: for 3 and 5 mean is 4, for 39 and 41 mean is 40. This can be extended for even no of consecutive odd integers. So the number of elements in set X will be odd and more than 2, that means, 3,5,7,9,11,13........ with mean of 37.
Same for Set Y but the number of elements ranges from 11,13,15,..... with mean of 37.
Now, Number in set X can be lower of higher than Set Y. because Set Y could be 11 elements and Set X could be 13 elements. Since Standard deviation varies with number of elements in the set. We cannot say which will turn out true between statements I and II so for MBT, both have conditions to turn out not true, so Eliminate I and II.
Now Set Z has all the elements Set X and Y have. But since. Either Set X will be a subset of Y or vice versa or Both could be same sets when both have same number of elements. Then Set Z will also have the same mean. (Statement III proven true). Hence Ans C.
CAMANISHPARMAR
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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