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Set A consists of 8 different integers from the list {1,3,5,7,9,11,13,

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Set A consists of 8 different integers from the list {1,3,5,7,9,11,13,  [#permalink]

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New post Updated on: 12 Aug 2018, 23:05
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Solve any Mean and Standard deviation question under a minute- Exercise Question #4

4- Set A consists of 8 different integers from the list {1,3,5,7,9,11,13,15,17,19}. What is standard deviation of the set A?

    1. Set A does not include 11.
    2. The average of the numbers in the given list is equal to the average of numbers in set A.

Options

    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 solve question 5: Question 5


To read the article: Solve any Mean and Standard deviation question under a minute

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Originally posted by EgmatQuantExpert on 04 Jul 2018, 06:51.
Last edited by EgmatQuantExpert on 12 Aug 2018, 23:05, edited 2 times in total.
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Re: Set A consists of 8 different integers from the list {1,3,5,7,9,11,13,  [#permalink]

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New post Updated on: 07 Jul 2018, 07:14
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Solution



Given:
    • List A consist of 8 different integers from 10 integers: 1,3,5,7,9,11,13,15,17,19.

To find:

    • The standard deviation of set A.
      o To find the standard deviation of set A, we need to find which 8 integers are in the set A
      o Or, which 2 integers are not in the set A.

Statement-1: “Set A does not include 11. “

This does not give any information about one more integer that is not in set A or 8 integers that are in set A.
Hence, Statement 1 alone is not sufficient to answer the question.

Statement-2: “The average of the numbers in the given list is equal to the average of numbers in set A. “

    • Average of 10 integers = Average of 8 integers.
    • 100/100= Sum of integers/8
      o Sum of 8 integers= 80
      o Thus, two integers whose sum is 20 are not included in the set.
      o There can be many case when sum of two integers is 20.
         (1,19) or (3, 17) or (5, 15) or (7,13) or (9,11).

Since we do not know certainly which two integers are not in set A, statement 2 alone is not sufficient to answer the question.

Combining both the statements:

From Statement 1:

    • Set A does not include 11.

From Statement 1:

    • Two number that are not included can be (1,19) or (3, 17) or (5, 15) or (7,13) or (9,11).

By combining both the statements, the two integers that are not included are 11 and 9.

Hence, we can find the answer by combining both the statements.

Hence, the correct answer is option C.

Answer: C
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Originally posted by EgmatQuantExpert on 04 Jul 2018, 06:52.
Last edited by EgmatQuantExpert on 07 Jul 2018, 07:14, edited 1 time in total.
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Re: Set A consists of 8 different integers from the list {1,3,5,7,9,11,13,  [#permalink]

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New post 04 Jul 2018, 22:48
EgmatQuantExpert wrote:
Solve any Mean and Standard deviation question under a minute- Exercise Question #4

4- Set A consists of 8 different integers from the list {1,3,5,7,9,11,13,15,17,19}. What is standard deviation of the set A?

    1. Set A does not include 11.
    2. The average of the numbers in the given list is equal to the average of numbers in set A.

Options

    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.



given list = {1,3,5,7,9,11,13,15,17,19}. For this list, Mean = 10 and Median = 10, Mean=Median since the elements in this list are evenly spaced.
Now we have to choose 8 integers out of the 10 odd integers given in the list, to form another set A.
Question asks for Std Dev of set A. If set A gets fixed (i.e., if we can uniquely determine the elements of set A) then we can uniquely determine the Std Dev of set A also. But if there are multiple sets of values for set A, then Std Dev of set A might not be unique.
Lets start with the statements.

(1) So if we have to pick 8 integers from the list, but 11 cannot be included.
One possible set A = {1, 3, 5, 7, 9, 13, 15, 17}
Another possible set A = {1, 3, 5, 7, 9, 13, 15, 19}
As we can see that in the second possibility for set A, deviation among values is more than that in first possibility, so Std Dev in second case will be more. So the answer is not unique. Not sufficient.

(2) So we have to pick 8 integers to form set A such that mean of set A is also 10. Which means sum of all 8 integers in set A should be = 80.
One possible set A = {1, 3, 5, 7, 13, 15, 17, 19}
Another possible set A = {3, 5, 7, 9, 11, 13, 15, 17}
In both the above cases we can see that sum is 80, but in first case values are further apart from mean that in second case. So Std Dev in first case will be more than that in second case. So the answer is not unique. Not sufficient.

Combining the statements, sum has to be 80, but 11 cannot be included in the set. Apart from 11, the 9 integers left in the list {1, 3, 5, 7, 9, 13, 15, 17, 19}. Their sum = 1+3+5+7+9+13+15+17+19 = 89. If we have to select 8 integers such that their sum = 80, then the only way is to remove '9' from the list.
So we are left with only one possibility for set A:
Set A = {1, 3, 5, 7, 13, 15, 17, 19}.
Since its a unique set, its Std Dev will also be unique. Sufficient.

Hence C answer
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Re: Set A consists of 8 different integers from the list {1,3,5,7,9,11,13, &nbs [#permalink] 04 Jul 2018, 22:48
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