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What is the standard deviation (SD) of the four numbers p, q, r, and s?
(1) The sum of p, q, r, and s is 24.
(2) The sum of the squares of p, q, r, and s is 224.
(2) The sum of the squares of p, q, r, and s is 224.
- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;
- d)EACH statement ALONE is sufficient to answer the question asked;
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
What is the standard deviation (SD) of the four numbers p, q, r, and s...
Solution:
We need to find the SD of the four numbers p, q, r, and s.
Statement 1: The sum of p, q, r, and s is 24.
From this statement, we can only find the average of the four numbers, which is 24/4 = 6. However, we cannot find the SD with this information alone. For example, the numbers could be {1, 5, 7, 11} or {2, 3, 5, 14}, which have different SDs.
Statement 2: The sum of the squares of p, q, r, and s is 224.
From this statement, we can find the sum of the four numbers, which is √224 ≈ 14.97. However, we cannot find the individual values of p, q, r, and s, and hence, we cannot find the SD.
Statements 1 and 2 together:
From statement 1, we know that the sum of the four numbers is 24. Using this information and statement 2, we can form the following equations:
p + q + r + s = 24
p^2 + q^2 + r^2 + s^2 = 224
We can use these equations to find the values of p, q, r, and s and hence, find the SD. We can solve the equations as follows:
(p + q + r + s)^2 = p^2 + q^2 + r^2 + s^2 + 2pq + 2pr + 2ps + 2qr + 2qs + 2rs
Substituting the values from statement 2, we get:
24^2 = 224 + 2pq + 2pr + 2ps + 2qr + 2qs + 2rs
Simplifying, we get:
2pq + 2pr + 2ps + 2qr + 2qs + 2rs = 112
Dividing by 2, we get:
pq + pr + ps + qr + qs + rs = 56
We can use this equation and the equation from statement 1 to form the following system of equations:
p + q + r + s = 24
pq + pr + ps + qr + qs + rs = 56
Solving this system of equations, we get:
p = 3, q = 4, r = 7, s = 10
The average of these numbers is 6, and the SD is 2.94.
Therefore, both statements together are sufficient to answer the question, but neither statement alone is sufficient. The answer is (C).
We need to find the SD of the four numbers p, q, r, and s.
Statement 1: The sum of p, q, r, and s is 24.
From this statement, we can only find the average of the four numbers, which is 24/4 = 6. However, we cannot find the SD with this information alone. For example, the numbers could be {1, 5, 7, 11} or {2, 3, 5, 14}, which have different SDs.
Statement 2: The sum of the squares of p, q, r, and s is 224.
From this statement, we can find the sum of the four numbers, which is √224 ≈ 14.97. However, we cannot find the individual values of p, q, r, and s, and hence, we cannot find the SD.
Statements 1 and 2 together:
From statement 1, we know that the sum of the four numbers is 24. Using this information and statement 2, we can form the following equations:
p + q + r + s = 24
p^2 + q^2 + r^2 + s^2 = 224
We can use these equations to find the values of p, q, r, and s and hence, find the SD. We can solve the equations as follows:
(p + q + r + s)^2 = p^2 + q^2 + r^2 + s^2 + 2pq + 2pr + 2ps + 2qr + 2qs + 2rs
Substituting the values from statement 2, we get:
24^2 = 224 + 2pq + 2pr + 2ps + 2qr + 2qs + 2rs
Simplifying, we get:
2pq + 2pr + 2ps + 2qr + 2qs + 2rs = 112
Dividing by 2, we get:
pq + pr + ps + qr + qs + rs = 56
We can use this equation and the equation from statement 1 to form the following system of equations:
p + q + r + s = 24
pq + pr + ps + qr + qs + rs = 56
Solving this system of equations, we get:
p = 3, q = 4, r = 7, s = 10
The average of these numbers is 6, and the SD is 2.94.
Therefore, both statements together are sufficient to answer the question, but neither statement alone is sufficient. The answer is (C).
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Community Answer
What is the standard deviation (SD) of the four numbers p, q, r, and s...
Standard deviation = √Mean of squares of the numbers−square of mean of the numbers
Evaluating Statement (1) ALONE: The sum of p, q, r, and s is 24.
From the information in statement 1 we can find the mean of the four numbers to be 6 and the square of the mean of the numbers to be 36.
We need additional information to find the SD.
This statement does not provide any information about the mean of the squares of the numbers.
From the information in statement 1 we can find the mean of the four numbers to be 6 and the square of the mean of the numbers to be 36.
We need additional information to find the SD.
This statement does not provide any information about the mean of the squares of the numbers.
Statement 1 alone is NOT sufficient.
Eliminate choices A and D. Choices narrow down to B, C, or E.
Eliminate choices A and D. Choices narrow down to B, C, or E.
Evaluating Statement (2) ALONE: The sum of the squares of p, q, r, and s is 224.
Hence, the mean of the squares of the numbers is 56.
However, this statement does not provide any information about the square of the mean of the numbers.
Hence, the mean of the squares of the numbers is 56.
However, this statement does not provide any information about the square of the mean of the numbers.
Statement 2 alone is NOT sufficient.
Eliminate choice B. Choices narrow down to C and E.
Eliminate choice B. Choices narrow down to C and E.
Evaluating the statements together.
From statement 1 we know that the square of the means is 36.
From statement 2 we know that the mean of the squares is 56.
Using the formula,
Standard deviation = √Mean of squares of the numbers−square of mean of the numbers,
we can find the SD of the 4 numbers.
From statement 1 we know that the square of the means is 36.
From statement 2 we know that the mean of the squares is 56.
Using the formula,
Standard deviation = √Mean of squares of the numbers−square of mean of the numbers,
we can find the SD of the 4 numbers.
Statements together are sufficient. Choice C is the answer.
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What is the standard deviation (SD) of the four numbers p, q, r, and s?(1) The sum of p, q, r, and s is 24.(2) The sum of the squares of p, q, r, and s is 224.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.Correct answer is option 'C'. Can you explain this answer?
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What is the standard deviation (SD) of the four numbers p, q, r, and s?(1) The sum of p, q, r, and s is 24.(2) The sum of the squares of p, q, r, and s is 224.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.Correct answer is option 'C'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about What is the standard deviation (SD) of the four numbers p, q, r, and s?(1) The sum of p, q, r, and s is 24.(2) The sum of the squares of p, q, r, and s is 224.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the standard deviation (SD) of the four numbers p, q, r, and s?(1) The sum of p, q, r, and s is 24.(2) The sum of the squares of p, q, r, and s is 224.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.Correct answer is option 'C'. Can you explain this answer?.
What is the standard deviation (SD) of the four numbers p, q, r, and s?(1) The sum of p, q, r, and s is 24.(2) The sum of the squares of p, q, r, and s is 224.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.Correct answer is option 'C'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about What is the standard deviation (SD) of the four numbers p, q, r, and s?(1) The sum of p, q, r, and s is 24.(2) The sum of the squares of p, q, r, and s is 224.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the standard deviation (SD) of the four numbers p, q, r, and s?(1) The sum of p, q, r, and s is 24.(2) The sum of the squares of p, q, r, and s is 224.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.Correct answer is option 'C'. Can you explain this answer?.
Solutions for What is the standard deviation (SD) of the four numbers p, q, r, and s?(1) The sum of p, q, r, and s is 24.(2) The sum of the squares of p, q, r, and s is 224.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
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What is the standard deviation (SD) of the four numbers p, q, r, and s?(1) The sum of p, q, r, and s is 24.(2) The sum of the squares of p, q, r, and s is 224.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.Correct answer is option 'C'. Can you explain this answer?, a detailed solution for What is the standard deviation (SD) of the four numbers p, q, r, and s?(1) The sum of p, q, r, and s is 24.(2) The sum of the squares of p, q, r, and s is 224.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of What is the standard deviation (SD) of the four numbers p, q, r, and s?(1) The sum of p, q, r, and s is 24.(2) The sum of the squares of p, q, r, and s is 224.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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