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What is the standard deviation (SD) of the four numbers p, q, r, and s?
Statement 1: The sum of p, q, r, and s is 24.
Statement 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
  • 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)
    Statements (1) and (2) TOGETHER are NOT sufficient
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
What is the standard deviation (SD) of the four numbers p, q, r, and s...
Statement 1:
The sum of p, q, r, and s is 24.
This statement alone does not provide enough information to calculate the standard deviation because we need individual values of p, q, r, and s to determine the spread from the mean.

Statement 2:
The sum of the squares of p, q, r, and s is 224.
This statement also does not give us the individual values of p, q, r, and s, which are required to calculate the standard deviation.

Both Statements Together:
When we combine both statements, we can solve for the individual values of p, q, r, and s. From Statement 1, we know that the sum of p, q, r, and s is 24. From Statement 2, we know that the sum of their squares is 224. Using these two equations, we can solve for the values of p, q, r, and s. Once we have these values, we can calculate the standard deviation.
Therefore, both statements together are sufficient to determine the standard deviation of the four numbers p, q, r, and s.
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Community Answer
What is the standard deviation (SD) of the four numbers p, q, r, and s...
Step 1: Understand the Question Stem
What kind of an answer will the question fetch?
The question is an "What is" question. Answer to the question should be a number that is the standard deviation of p, q, r, and s.
When is the data sufficient?
The data is sufficient if we are able to get a UNIQUE value for the SD of the four numbers from the information given in the statements.
How to find the standard deviation of a set of numbers?
Step 2: 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.
Statement 1 alone is NOT sufficient.
Eliminate choices A and D. Choices narrow down to B, C, or E.
Step 3: 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.
Statement 2 alone is NOT sufficient.
Eliminate choice B. Choices narrow down to C and E.
Step 4: 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,

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?Statement 1: The sum of p, q, r, and s is 24.Statement 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 sufficientb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficientc)Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficiente)Statements (1) and (2) TOGETHER are NOT sufficientCorrect 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?Statement 1: The sum of p, q, r, and s is 24.Statement 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 sufficientb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficientc)Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficiente)Statements (1) and (2) TOGETHER are NOT sufficientCorrect 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?Statement 1: The sum of p, q, r, and s is 24.Statement 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 sufficientb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficientc)Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficiente)Statements (1) and (2) TOGETHER are NOT sufficientCorrect 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?Statement 1: The sum of p, q, r, and s is 24.Statement 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 sufficientb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficientc)Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficiente)Statements (1) and (2) TOGETHER are NOT sufficientCorrect answer is option 'C'. Can you explain this answer?.
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