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If m, s are the average and standard deviation of integers a, b, c, and d, is s > 0?
I. m > a
II. a + b + c + d = 0
II. a + b + c + d = 0
- 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 'A'. Can you explain this answer?
Verified Answer
If m, s are the average and standard deviation of integers a, b, c, an...
Step 1: Understand the Question Stem
What kind of an answer will the question fetch?
The question is an "Is" question. Answer to an "is" questions is either YES or NO.
The question is an "Is" question. Answer to an "is" questions is either YES or NO.
When is the data sufficient?
The data is sufficient if we are able to get a DEFINITE Yes or No.
If the statements do not have adequate data to determine whether the standard deviation is greater than 0, the data is NOT sufficient.
The data is sufficient if we are able to get a DEFINITE Yes or No.
If the statements do not have adequate data to determine whether the standard deviation is greater than 0, the data is NOT sufficient.
When will the standard deviation be 0?
The standard deviation, s, will be 0 in two instances.
The standard deviation, s, will be 0 in two instances.
- when all the elements in the set are the same.
- the set contains only one element, which in this case is not possible.
Step 2: Evaluating Statement (1) ALONE: m > a
If a = b = c = d, the average m will be the same as a.
Since m > a, all the elements in the set cannot be the same, and therefore, s > 0.
Since m > a, all the elements in the set cannot be the same, and therefore, s > 0.
Statement 1 ALONE is sufficient.
Eliminate choices B, C and E. Choices narrow down to A or D.
Eliminate choices B, C and E. Choices narrow down to A or D.
Step 3: Evaluating Statement (2) ALONE: a + b + c + d = 0
Approach: Look for a counter example
Example: When a = b = c = d = 0, s = 0
Counter Example: When a = -4, b = 0, c = 0, and d = 4, s > 0
Counter Example: When a = -4, b = 0, c = 0, and d = 4, s > 0
Statement 2 ALONE is NOT sufficient.
Eliminate choice D.
Eliminate choice D.
Statement 1 ALONE is sufficient. Choice A is the answer.
Most Upvoted Answer
If m, s are the average and standard deviation of integers a, b, c, an...
Understanding the Problem
We need to determine if the standard deviation (s) of integers a, b, c, and d is greater than 0. The average (m) is given by the formula:
m = (a + b + c + d) / 4
The standard deviation is 0 only if all values are identical; otherwise, it is greater than 0.
Analyzing the Statements
Statement I: m > a
- If m > a, it implies that the average of a, b, c, and d is greater than the value of a.
- For the average to be greater than a, at least one of the other integers (b, c, or d) must be greater than a, which means they cannot all be the same.
- Hence, different values exist among a, b, c, and d, indicating that the standard deviation s must be greater than 0.
Statement II: a + b + c + d = 0
- This equation implies that the sum of the four integers equals zero.
- It is possible for these integers to be equal, for example, if a = b = c = d = 0, then s = 0.
- Thus, this statement alone does not guarantee that s > 0, as it allows for the possibility of no variation among the integers.
Conclusion
- Statement I alone is sufficient to conclude that s > 0.
- Statement II does not provide enough information to make this conclusion.
Thus, the correct answer is option 'A': Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
We need to determine if the standard deviation (s) of integers a, b, c, and d is greater than 0. The average (m) is given by the formula:
m = (a + b + c + d) / 4
The standard deviation is 0 only if all values are identical; otherwise, it is greater than 0.
Analyzing the Statements
Statement I: m > a
- If m > a, it implies that the average of a, b, c, and d is greater than the value of a.
- For the average to be greater than a, at least one of the other integers (b, c, or d) must be greater than a, which means they cannot all be the same.
- Hence, different values exist among a, b, c, and d, indicating that the standard deviation s must be greater than 0.
Statement II: a + b + c + d = 0
- This equation implies that the sum of the four integers equals zero.
- It is possible for these integers to be equal, for example, if a = b = c = d = 0, then s = 0.
- Thus, this statement alone does not guarantee that s > 0, as it allows for the possibility of no variation among the integers.
Conclusion
- Statement I alone is sufficient to conclude that s > 0.
- Statement II does not provide enough information to make this conclusion.
Thus, the correct answer is option 'A': Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
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If m, s are the average and standard deviation of integers a, b, c, and d, is s > 0?I. m > aII. a + b + c + d = 0a)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 'A'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about If m, s are the average and standard deviation of integers a, b, c, and d, is s > 0?I. m > aII. a + b + c + d = 0a)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 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If m, s are the average and standard deviation of integers a, b, c, and d, is s > 0?I. m > aII. a + b + c + d = 0a)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 'A'. Can you explain this answer?.
If m, s are the average and standard deviation of integers a, b, c, and d, is s > 0?I. m > aII. a + b + c + d = 0a)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 'A'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about If m, s are the average and standard deviation of integers a, b, c, and d, is s > 0?I. m > aII. a + b + c + d = 0a)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 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If m, s are the average and standard deviation of integers a, b, c, and d, is s > 0?I. m > aII. a + b + c + d = 0a)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 'A'. Can you explain this answer?.
Solutions for If m, s are the average and standard deviation of integers a, b, c, and d, is s > 0?I. m > aII. a + b + c + d = 0a)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 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
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If m, s are the average and standard deviation of integers a, b, c, and d, is s > 0?I. m > aII. a + b + c + d = 0a)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 'A'. Can you explain this answer?, a detailed solution for If m, s are the average and standard deviation of integers a, b, c, and d, is s > 0?I. m > aII. a + b + c + d = 0a)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 'A'. Can you explain this answer? has been provided alongside types of If m, s are the average and standard deviation of integers a, b, c, and d, is s > 0?I. m > aII. a + b + c + d = 0a)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 'A'. Can you explain this answer? theory, EduRev gives you an
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