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If M is a sequence of consecutive integers which contains more than 11 terms, what is the average of M?

(1) In M, the number of terms that are less than 10 is equal to the number of terms greater than 21.
(2) There are 20 terms in M.
  • 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 'A'. Can you explain this answer?
Most Upvoted Answer
If M is a sequence of consecutive integers which contains more than 11...
Statement (1) states that in M, the number of terms that are less than 10 is equal to the number of terms greater than 21. This information alone is sufficient to answer the question. If the number of terms less than 10 is equal to the number of terms greater than 21, it means that the average value of the sequence M will be between 10 and 21. Since M contains more than 11 terms, we can conclude that the average of M lies between 10 and 21.
Statement (2) says that there are 20 terms in M. This information alone is not sufficient to determine the average of M. Knowing the number of terms is not enough to calculate the average as we don't have information about the actual values of the terms in the sequence.
Since Statement (1) alone is sufficient to answer the question, while Statement (2) alone is not sufficient, the answer is A: Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
Community Answer
If M is a sequence of consecutive integers which contains more than 11...
Understanding the Problem
To find the average of the sequence M of consecutive integers, we need to determine the values of the integers in the sequence. The average of a sequence can be calculated using the formula:
Average = (First term + Last term) / 2
Given that M has more than 11 terms, we will evaluate the statements to see if they provide enough information to find the average.
Analysis of Statement (1)
- The statement indicates that the number of terms less than 10 is equal to the number of terms greater than 21.
- Let’s denote the number of terms less than 10 as x and the number greater than 21 as x.
- Therefore, the total number of terms in M can be expressed as:
Total terms = x (less than 10) + x (greater than 21) + y (terms between 10 and 21), where y is the count of terms between 10 and 21.
- Since M contains more than 11 terms, we have:
2x + y > 11
- This implies that we can derive specific bounds for the sequence. Knowing the values below 10 and above 21 helps find the average.
Analysis of Statement (2)
- The second statement provides that there are exactly 20 terms in M.
- While this information specifies the total count of terms, it does not give the range of values in M or their distribution, which is necessary to determine the average.
Hence, this statement alone is insufficient.
Conclusion
- Statement (1) provides specific relationships between the terms and their ranges, allowing us to calculate the average.
- Statement (2) lacks the necessary detail to derive the average on its own.
Therefore, the correct answer is that statement (1) alone is sufficient, while statement (2) is not.
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If M is a sequence of consecutive integers which contains more than 11 terms, what is the average of M?(1) In M, the number of terms that are less than 10 is equal to the number of terms greater than 21.(2) There are 20 terms in M.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'A'. Can you explain this answer?
Question Description
If M is a sequence of consecutive integers which contains more than 11 terms, what is the average of M?(1) In M, the number of terms that are less than 10 is equal to the number of terms greater than 21.(2) There are 20 terms in M.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'A'. 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 If M is a sequence of consecutive integers which contains more than 11 terms, what is the average of M?(1) In M, the number of terms that are less than 10 is equal to the number of terms greater than 21.(2) There are 20 terms in M.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If M is a sequence of consecutive integers which contains more than 11 terms, what is the average of M?(1) In M, the number of terms that are less than 10 is equal to the number of terms greater than 21.(2) There are 20 terms in M.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'A'. Can you explain this answer?.
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