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An infinite sequence of positive integers is called a "beta Sequence" if the number of odd integers in the sequence is finite. If S is an infinite sequence of positive integers, is S a beta sequence?

(1) The first ten integers in S are even.
(2) The difference between each successive pair of terms in S is a constant
  • 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?
Most Upvoted Answer
An infinite sequence of positive integers is called a "beta Seque...
Statement (1) tells us that the first ten integers in S are even. This means that there are no odd integers among the first ten terms. However, we cannot conclude whether the number of odd integers in the sequence is finite or infinite based on this information alone.
Statement (2) states that the difference between each successive pair of terms in S is a constant. This implies that the sequence is an arithmetic progression. However, an arithmetic progression can contain both odd and even terms. For example, the sequence {2, 5, 8, 11, ...} is an arithmetic progression with an infinite number of odd integers. Therefore, statement (2) alone does not provide enough information to determine if S is a beta sequence.
When we consider both statements together, we know that the first ten terms of S are even, and the sequence is an arithmetic progression. However, this still doesn't give us enough information to determine if the number of odd integers in the sequence is finite or infinite. Therefore, both statements (1) and (2) together are sufficient to answer the question asked, but neither statement alone is sufficient.
Hence, the correct answer is C: BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.
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An infinite sequence of positive integers is called a "beta Sequence" if the number of odd integers in the sequence is finite. If S is an infinite sequence of positive integers, is S a beta sequence?(1) The first ten integers in S are even.(2) The difference between each successive pair of terms in S is a constanta)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 'C'. Can you explain this answer?
Question Description
An infinite sequence of positive integers is called a "beta Sequence" if the number of odd integers in the sequence is finite. If S is an infinite sequence of positive integers, is S a beta sequence?(1) The first ten integers in S are even.(2) The difference between each successive pair of terms in S is a constanta)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 '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 An infinite sequence of positive integers is called a "beta Sequence" if the number of odd integers in the sequence is finite. If S is an infinite sequence of positive integers, is S a beta sequence?(1) The first ten integers in S are even.(2) The difference between each successive pair of terms in S is a constanta)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 '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 An infinite sequence of positive integers is called a "beta Sequence" if the number of odd integers in the sequence is finite. If S is an infinite sequence of positive integers, is S a beta sequence?(1) The first ten integers in S are even.(2) The difference between each successive pair of terms in S is a constanta)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 'C'. Can you explain this answer?.
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