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An arithmetic sequence is a sequence in which each term after the first is equal to the sum of the preceding term and a constant, which is also known as the common difference of that arithmetic sequence. The sequence S contains all the terms of two different increasing arithmetic sequences P and Q such that the number of terms in sequence S is equal to the sum of the number of terms in sequences P and Q. If each of the arithmetic sequences P and Q consists of 10 positive integral terms, how many distinct terms does sequence S have?
(1) The least common multiple of the common differences of the sequences P and Q is 6
(2) The third term of the sequence P is equal to the second term of the sequence Q
  • 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 to answer the question asked.
  • 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 specific to the problem are needed.
Correct answer is option 'E'. Can you explain this answer?
Verified Answer
An arithmetic sequence is a sequence in which each term after the firs...
Steps 1 & 2: Understand Question and Draw Inferences
  • Increasing arithmetic sequence P with 10 positive integral terms with a common difference of p
  • Increasing arithmetic sequence Q with 10 positive integral terms with a common difference of q.
  • Sequence S consists of all the terms of sequences P and Q only, i.e. it consists of 20 terms only
To Find: Number of distinct terms of sequence S
  • Number of distinct terms in sequence S = 20 – number of terms that are common to sequences P and Q ( as sequence S consists of terms from sequences P and Q only)
  • To find the number of terms that are common to sequences P and Q, we need to find:
    • The smallest term that is common to both the sequences
    • The common difference of both the sequences i.e. values of p and q.
Step 3: Analyze Statement 1 independently
(1) The least common multiple of the common differences of the sequences P and Q is 6
  • We are given the LCM of the common differences of the sequences P and Q is 6.
    • 6 = 2 * 3.
    • Hence the common differences (p, q) can be (1, 6) , (2, 6), (3, 6), (6, 6) or (2, 3) in any order
    • So, we not have the unique values of the common difference of the two sequences
  • Also, we do not know the smallest term, which is common to both the sequences.
Insufficient to answer.
 
Step 4: Analyze Statement 2 independently
(2) The third term of the sequence P is equal to the second term of the sequence Q
  • We are given that P3 = Q2
  • We do not know if these are the smallest  terms of the sequences P and Q that are common.Let us assume that these are not the smallest terms that are common to sequences P and Q. So, the possible cases can be:
  • All the three cases are possible(i.e. Q1 and P1, or Q1 and P2 or Q2 and P3 are the smallest terms of the sequences that are common). So we cannot identify the smallest terms of the sequences P and Q that are common.
Also, we do not know the common difference of the two sequences. Hence the statement is insufficient to answer.
 
Step 5: Analyze Both Statements Together (if needed)
  1. Common differences of sequences P and Q = (1, 6) , (2, 6), (3, 6), (6, 6) or (2, 3) in any order
  2. P3 = Q2
Uisng (1) and (2), we cannot calculate the unique common values of the common differences as well as we do not know if P3 and Q2 are the smallest terms of the sequences P and Q that are common.
Hence, insufficient to answer.
 
Answer: E
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An arithmetic sequence is a sequence in which each term after the first is equal to the sum of the preceding term and a constant, which is also known as the common difference of that arithmetic sequence. The sequence S contains all the terms of two different increasing arithmetic sequences P and Q such that the number of terms in sequence S is equal to the sum of the number of terms in sequences P and Q. If each of the arithmetic sequences P and Q consists of 10 positive integral terms, how many distinct terms does sequence S have?(1) The least common multiple of the common differences of the sequences P and Q is 6(2) The third term of the sequence P is equal to the second term of the sequence Qa)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 askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.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 specific to the problem are needed.Correct answer is option 'E'. Can you explain this answer?
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An arithmetic sequence is a sequence in which each term after the first is equal to the sum of the preceding term and a constant, which is also known as the common difference of that arithmetic sequence. The sequence S contains all the terms of two different increasing arithmetic sequences P and Q such that the number of terms in sequence S is equal to the sum of the number of terms in sequences P and Q. If each of the arithmetic sequences P and Q consists of 10 positive integral terms, how many distinct terms does sequence S have?(1) The least common multiple of the common differences of the sequences P and Q is 6(2) The third term of the sequence P is equal to the second term of the sequence Qa)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 askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.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 specific to the problem are needed.Correct answer is option 'E'. 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 arithmetic sequence is a sequence in which each term after the first is equal to the sum of the preceding term and a constant, which is also known as the common difference of that arithmetic sequence. The sequence S contains all the terms of two different increasing arithmetic sequences P and Q such that the number of terms in sequence S is equal to the sum of the number of terms in sequences P and Q. If each of the arithmetic sequences P and Q consists of 10 positive integral terms, how many distinct terms does sequence S have?(1) The least common multiple of the common differences of the sequences P and Q is 6(2) The third term of the sequence P is equal to the second term of the sequence Qa)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 askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.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 specific to the problem are needed.Correct answer is option 'E'. 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 arithmetic sequence is a sequence in which each term after the first is equal to the sum of the preceding term and a constant, which is also known as the common difference of that arithmetic sequence. The sequence S contains all the terms of two different increasing arithmetic sequences P and Q such that the number of terms in sequence S is equal to the sum of the number of terms in sequences P and Q. If each of the arithmetic sequences P and Q consists of 10 positive integral terms, how many distinct terms does sequence S have?(1) The least common multiple of the common differences of the sequences P and Q is 6(2) The third term of the sequence P is equal to the second term of the sequence Qa)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 askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.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 specific to the problem are needed.Correct answer is option 'E'. Can you explain this answer?.
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If each of the arithmetic sequences P and Q consists of 10 positive integral terms, how many distinct terms does sequence S have?(1) The least common multiple of the common differences of the sequences P and Q is 6(2) The third term of the sequence P is equal to the second term of the sequence Qa)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 askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.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 specific to the problem are needed.Correct answer is option 'E'. Can you explain this answer? defined & explained in the simplest way possible. 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If each of the arithmetic sequences P and Q consists of 10 positive integral terms, how many distinct terms does sequence S have?(1) The least common multiple of the common differences of the sequences P and Q is 6(2) The third term of the sequence P is equal to the second term of the sequence Qa)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 askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.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 specific to the problem are needed.Correct answer is option 'E'. 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If each of the arithmetic sequences P and Q consists of 10 positive integral terms, how many distinct terms does sequence S have?(1) The least common multiple of the common differences of the sequences P and Q is 6(2) The third term of the sequence P is equal to the second term of the sequence Qa)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 askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.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 specific to the problem are needed.Correct answer is option 'E'. Can you explain this answer? has been provided alongside types of An arithmetic sequence is a sequence in which each term after the first is equal to the sum of the preceding term and a constant, which is also known as the common difference of that arithmetic sequence. The sequence S contains all the terms of two different increasing arithmetic sequences P and Q such that the number of terms in sequence S is equal to the sum of the number of terms in sequences P and Q. If each of the arithmetic sequences P and Q consists of 10 positive integral terms, how many distinct terms does sequence S have?(1) The least common multiple of the common differences of the sequences P and Q is 6(2) The third term of the sequence P is equal to the second term of the sequence Qa)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 askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.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 specific to the problem are needed.Correct answer is option 'E'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice An arithmetic sequence is a sequence in which each term after the first is equal to the sum of the preceding term and a constant, which is also known as the common difference of that arithmetic sequence. The sequence S contains all the terms of two different increasing arithmetic sequences P and Q such that the number of terms in sequence S is equal to the sum of the number of terms in sequences P and Q. If each of the arithmetic sequences P and Q consists of 10 positive integral terms, how many distinct terms does sequence S have?(1) The least common multiple of the common differences of the sequences P and Q is 6(2) The third term of the sequence P is equal to the second term of the sequence Qa)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 askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.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 specific to the problem are needed.Correct answer is option 'E'. Can you explain this answer? tests, examples and also practice GMAT tests.
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