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If a and b are positive integers such that a = 24b + 56, what is the highest common factor for a and b?
(1) a = 8p, where p is a positive integer.
(2) b= 7q, where q is a positive integer.
  • 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 'E'. Can you explain this answer?
Verified Answer
If a and b are positive integers such that a = 24b + 56, what is the h...
Let's examine each statement individually:
Statement (1): a = 8p, where p is a positive integer.
This statement tells us that a is divisible by 8. However, it does not provide any information about b or its divisibility by 8. Since we need information about both a and b to determine their HCF, statement (1) alone is not sufficient.
Statement (2): b = 7q, where q is a positive integer.
This statement tells us that b is divisible by 7. However, it does not provide any information about a or its divisibility by 7. Similar to statement (1), statement (2) alone is not sufficient.
Now let's consider both statements together:
From the original equation, a = 24b + 56, we can rewrite it as a = 8(3b) + 56. This shows that a is divisible by 8.
Additionally, using statement (2), we have b = 7q, which indicates that b is divisible by 7.
Combining both pieces of information, we know that a is divisible by 8 and b is divisible by 7. However, this is not enough to determine the HCF for a and b. For example, a could be 56 (divisible by 8) and b could be 7 (divisible by 7), resulting in an HCF of 1. Alternatively, a could be 112 (divisible by 8) and b could be 14 (divisible by 7), which would give an HCF of 2.
Since we cannot definitively determine the HCF for a and b based on the given information, the correct answer is (E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.
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Most Upvoted Answer
If a and b are positive integers such that a = 24b + 56, what is the h...
Let's examine each statement individually:
Statement (1): a = 8p, where p is a positive integer.
This statement tells us that a is divisible by 8. However, it does not provide any information about b or its divisibility by 8. Since we need information about both a and b to determine their HCF, statement (1) alone is not sufficient.
Statement (2): b = 7q, where q is a positive integer.
This statement tells us that b is divisible by 7. However, it does not provide any information about a or its divisibility by 7. Similar to statement (1), statement (2) alone is not sufficient.
Now let's consider both statements together:
From the original equation, a = 24b + 56, we can rewrite it as a = 8(3b) + 56. This shows that a is divisible by 8.
Additionally, using statement (2), we have b = 7q, which indicates that b is divisible by 7.
Combining both pieces of information, we know that a is divisible by 8 and b is divisible by 7. However, this is not enough to determine the HCF for a and b. For example, a could be 56 (divisible by 8) and b could be 7 (divisible by 7), resulting in an HCF of 1. Alternatively, a could be 112 (divisible by 8) and b could be 14 (divisible by 7), which would give an HCF of 2.
Since we cannot definitively determine the HCF for a and b based on the given information, the correct answer is (E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.
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If a and b are positive integers such that a = 24b + 56, what is the highest common factor for a and b?(1) a = 8p, where p is a positive integer.(2) b= 7q, where q is a positive integer.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 'E'. Can you explain this answer?
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If a and b are positive integers such that a = 24b + 56, what is the highest common factor for a and b?(1) a = 8p, where p is a positive integer.(2) b= 7q, where q is a positive integer.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 '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 If a and b are positive integers such that a = 24b + 56, what is the highest common factor for a and b?(1) a = 8p, where p is a positive integer.(2) b= 7q, where q is a positive integer.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 '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 If a and b are positive integers such that a = 24b + 56, what is the highest common factor for a and b?(1) a = 8p, where p is a positive integer.(2) b= 7q, where q is a positive integer.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 'E'. Can you explain this answer?.
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