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What is the range of 3 positive integers a, b, and c?
Statement 1: 21a = 9b = 7c
Statement 2: a + 8, b, and c, in that order are in AP.
Statement 2: a + 8, b, and c, in that order are in AP.
- 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?
Verified Answer
What is the range of 3 positive integers a, b, and c?Statement 1: 21a ...
Evaluate Statement 2 ALONE
Statement 2: a + 8, b, and c, in that order are in AP.
Approach : Counter example
Example : a = 1, b = 10, and c = 11. a + 8 = 9
So, 9, 10, 11 are in AP. Range = 11 - 1 = 10
Counter Example : a = 1, b = 11, c = 13. a + 8 = 9
So, 9, 11, 13 are in AP. Range = 13 - 1 = 12
Counter example exists.
Example : a = 1, b = 10, and c = 11. a + 8 = 9
So, 9, 10, 11 are in AP. Range = 11 - 1 = 10
Counter Example : a = 1, b = 11, c = 13. a + 8 = 9
So, 9, 11, 13 are in AP. Range = 13 - 1 = 12
Counter example exists.
We are not able to find a UNIQUE value for the range using Statement 2.
Hence, statement 2 is not sufficient.
Eliminate answer option B.
Hence, statement 2 is not sufficient.
Eliminate answer option B.
Evaluate Statements TOGETHER
Statements: Statement 1: 21a = 9b = 7c
Statement 2: a + 8, b, and c in that order are in AP.
Statement 2: a + 8, b, and c in that order are in AP.
Key inferences:
From statement 1: we know a = 3k, b = 7k and c = 9k
From statement 2: we know c - b = b - (a + 8) (because a + 8, b, and c are in AP) ... (1)
Substiute c = 9k, b = 7k and a = 3k in equation (1)
So, 9k - 7k = 7k - (3k + 8)
2k = 4k - 8
or k = 4
Therefore, the range (9k - 3k) = 6k = 6(4) = 24
From statement 1: we know a = 3k, b = 7k and c = 9k
From statement 2: we know c - b = b - (a + 8) (because a + 8, b, and c are in AP) ... (1)
Substiute c = 9k, b = 7k and a = 3k in equation (1)
So, 9k - 7k = 7k - (3k + 8)
2k = 4k - 8
or k = 4
Therefore, the range (9k - 3k) = 6k = 6(4) = 24
We are able to find a UNIQUE value for range using the statements together.
Statements together are sufficient.
Eliminate answer option E.
Statements together are sufficient.
Eliminate answer option E.
Choice C is the correct answer.
Most Upvoted Answer
What is the range of 3 positive integers a, b, and c?Statement 1: 21a ...
Evaluate Statement 2 ALONE
Statement 2: a + 8, b, and c, in that order are in AP.
Approach : Counter example
Example : a = 1, b = 10, and c = 11. a + 8 = 9
So, 9, 10, 11 are in AP. Range = 11 - 1 = 10
Counter Example : a = 1, b = 11, c = 13. a + 8 = 9
So, 9, 11, 13 are in AP. Range = 13 - 1 = 12
Counter example exists.
Example : a = 1, b = 10, and c = 11. a + 8 = 9
So, 9, 10, 11 are in AP. Range = 11 - 1 = 10
Counter Example : a = 1, b = 11, c = 13. a + 8 = 9
So, 9, 11, 13 are in AP. Range = 13 - 1 = 12
Counter example exists.
We are not able to find a UNIQUE value for the range using Statement 2.
Hence, statement 2 is not sufficient.
Eliminate answer option B.
Hence, statement 2 is not sufficient.
Eliminate answer option B.
Evaluate Statements TOGETHER
Statements: Statement 1: 21a = 9b = 7c
Statement 2: a + 8, b, and c in that order are in AP.
Statement 2: a + 8, b, and c in that order are in AP.
Key inferences:
From statement 1: we know a = 3k, b = 7k and c = 9k
From statement 2: we know c - b = b - (a + 8) (because a + 8, b, and c are in AP) ... (1)
Substiute c = 9k, b = 7k and a = 3k in equation (1)
So, 9k - 7k = 7k - (3k + 8)
2k = 4k - 8
or k = 4
Therefore, the range (9k - 3k) = 6k = 6(4) = 24
From statement 1: we know a = 3k, b = 7k and c = 9k
From statement 2: we know c - b = b - (a + 8) (because a + 8, b, and c are in AP) ... (1)
Substiute c = 9k, b = 7k and a = 3k in equation (1)
So, 9k - 7k = 7k - (3k + 8)
2k = 4k - 8
or k = 4
Therefore, the range (9k - 3k) = 6k = 6(4) = 24
We are able to find a UNIQUE value for range using the statements together.
Statements together are sufficient.
Eliminate answer option E.
Statements together are sufficient.
Eliminate answer option E.
Choice C is the correct answer.
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Community Answer
What is the range of 3 positive integers a, b, and c?Statement 1: 21a ...
Statement 1:
- Given: 21a = 9b = 7c
- To find the range of a, b, and c, we need to determine the possible values for each integer.
- From the given equation, we can find the ratios between a, b, and c. However, there are multiple sets of positive integers that satisfy this equation, so we cannot determine the exact values of a, b, and c.
Statement 2:
- Given: a + 8, b, and c are in AP (Arithmetic Progression).
- This means that the common difference between consecutive terms is the same.
- While this provides some information about the relationship between a, b, and c, it does not give us enough information to determine the exact values of a, b, and c.
Combined Statements 1 and 2:
- Combining both statements, we know the ratios between a, b, and c from Statement 1 and that a, b, and c are in AP from Statement 2.
- The information from both statements helps us uniquely determine the values of a, b, and c.
- Therefore, together, the statements are sufficient to find the range of the positive integers a, b, and c.
Therefore, the correct answer is option C.
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What is the range of 3 positive integers a, b, and c?Statement 1: 21a = 9b = 7cStatement 2: a + 8, b, and c, in that order are in AP.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?
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What is the range of 3 positive integers a, b, and c?Statement 1: 21a = 9b = 7cStatement 2: a + 8, b, and c, in that order are in AP.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? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about What is the range of 3 positive integers a, b, and c?Statement 1: 21a = 9b = 7cStatement 2: a + 8, b, and c, in that order are in AP.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? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the range of 3 positive integers a, b, and c?Statement 1: 21a = 9b = 7cStatement 2: a + 8, b, and c, in that order are in AP.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?.
What is the range of 3 positive integers a, b, and c?Statement 1: 21a = 9b = 7cStatement 2: a + 8, b, and c, in that order are in AP.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? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about What is the range of 3 positive integers a, b, and c?Statement 1: 21a = 9b = 7cStatement 2: a + 8, b, and c, in that order are in AP.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? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the range of 3 positive integers a, b, and c?Statement 1: 21a = 9b = 7cStatement 2: a + 8, b, and c, in that order are in AP.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?.
Solutions for What is the range of 3 positive integers a, b, and c?Statement 1: 21a = 9b = 7cStatement 2: a + 8, b, and c, in that order are in AP.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? in English & in Hindi are available as part of our courses for GMAT.
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