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For all integers n, the function f is defined by f(n) = (a)6/n, where a is a constant. What is the value of f(1)?
(1) f(2) = 64
(2) f(3) = 16
(2) f(3) = 16
- 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 'D'. Can you explain this answer?
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Most Upvoted Answer
For all integers n, the function f is defined by f(n) = (a)6/n, where ...
**Given Information:**
The function f is defined as f(n) = (a)6/n, where a is a constant.
**To Find:**
The value of f(1).
**Statements:**
(1) f(2) = 64
(2) f(3) = 16
**Analyzing Statement (1):**
We are given that f(2) = 64.
Substituting the value of n = 2 in the given function, we have:
f(2) = (a)6/2 = 6a/2 = 3a
Therefore, 3a = 64.
From this equation, we can find the value of a, and subsequently, we can find the value of f(1).
**Analyzing Statement (2):**
We are given that f(3) = 16.
Substituting the value of n = 3 in the given function, we have:
f(3) = (a)6/3 = 6a/3 = 2a
Therefore, 2a = 16.
From this equation, we can find the value of a, and subsequently, we can find the value of f(1).
**Combining Both Statements:**
From both statements, we can find the value of a by solving the equations:
3a = 64 (from Statement 1)
2a = 16 (from Statement 2)
Solving these equations, we find that a = 32.
Once we know the value of a, we can find the value of f(1) by substituting n = 1 in the given function:
f(1) = (a)6/1 = 6a/1 = 6a = 6(32) = 192.
**Conclusion:**
Both statements together are sufficient to determine the value of f(1), so the correct answer is option (C) BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.
The function f is defined as f(n) = (a)6/n, where a is a constant.
**To Find:**
The value of f(1).
**Statements:**
(1) f(2) = 64
(2) f(3) = 16
**Analyzing Statement (1):**
We are given that f(2) = 64.
Substituting the value of n = 2 in the given function, we have:
f(2) = (a)6/2 = 6a/2 = 3a
Therefore, 3a = 64.
From this equation, we can find the value of a, and subsequently, we can find the value of f(1).
**Analyzing Statement (2):**
We are given that f(3) = 16.
Substituting the value of n = 3 in the given function, we have:
f(3) = (a)6/3 = 6a/3 = 2a
Therefore, 2a = 16.
From this equation, we can find the value of a, and subsequently, we can find the value of f(1).
**Combining Both Statements:**
From both statements, we can find the value of a by solving the equations:
3a = 64 (from Statement 1)
2a = 16 (from Statement 2)
Solving these equations, we find that a = 32.
Once we know the value of a, we can find the value of f(1) by substituting n = 1 in the given function:
f(1) = (a)6/1 = 6a/1 = 6a = 6(32) = 192.
**Conclusion:**
Both statements together are sufficient to determine the value of f(1), so the correct answer is option (C) BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.
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Community Answer
For all integers n, the function f is defined by f(n) = (a)6/n, where ...
We are given that f(n) = (a)6/n, where a is a constant.
We have to find out the value of f(1).
Statement 1:
Given that f(2) = 64
Thus, f(2) = (a)6/2 = a3 = 64
⇒ a = (64)1/3 = 4
Thus, f(1) = (a)6/1 = a6 = 46. - Sufficient
Thus, f(2) = (a)6/2 = a3 = 64
⇒ a = (64)1/3 = 4
Thus, f(1) = (a)6/1 = a6 = 46. - Sufficient
Statement 2:
Given that f(3) = 16
Thus, f(3) = (a)6/3 = a2 = 16
⇒ a = (16)1/2 = ±4
Thus, f(1) = (a)6/1 = a6 = (±4)6 = 46. - Sufficient
Thus, f(3) = (a)6/3 = a2 = 16
⇒ a = (16)1/2 = ±4
Thus, f(1) = (a)6/1 = a6 = (±4)6 = 46. - Sufficient
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For all integers n, the function f is defined by f(n) = (a)6/n, where a is a constant. What is the value of f(1)?(1) f(2) = 64(2) f(3) = 16a)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 'D'. Can you explain this answer?
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For all integers n, the function f is defined by f(n) = (a)6/n, where a is a constant. What is the value of f(1)?(1) f(2) = 64(2) f(3) = 16a)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 'D'. 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 For all integers n, the function f is defined by f(n) = (a)6/n, where a is a constant. What is the value of f(1)?(1) f(2) = 64(2) f(3) = 16a)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 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For all integers n, the function f is defined by f(n) = (a)6/n, where a is a constant. What is the value of f(1)?(1) f(2) = 64(2) f(3) = 16a)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 'D'. Can you explain this answer?.
For all integers n, the function f is defined by f(n) = (a)6/n, where a is a constant. What is the value of f(1)?(1) f(2) = 64(2) f(3) = 16a)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 'D'. 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 For all integers n, the function f is defined by f(n) = (a)6/n, where a is a constant. What is the value of f(1)?(1) f(2) = 64(2) f(3) = 16a)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 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For all integers n, the function f is defined by f(n) = (a)6/n, where a is a constant. What is the value of f(1)?(1) f(2) = 64(2) f(3) = 16a)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 'D'. Can you explain this answer?.
Solutions for For all integers n, the function f is defined by f(n) = (a)6/n, where a is a constant. What is the value of f(1)?(1) f(2) = 64(2) f(3) = 16a)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 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
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