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If x, y, z, and n are positive integers and f(n) = f(n - 1) + n, is f(x) - f(y + z) = 0?
(1) x = y + z
(2) f(0) = 1
  • 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 'A'. Can you explain this answer?
Most Upvoted Answer
If x, y, z, and n are positive integers and f(n) = f(n - 1) + n, is f(...
(1) x = y + z
From this statement, we know that x is equal to y + z. Substituting this into the expression f(x) - f(y + z), we get f(x) - f(y + z) = f(y + z) - f(y + z). Since y + z is the same on both sides of the equation, f(y + z) - f(y + z) equals 0. Therefore, statement (1) alone is sufficient to answer the question.
(2) f(0) = 1
From this statement, we know the value of f(0) is 1. However, this information does not provide any direct information about the value of f(x) - f(y + z). It doesn't provide any relationship between x, y, z, or the function f(n). Therefore, statement (2) alone is not sufficient to answer the question.
By analyzing each statement individually, we can see that statement (1) alone is sufficient to determine that f(x) - f(y + z) is equal to 0, but statement (2) alone is not sufficient. Hence, the answer is (A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
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If x, y, z, and n are positive integers and f(n) = f(n - 1) + n, is f(x) - f(y + z) = 0?(1) x = y + z(2) f(0) = 1a)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 'A'. 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 If x, y, z, and n are positive integers and f(n) = f(n - 1) + n, is f(x) - f(y + z) = 0?(1) x = y + z(2) f(0) = 1a)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 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x, y, z, and n are positive integers and f(n) = f(n - 1) + n, is f(x) - f(y + z) = 0?(1) x = y + z(2) f(0) = 1a)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 'A'. Can you explain this answer?.
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