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If a, b and c are integers such that ab + c is an odd integer, is a an even integer?
(1) ab + ac is an even integer.
(2) b + ac is an odd integer.
(1) ab + ac is an even integer.
(2) b + ac is an odd integer.
- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient
- c)Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient
- e)Statements (1) and (2) TOGETHER are NOT sufficient
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If a, b and c are integers such that ab + c is an odd integer, is a an...
Given that ab + c = odd, determine whether a is even.
(1) ab + ac is an even integer. ab + ac = even. Subtract this equation from the equation above: (ab + ac) − (ab + c) = ac − c = even − odd = odd ⇒ c(a − 1) = odd ⇒ both multiples must be odd ⇒ a − 1 = odd ⇒ a = odd + 1 = even. Sufficient.
(2) b + ac is an odd integer. a = even, b = odd and c = odd OR a = odd, b = odd and c = even. Not sufficient.
Answer: A.
(1) ab + ac is an even integer. ab + ac = even. Subtract this equation from the equation above: (ab + ac) − (ab + c) = ac − c = even − odd = odd ⇒ c(a − 1) = odd ⇒ both multiples must be odd ⇒ a − 1 = odd ⇒ a = odd + 1 = even. Sufficient.
(2) b + ac is an odd integer. a = even, b = odd and c = odd OR a = odd, b = odd and c = even. Not sufficient.
Answer: A.
Most Upvoted Answer
If a, b and c are integers such that ab + c is an odd integer, is a an...
Explanation:
Statement 1:
- Given: ab + ac is an even integer
- Since ab + c is an odd integer, it implies that c must be an odd integer.
- If c is odd, then a must be even for the product ab + c to result in an odd integer.
- Therefore, statement 1 alone is sufficient to determine that a is an even integer.
Statement 2:
- Given: b + ac is an odd integer
- However, this statement does not provide any information about the value of a.
- It is possible for a to be either even or odd, depending on the specific values of b and c.
- Therefore, statement 2 alone is not sufficient to determine the parity of a.
Therefore, the correct answer is option A as statement 1 alone is sufficient to determine that a is an even integer.
Statement 1:
- Given: ab + ac is an even integer
- Since ab + c is an odd integer, it implies that c must be an odd integer.
- If c is odd, then a must be even for the product ab + c to result in an odd integer.
- Therefore, statement 1 alone is sufficient to determine that a is an even integer.
Statement 2:
- Given: b + ac is an odd integer
- However, this statement does not provide any information about the value of a.
- It is possible for a to be either even or odd, depending on the specific values of b and c.
- Therefore, statement 2 alone is not sufficient to determine the parity of a.
Therefore, the correct answer is option A as statement 1 alone is sufficient to determine that a is an even integer.
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If a, b and c are integers such that ab + c is an odd integer, is a an even integer?(1) ab + ac is an even integer.(2) b + ac is an odd integer.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficientb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficientc)Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficiente)Statements (1) and (2) TOGETHER are NOT sufficientCorrect answer is option 'A'. Can you explain this answer?
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If a, b and c are integers such that ab + c is an odd integer, is a an even integer?(1) ab + ac is an even integer.(2) b + ac is an odd integer.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficientb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficientc)Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficiente)Statements (1) and (2) TOGETHER are NOT sufficientCorrect 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 a, b and c are integers such that ab + c is an odd integer, is a an even integer?(1) ab + ac is an even integer.(2) b + ac is an odd integer.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficientb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficientc)Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficiente)Statements (1) and (2) TOGETHER are NOT sufficientCorrect 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 a, b and c are integers such that ab + c is an odd integer, is a an even integer?(1) ab + ac is an even integer.(2) b + ac is an odd integer.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficientb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficientc)Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficiente)Statements (1) and (2) TOGETHER are NOT sufficientCorrect answer is option 'A'. Can you explain this answer?.
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