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If A and B are positive integers, is A – B even?
1. The product of A and B is even
2. A + B is odd
- 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 to answer the question asked.
- 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 specific to the problem are needed.
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If A and B are positive integers, is A – B even?1. The product o...
Steps 1 & 2: Understand Question and Draw Inferences
Given: Integers A, B > 0
To find: Is A – B even?
- The answer will be YES if A and B have the same even-odd nature, i.e. A and B are both even or both odd
Step 3: Analyze Statement 1 independently
Statement 1 says that ‘The product of A and B is even’
- This means, that one number out of A and B is definitely even
- The other number may be even or odd
- So, A – B may be:
- Either Even – Odd = Odd
- Or Even – Even = Even
- Thus, Statement 1 is not sufficient to give a unique Yes/ No answer to the question
Step 4: Analyze Statement 2 independently
Statement 2 says that ‘A + B is odd’
- For A + B to be odd, one of A or B has to be even and the other odd.
- So, Even – Odd = Odd OR Odd – Even = Odd
- Hence A – B will be odd.
- Therefore, Statement 2 is sufficient to answer the question
Step 5: Analyze Both Statements Together (if needed)
Since we’ve already arrived at a unique answer in Step 4, this step is not required
Answer: Option B
Most Upvoted Answer
If A and B are positive integers, is A – B even?1. The product o...
Statement 1: The product of A and B is even.
If the product of A and B is even, it means that at least one of A or B is even.
Let's consider two scenarios:
Scenario 1: A is even and B is odd
In this case, A - B will be odd.
Scenario 2: A is odd and B is even
In this case, A - B will be odd.
Therefore, based on statement 1 alone, we cannot determine if A - B is even or odd.
Statement 2: A + B is odd
If A + B is odd, it means that either A is odd and B is even or A is even and B is odd. In both cases, A - B will always be odd.
Therefore, based on statement 2 alone, we can determine that A - B is odd.
Combining both statements:
From statement 1, we know that the product of A and B is even. This means that at least one of A or B is even.
From statement 2, we know that A + B is odd. This means that either A is odd and B is even or A is even and B is odd.
In both cases, A - B will always be odd.
Therefore, combining both statements, we can determine that A - B is odd.
Hence, statement 2 alone is sufficient to answer the question, while statement 1 alone is not sufficient.
Therefore, the correct answer is option B.
If the product of A and B is even, it means that at least one of A or B is even.
Let's consider two scenarios:
Scenario 1: A is even and B is odd
In this case, A - B will be odd.
Scenario 2: A is odd and B is even
In this case, A - B will be odd.
Therefore, based on statement 1 alone, we cannot determine if A - B is even or odd.
Statement 2: A + B is odd
If A + B is odd, it means that either A is odd and B is even or A is even and B is odd. In both cases, A - B will always be odd.
Therefore, based on statement 2 alone, we can determine that A - B is odd.
Combining both statements:
From statement 1, we know that the product of A and B is even. This means that at least one of A or B is even.
From statement 2, we know that A + B is odd. This means that either A is odd and B is even or A is even and B is odd.
In both cases, A - B will always be odd.
Therefore, combining both statements, we can determine that A - B is odd.
Hence, statement 2 alone is sufficient to answer the question, while statement 1 alone is not sufficient.
Therefore, the correct answer is option B.
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If A and B are positive integers, is A – B even?1. The product of A and B is even2. A + B is odda)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 to answer the question asked.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 specific to the problem are needed.Correct answer is option 'B'. 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 and B are positive integers, is A – B even?1. The product of A and B is even2. A + B is odda)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 to answer the question asked.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 specific to the problem are needed.Correct answer is option 'B'. 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 and B are positive integers, is A – B even?1. The product of A and B is even2. A + B is odda)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 to answer the question asked.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 specific to the problem are needed.Correct answer is option 'B'. Can you explain this answer?.
If A and B are positive integers, is A – B even?1. The product of A and B is even2. A + B is odda)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 to answer the question asked.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 specific to the problem are needed.Correct answer is option 'B'. 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 and B are positive integers, is A – B even?1. The product of A and B is even2. A + B is odda)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 to answer the question asked.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 specific to the problem are needed.Correct answer is option 'B'. 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 and B are positive integers, is A – B even?1. The product of A and B is even2. A + B is odda)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 to answer the question asked.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 specific to the problem are needed.Correct answer is option 'B'. Can you explain this answer?.
Solutions for If A and B are positive integers, is A – B even?1. The product of A and B is even2. A + B is odda)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 to answer the question asked.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 specific to the problem are needed.Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
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ample number of questions to practice If A and B are positive integers, is A – B even?1. The product of A and B is even2. A + B is odda)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 to answer the question asked.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 specific to the problem are needed.Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice GMAT tests.
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