If A and B are integers, is the product AB even?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 'A'. Can you explain this answer?

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If A and B are integers, is the product AB even?

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 'A'. Can you explain this answer?

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Test: Even And Odd Integers- 1

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If A and B are integers, is the product AB even?a)Statement (1) ALONE ...

Steps 1 & 2: Understand Question and Draw Inferences

Given: Integers A and B

To find: Is the product AB even?

The answer will be YES if at least one of A and B is even

Step 3: Analyze Statement 1 independently

In the above equation, 2AB and 10A will always be even. So, we can write:

Case 1: B is even

Then, B² and 3B will both be even
The difference of B² – 3B will be Even as well
A²+ Even = Even

This is possible only if A is even
Since both A and B are even, the product AB will be even

Case 2: B is odd

Then, B² and 3B will both be odd
The difference of B² – 3B will be Even
A²+ Even = Even

This is possible only if A is even
Since A is even, the product AB will be even

This means, the product AB is definitely even.

Statement 1 is sufficient to answer the question

Step 4: Analyze Statement 2 independently

The left hand side of this equation is the difference of 2 even terms. So, the left hand side is Even
This means, the Right hand side of the equation must be Even as well. So, we can write:

13A²- AB =Even

Case 1: B is even
- Then, AB is even
- Since the above equation holds true, 13A² must be Even as well.
- This means, A is even as well (since 13A² has the same even-odd nature as A)
- Since both A and B are even, the product AB is Even.

Case 2: B is odd
- Then, AB has the same even-odd nature as A
- Also, 13A² will have the same even-odd nature as A
- Thus, the left hand side of the equation has the difference of two terms which are either both odd or both even.
- We know that Odd – Odd = Even and Even- Even = Even
- Thus, the above equation will be satisfied whether A is even or odd
- If A is even, then the product AB will be even
- But if A is odd, then the product AB will be odd
Thus, we see that the product AB may be either even or odd. Statement 2 is not sufficient to determine a definite answer about the even-odd nature of AB.

Step 5: Analyze Both Statements Together (if needed)

Since we’ve already arrived at a unique answer in Step 3, this step is not required
Answer: Option A

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Most Upvoted Answer

If A and B are integers, is the product AB even?a)Statement (1) ALONE ...

Steps 1 & 2: Understand Question and Draw Inferences

Given: Integers A and B

To find: Is the product AB even?

The answer will be YES if at least one of A and B is even

Step 3: Analyze Statement 1 independently

In the above equation, 2AB and 10A will always be even. So, we can write:

Case 1: B is even

Then, B² and 3B will both be even
The difference of B² – 3B will be Even as well
A²+ Even = Even

This is possible only if A is even
Since both A and B are even, the product AB will be even

Case 2: B is odd

Then, B² and 3B will both be odd
The difference of B² – 3B will be Even
A²+ Even = Even

This is possible only if A is even
Since A is even, the product AB will be even

This means, the product AB is definitely even.

Statement 1 is sufficient to answer the question

Step 4: Analyze Statement 2 independently

The left hand side of this equation is the difference of 2 even terms. So, the left hand side is Even
This means, the Right hand side of the equation must be Even as well. So, we can write:

13A²- AB =Even

Case 1: B is even
- Then, AB is even
- Since the above equation holds true, 13A² must be Even as well.
- This means, A is even as well (since 13A² has the same even-odd nature as A)
- Since both A and B are even, the product AB is Even.

Case 2: B is odd
- Then, AB has the same even-odd nature as A
- Also, 13A² will have the same even-odd nature as A
- Thus, the left hand side of the equation has the difference of two terms which are either both odd or both even.
- We know that Odd – Odd = Even and Even- Even = Even
- Thus, the above equation will be satisfied whether A is even or odd
- If A is even, then the product AB will be even
- But if A is odd, then the product AB will be odd
Thus, we see that the product AB may be either even or odd. Statement 2 is not sufficient to determine a definite answer about the even-odd nature of AB.

Step 5: Analyze Both Statements Together (if needed)

Since we’ve already arrived at a unique answer in Step 3, this step is not required
Answer: Option A

Answered by Talent Skill Learning · View profile

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If A and B are integers, is the product AB even?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 'A'. Can you explain this answer?

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If A and B are integers, is the product AB even?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 'A'. 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 If A and B are integers, is the product AB even?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 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A and B are integers, is the product AB even?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 'A'. Can you explain this answer?.

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