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Is ab positive?
Statement 1: (a + b)2 < (a - b)2
Statement 2: a = b
Statement 2: a = b
- 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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Most Upvoted Answer
Is ab positive?Statement 1: (a + b)2 < (a - b)2Statement 2: a = ba)...
Step 1 of solving this GMAT DS question: Understand the Question Stem
What kind of an answer will the question fetch?
The question is an "Is" question. Answer to an "is" questions is either YES or NO.
The question is an "Is" question. Answer to an "is" questions is either YES or NO.
When is the data sufficient?
The data is sufficient if we are able to get a DEFINITE YES or a DEFINITE NO from the information given in the statements.
The data is sufficient if we are able to get a DEFINITE YES or a DEFINITE NO from the information given in the statements.
Step 2 of solving this GMAT DS question:
Evaluate Statement (1) ALONE: (a + b)2 < (a - b)2
Evaluate Statement (1) ALONE: (a + b)2 < (a - b)2
Expanding both sides of the inequality, we get a2 + b2 + 2ab < a2 + b2 - 2ab
Simplifying we get, 4ab < 0 or ab < 0.
So, we can conclude that ab is not positive. We have got a definite NO as the answer.
Simplifying we get, 4ab < 0 or ab < 0.
So, we can conclude that ab is not positive. We have got a definite NO as the answer.
Statement 1 ALONE is sufficient.
Eliminate choices B, C and E. Choices narrow down to A or D.
Eliminate choices B, C and E. Choices narrow down to A or D.
Step 3 of solving this GMAT DS question:
Evaluate Statement (2) ALONE: a = b
Evaluate Statement (2) ALONE: a = b
This is actually the statement that could trick you.
a = b.
So, either both a and b or positive or both a and b are negative. In either case ab is positive.
We will certainly be "tempted" to decide that statement 2 is also sufficient.
a = b.
So, either both a and b or positive or both a and b are negative. In either case ab is positive.
We will certainly be "tempted" to decide that statement 2 is also sufficient.
The catch is that, both a and b could be 0. In that case ab = 0, which is not positive.
If 'a' and 'b' are either both positive or both negative, the answer is yes. If both are 0, the answer is no.
As we are not able to conclude whether ab is positive with statement 2, it is not sufficient.
If 'a' and 'b' are either both positive or both negative, the answer is yes. If both are 0, the answer is no.
As we are not able to conclude whether ab is positive with statement 2, it is not sufficient.
Statement 2 ALONE is NOT sufficient.
Eliminate choice D.
Eliminate choice D.
Statement 1 ALONE is sufficient but statement 2 is not sufficient. Choice A is the answer.
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Community Answer
Is ab positive?Statement 1: (a + b)2 < (a - b)2Statement 2: a = ba)...
Understanding the Problem
We need to determine whether both a and b are positive numbers based on the given statements.
Statement 1: (a + b)² < (a="" -="" />
- This statement can be simplified:
- Expanding both sides:
- Left: (a + b)² = a² + 2ab + b²
- Right: (a - b)² = a² - 2ab + b²
- Therefore, the inequality can be rewritten as:
- a² + 2ab + b² < a²="" -="" 2ab="" +="" />
- Simplifying this gives us:
- 4ab < />
- Therefore, ab < />
Since the product ab is negative, at least one of a or b must be negative, which indicates that both cannot be positive.
Conclusion for Statement 1
- Statement 1 alone is sufficient to conclude that both a and b cannot be positive.
Statement 2: a = b
- This statement tells us that a and b are equal.
- If a and b are equal, they could both be positive, both be negative, or one could be zero.
Conclusion for Statement 2
- Since we cannot definitively conclude that both are positive based solely on this statement, it is not sufficient alone.
Final Analysis
- Statement 1 alone is sufficient to determine that both a and b cannot be positive.
- Statement 2 alone does not provide enough information to conclude that both a and b are positive.
Therefore, the correct answer is option 'A': Statement (1) alone is sufficient, but statement (2) alone is not sufficient to answer the question asked.
We need to determine whether both a and b are positive numbers based on the given statements.
Statement 1: (a + b)² < (a="" -="" />
- This statement can be simplified:
- Expanding both sides:
- Left: (a + b)² = a² + 2ab + b²
- Right: (a - b)² = a² - 2ab + b²
- Therefore, the inequality can be rewritten as:
- a² + 2ab + b² < a²="" -="" 2ab="" +="" />
- Simplifying this gives us:
- 4ab < />
- Therefore, ab < />
Since the product ab is negative, at least one of a or b must be negative, which indicates that both cannot be positive.
Conclusion for Statement 1
- Statement 1 alone is sufficient to conclude that both a and b cannot be positive.
Statement 2: a = b
- This statement tells us that a and b are equal.
- If a and b are equal, they could both be positive, both be negative, or one could be zero.
Conclusion for Statement 2
- Since we cannot definitively conclude that both are positive based solely on this statement, it is not sufficient alone.
Final Analysis
- Statement 1 alone is sufficient to determine that both a and b cannot be positive.
- Statement 2 alone does not provide enough information to conclude that both a and b are positive.
Therefore, the correct answer is option 'A': Statement (1) alone is sufficient, but statement (2) alone is not sufficient to answer the question asked.
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Is ab positive?Statement 1: (a + b)2 < (a - b)2Statement 2: a = ba)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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Is ab positive?Statement 1: (a + b)2 < (a - b)2Statement 2: a = ba)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 Is ab positive?Statement 1: (a + b)2 < (a - b)2Statement 2: a = ba)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 Is ab positive?Statement 1: (a + b)2 < (a - b)2Statement 2: a = ba)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?.
Is ab positive?Statement 1: (a + b)2 < (a - b)2Statement 2: a = ba)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 Is ab positive?Statement 1: (a + b)2 < (a - b)2Statement 2: a = ba)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 Is ab positive?Statement 1: (a + b)2 < (a - b)2Statement 2: a = ba)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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ample number of questions to practice Is ab positive?Statement 1: (a + b)2 < (a - b)2Statement 2: a = ba)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? tests, examples and also practice GMAT tests.
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