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The function {x} is defined as the lowest odd integer greater than x. What is the value of {x}?
(1) -3.1 < x < -2.5
(2) x2 < 9
- 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 'C'. Can you explain this answer?
Verified Answer
The function {x} is defined as the lowest odd integer greater than x. ...
Steps 1 & 2: Understand Question and Draw Inferences
Let’s understand the meaning of {x}. If x = 2, then the odd integers greater than 2 are 3, 5, etc. The lowest among them is 3. Therefore {2} = 3.
Step 3: Analyze Statement 1
If x is between -3.1 and -3, then {x} = -3. If x is between -3 and -2.5, then {x} = -1.
INSUFFICIENT.
Step 4: Analyze Statement 2
x2 < 9 only for values of x between -3 and 3.
If x = is between -3 and – 1, {x} = -1, if x is between -1 and 1, {x} = 1 and if x is between 1 and 3, {x} = 3.
Therefore, {x} can be -1, 1 or 3.
INSUFFICIENT.
Step 5: Analyze Both Statements Together (if needed)
When we combine statements (1) and (2),
We know that
-3.1 < x < -2.5
AND
-3 < x < 3
The common solution is: -3 < x < -2.5
For this set of values, {x} = -1.
SUFFICIENT.
Answer: Option (C)
Most Upvoted Answer
The function {x} is defined as the lowest odd integer greater than x. ...
Understanding the Function {x}
The function {x} is defined as the lowest odd integer greater than x. To solve for {x}, we need to analyze the provided statements.
Statement (1): -3.1 < x="" />< />
- The range of x here is between -3.1 and -2.5.
- The lowest odd integer greater than -3.1 is -3.
- The lowest odd integer greater than -2.5 is -1.
- Therefore, {x} must be an odd integer in the range from -3 to -1. The possible values are -3, -1.
- However, we cannot determine a unique value for {x} based solely on this statement.
Statement (2): x^2 < />
- This implies that -3 < x="" />< />
- For this range, we can analyze the possible values of x:
- If x is less than -3, the lowest odd integer greater than x will be -1.
- If x is between -3 and -1, {x} will be -1.
- If x is between -1 and 1, {x} will be 1.
- If x is between 1 and 3, {x} will be 3.
- As x can take any value in this range, we do not get a unique value for {x} based solely on this statement.
Combining Both Statements
- From Statement (1), we know that x is strictly between -3.1 and -2.5, which means x is less than -2.5 and greater than -3.1.
- From Statement (2), we know that x must also be greater than -3 and less than 3.
- The combined information restricts x to be between -3.1 and -2.5, confirming that {x} is -3.
Conclusion
Both statements together provide sufficient information to determine a unique value for {x}. Therefore, the answer is option 'C': BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
The function {x} is defined as the lowest odd integer greater than x. To solve for {x}, we need to analyze the provided statements.
Statement (1): -3.1 < x="" />< />
- The range of x here is between -3.1 and -2.5.
- The lowest odd integer greater than -3.1 is -3.
- The lowest odd integer greater than -2.5 is -1.
- Therefore, {x} must be an odd integer in the range from -3 to -1. The possible values are -3, -1.
- However, we cannot determine a unique value for {x} based solely on this statement.
Statement (2): x^2 < />
- This implies that -3 < x="" />< />
- For this range, we can analyze the possible values of x:
- If x is less than -3, the lowest odd integer greater than x will be -1.
- If x is between -3 and -1, {x} will be -1.
- If x is between -1 and 1, {x} will be 1.
- If x is between 1 and 3, {x} will be 3.
- As x can take any value in this range, we do not get a unique value for {x} based solely on this statement.
Combining Both Statements
- From Statement (1), we know that x is strictly between -3.1 and -2.5, which means x is less than -2.5 and greater than -3.1.
- From Statement (2), we know that x must also be greater than -3 and less than 3.
- The combined information restricts x to be between -3.1 and -2.5, confirming that {x} is -3.
Conclusion
Both statements together provide sufficient information to determine a unique value for {x}. Therefore, the answer is option 'C': BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
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The function {x} is defined as the lowest odd integer greater than x. What is the value of {x}?(1) -3.1 < x < -2.5(2) x2 < 9a)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 'C'. 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 The function {x} is defined as the lowest odd integer greater than x. What is the value of {x}?(1) -3.1 < x < -2.5(2) x2 < 9a)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 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The function {x} is defined as the lowest odd integer greater than x. What is the value of {x}?(1) -3.1 < x < -2.5(2) x2 < 9a)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 'C'. Can you explain this answer?.
The function {x} is defined as the lowest odd integer greater than x. What is the value of {x}?(1) -3.1 < x < -2.5(2) x2 < 9a)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 'C'. 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 The function {x} is defined as the lowest odd integer greater than x. What is the value of {x}?(1) -3.1 < x < -2.5(2) x2 < 9a)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 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The function {x} is defined as the lowest odd integer greater than x. What is the value of {x}?(1) -3.1 < x < -2.5(2) x2 < 9a)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 'C'. Can you explain this answer?.
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