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In the xy- plane, lines l and k intersect at point A whose x and y coordinates are positive. If the lines l and k are not parallel to either of the axes, is the product of the slopes of line l and k greater than zero?
(1) The product of the x-intercepts of the lines l and k is negative.
(2) The product of the y-intercepts of the lines l and k is positive.
(1) The product of the x-intercepts of the lines l and k is negative.
(2) The product of the y-intercepts of the lines l and k is positive.
- 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 'C'. Can you explain this answer?
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Verified Answer
In the xy- plane, lines l and k intersect at point A whose x and y coo...
Step 1 & 2: Understand Question and Draw Inference
- Lines l and k intersect in quadrant I
- Lines l and k are not parallel to x or y –axis.
- Let the slopes of lines l and k be m and m respectively
To Find: Is m * m > 0?
- The answer to the question will be YES if slope of lines l and k are both positive or both negative
- Lines with positive slopes can pass through:
- Either quadrant I, III and IV or
- Quadrant I, II and III or
- Quadrant I, III through the origin
- Here all the 3 types of lines pass through quadrant-I. So, all the 3 cases are possible.
- We should also take note the positive-negative nature of x-intercepts and the y-intercepts of the lines above:
- Lines with positive slopes can pass through:
- Lines with negative slopes can pass through:
- Quadrants II, III and IV or
- Quadrant II, IV through the origin or
- Quadrant II, I and IV
- Out of the above cases only one line passes through quadrant-I, the only possible case is a line passing through quadrants II, I and IV.
- Also note that for a line having a negative slope and passing through quadrant-I has a positive x-intercept as well as a positive y-intercept
Step 3 : Analyze Statement 1 independent
(1) The product of the x-intercepts of the lines l and k is negative.
- We are given that the product of the x-intercepts of lines l and k is negative
- Possible cases can be case-I, II and IV
- For these cases we may have the product of slopes of lines l and k as negative or positive.
Insufficient to answer.
Step 4 : Analyze Statement 2 independent
(2) The product of the y-intercepts of the lines l and k is positive.
- We are given that product of the y-intercepts of lines l and k is positive
- All the four cases are possible
- For these cases we may have the product of slopes of lines l and k as negative or positive.
Insufficient to answer.
Step 5: Analyze Both Statements Together (if needed)
Combining both the statements, we can reject case-III, where slopes of both the lines is negative. Now, let’s evaluate the other cases one by one:
- Case-I and IV: Slopes of both the lines are positive
- A line with a positive slope will have
- A positive y-intercept and a negative x- intercept or
- A negative y –intercept and a positive x- intercept
- For product of y-intercepts of the line to be positive, both the lines should have a positive y-intercept(in this case the product of x-intercepts will also be positive) or negative yintercepts(
in this case the product of x – intercept will be positive) - Thus it is not possible to have a case where the product of
y-intercepts is positive and the product of x-intercepts of the
line is negative. - Case Rejected
- A line with a positive slope will have
Case-II: Lines have opposite slopes
- A line with a positive slope will have
- A positive y-intercept and a negative x- intercept or
- A negative y –intercept and a positive x- intercept
- A line with a negative slope will have
- A positive y-intercept and a positive x-intercept
- For product of y-intercepts to be positive and x-intercepts to be negative, the only possible case is when one of the line has positive slope and the other has negative slope.
Case Accepted: the product of Slope in such a case will be negetive
Thus, we have a unique answer. Sufficient to answer Answer: C
Most Upvoted Answer
In the xy- plane, lines l and k intersect at point A whose x and y coo...
Understanding the Problem
To determine if the product of the slopes of lines l and k is greater than zero, we analyze the slopes based on their intercepts.
Key Concepts
- Lines in the Plane: The slopes of two lines can indicate whether they are increasing or decreasing. If both slopes are positive or both are negative, their product is positive. If one is positive and the other is negative, the product is negative.
- Intercepts: The x-intercepts and y-intercepts provide insight into the slopes of the lines.
Statement Analysis
Statement (1): The product of the x-intercepts of lines l and k is negative.
- If the product of the x-intercepts is negative, one line must cross the x-axis to the left of the origin (negative x-intercept) and the other must cross to the right (positive x-intercept).
- This indicates that one line has a positive slope and the other has a negative slope, leading to a product of slopes that is negative.
- Thus, this statement alone is sufficient.
Statement (2): The product of the y-intercepts of lines l and k is positive.
- If the product of the y-intercepts is positive, both y-intercepts could either be positive or both could be negative.
- However, this does not provide clear information about the slopes of the lines; they could be either both positive or both negative.
- Therefore, this statement alone is insufficient.
Combining Statements
By combining both statements:
- Statement (1) indicates that one slope is positive and the other is negative.
- Statement (2, while not sufficient alone) confirms that both y-intercepts maintain a consistent slope behavior.
Since we know from Statement (1) that the slopes are of opposite signs, we conclude the product of the slopes is negative.
Conclusion
- Statement (1) alone is sufficient, while Statement (2) alone is not sufficient.
- Together, they reinforce the conclusions about slope behavior, confirming that both statements together are necessary to fully understand the relationships.
Thus, the correct answer is option 'C': both statements together are sufficient, but neither is sufficient alone.
To determine if the product of the slopes of lines l and k is greater than zero, we analyze the slopes based on their intercepts.
Key Concepts
- Lines in the Plane: The slopes of two lines can indicate whether they are increasing or decreasing. If both slopes are positive or both are negative, their product is positive. If one is positive and the other is negative, the product is negative.
- Intercepts: The x-intercepts and y-intercepts provide insight into the slopes of the lines.
Statement Analysis
Statement (1): The product of the x-intercepts of lines l and k is negative.
- If the product of the x-intercepts is negative, one line must cross the x-axis to the left of the origin (negative x-intercept) and the other must cross to the right (positive x-intercept).
- This indicates that one line has a positive slope and the other has a negative slope, leading to a product of slopes that is negative.
- Thus, this statement alone is sufficient.
Statement (2): The product of the y-intercepts of lines l and k is positive.
- If the product of the y-intercepts is positive, both y-intercepts could either be positive or both could be negative.
- However, this does not provide clear information about the slopes of the lines; they could be either both positive or both negative.
- Therefore, this statement alone is insufficient.
Combining Statements
By combining both statements:
- Statement (1) indicates that one slope is positive and the other is negative.
- Statement (2, while not sufficient alone) confirms that both y-intercepts maintain a consistent slope behavior.
Since we know from Statement (1) that the slopes are of opposite signs, we conclude the product of the slopes is negative.
Conclusion
- Statement (1) alone is sufficient, while Statement (2) alone is not sufficient.
- Together, they reinforce the conclusions about slope behavior, confirming that both statements together are necessary to fully understand the relationships.
Thus, the correct answer is option 'C': both statements together are sufficient, but neither is sufficient alone.
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In the xy- plane, lines l and k intersect at point A whose x and y coordinates are positive. If the lines l and k are not parallel to either of the axes, is the product of the slopes of line l and k greater than zero?(1) The product of the x-intercepts of the lines l and k is negative.(2) The product of the y-intercepts of the lines l and k is positive.a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'C'. Can you explain this answer?
Question Description
In the xy- plane, lines l and k intersect at point A whose x and y coordinates are positive. If the lines l and k are not parallel to either of the axes, is the product of the slopes of line l and k greater than zero?(1) The product of the x-intercepts of the lines l and k is negative.(2) The product of the y-intercepts of the lines l and k is positive.a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'C'. 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 In the xy- plane, lines l and k intersect at point A whose x and y coordinates are positive. If the lines l and k are not parallel to either of the axes, is the product of the slopes of line l and k greater than zero?(1) The product of the x-intercepts of the lines l and k is negative.(2) The product of the y-intercepts of the lines l and k is positive.a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the xy- plane, lines l and k intersect at point A whose x and y coordinates are positive. If the lines l and k are not parallel to either of the axes, is the product of the slopes of line l and k greater than zero?(1) The product of the x-intercepts of the lines l and k is negative.(2) The product of the y-intercepts of the lines l and k is positive.a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'C'. Can you explain this answer?.
In the xy- plane, lines l and k intersect at point A whose x and y coordinates are positive. If the lines l and k are not parallel to either of the axes, is the product of the slopes of line l and k greater than zero?(1) The product of the x-intercepts of the lines l and k is negative.(2) The product of the y-intercepts of the lines l and k is positive.a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'C'. 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 In the xy- plane, lines l and k intersect at point A whose x and y coordinates are positive. If the lines l and k are not parallel to either of the axes, is the product of the slopes of line l and k greater than zero?(1) The product of the x-intercepts of the lines l and k is negative.(2) The product of the y-intercepts of the lines l and k is positive.a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the xy- plane, lines l and k intersect at point A whose x and y coordinates are positive. If the lines l and k are not parallel to either of the axes, is the product of the slopes of line l and k greater than zero?(1) The product of the x-intercepts of the lines l and k is negative.(2) The product of the y-intercepts of the lines l and k is positive.a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'C'. Can you explain this answer?.
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In the xy- plane, lines l and k intersect at point A whose x and y coordinates are positive. If the lines l and k are not parallel to either of the axes, is the product of the slopes of line l and k greater than zero?(1) The product of the x-intercepts of the lines l and k is negative.(2) The product of the y-intercepts of the lines l and k is positive.a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'C'. Can you explain this answer?, a detailed solution for In the xy- plane, lines l and k intersect at point A whose x and y coordinates are positive. If the lines l and k are not parallel to either of the axes, is the product of the slopes of line l and k greater than zero?(1) The product of the x-intercepts of the lines l and k is negative.(2) The product of the y-intercepts of the lines l and k is positive.a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of In the xy- plane, lines l and k intersect at point A whose x and y coordinates are positive. If the lines l and k are not parallel to either of the axes, is the product of the slopes of line l and k greater than zero?(1) The product of the x-intercepts of the lines l and k is negative.(2) The product of the y-intercepts of the lines l and k is positive.a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice In the xy- plane, lines l and k intersect at point A whose x and y coordinates are positive. If the lines l and k are not parallel to either of the axes, is the product of the slopes of line l and k greater than zero?(1) The product of the x-intercepts of the lines l and k is negative.(2) The product of the y-intercepts of the lines l and k is positive.a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice GMAT tests.
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