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In the xy-plane shown, is the slope of line l non-negative?
1. The line passes through quadrants II and III.
2. For each pair of coordinates (x,y) lying on line l, the product of x and y is not always non-negative.
  • 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 'E'. Can you explain this answer?
Verified Answer
In the xy-plane shown, is the slope of line l non-negative?1. The line...
Step 1 & 2: Understand Question and Draw Inference
To Find:
  • Is the slope of line l negative?
Step 3 : Analyze Statement 1 independent
(1) Statement 1 states that "The line passes through quadrants II and III".
  • Following cases are possible:
    • If the line also passes through quadrant-I, the slope of the line will be positive
    • If the line also passes through quadrant- IV, the slope of the line will be negative.
    •  If the line passes through quadrants II and III only and is parallel to y-axis, the slope of the line will be infinity.
Hence, Statement 1 is insufficient to answer
Step 4 : Analyze Statement 2 independent
(2) Statement 2 states that "For each pair of coordinates (x, y) lying on the line l, the product of x and y is not always non-negative."
  • x * y < 0 for some points on line l. This is possible when the line passes through either quadrant-II, IV or both:
    • If Line l passes through quadrant- II but not quadrant-IV, then Slope of the line is positive
    • If Line l passes through quadrant- IV but not quadrant-II, then Slope of the line is positive
    • If Line l passes through both quadrant –II and IV, then Slope of the line is negative
Hence, Statement 2 is insufficient to answer
Step 5: Analyze Both Statements Together (if needed)
1. Line l passes through quadrants-II and III
2. Line l passes through quadrant II, or IV or both
Following cases are possible:
  • Line l passes through quadrants II, III and IV : Slope of the line is negative
  • Line l passes through I, II and III : Slope of the line is positive
As we do not have a unique answer, hence by combining both the statements also it is insufficient to answer the question.
Thus, the correct answer is Option E .
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In the xy-plane shown, is the slope of line l non-negative?1. The line passes through quadrants II and III.2. For each pair of coordinates (x,y) lying on line l, the product of x and y is not always non-negative.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 'E'. Can you explain this answer?
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