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Does the line L whose equation is y = mx + c cut the x-axis in the positive direction of x-axis?
Statement 1: The intercepts of Line K, perpendicular to L, are of the opposite signs.
Statement 2: Line L passes through the 4th quadrant.
  • a)
    Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;
  • b)
    Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion asked;
  • c)
    BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;
  • 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 are needed. 
Correct answer is option 'E'. Can you explain this answer?
Most Upvoted Answer
Does the line L whose equation is y = mx + c cut the x-axis in the pos...
Statement (1): The intercepts of Line K, perpendicular to L, are of the opposite signs.

The intercepts of Line K, which is perpendicular to Line L, will help us determine if Line L cuts the x-axis in the positive direction of the x-axis. If the intercepts have opposite signs, it means that one intercept is positive and the other is negative. This would indicate that Line L does cut the x-axis in the positive direction of the x-axis.

However, this information alone is not sufficient to determine whether Line L cuts the x-axis in the positive direction of the x-axis. We need more information.

Statement (2): Line L passes through the 4th quadrant.

If Line L passes through the 4th quadrant, it means that Line L has a negative slope (m) because the y-coordinate decreases as the x-coordinate increases in the 4th quadrant.

But knowing that Line L passes through the 4th quadrant does not provide enough information to determine whether Line L cuts the x-axis in the positive direction of the x-axis. We still need more information.

Combined statements:

By combining the information from both statements, we know that Line L has a negative slope (m) and the intercepts of Line K, which is perpendicular to Line L, have opposite signs.

However, this information is still not sufficient to determine whether Line L cuts the x-axis in the positive direction of the x-axis. We need to know the value of the y-intercept (c) in the equation y = mx + c to determine the exact position of Line L with respect to the x-axis.

Therefore, both statements together are not sufficient to answer the question. Additional information is needed to determine if Line L cuts the x-axis in the positive direction of the x-axis.

Hence, the correct answer is option E.
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Community Answer
Does the line L whose equation is y = mx + c cut the x-axis in the pos...
Statement 1: The intercepts of Line K, perpendicular to L, are of the opposite signs.
Inference 1: If the intercepts of line K are of opposite signs, line K is a positive sloping line.
Inference 2: So, we can infer that line L is a negative sloping line.
Possibility 1: Negative sloping Line L with a positive x-intercept

 
In this possibility, answer to the question is YES
Possibility 2: Negative sloping Line L with a negative x-intercept

In this possibility, answer to the question is NO
Because both possibilities exist, we are not able to answer the question using statement 1.
Statement 1 alone is NOT sufficient.
Eliminate answer options A and D.
Step 2: Evaluate Statement 2 ALONE
Statement 2:
Line L passes through the 4th quadrant.
Possibility 1: Line L passes through IV quadrant. Has a positive x-intercept.

 
In this possibility, answer to the question is YES
Possibility 2: Line L passes through IV quadrant. Has a negative x-intercept

 
In this possibility, answer to the question is NO
Because both possibilities exist, we are not able to answer the question using statement 2.
Statement 2 alone is NOT sufficient.
Eliminate answer option B.
Step 3: Evaluate Statements TOGETHER
Statement 1:
The intercepts of Line K, perpendicular to L, are of the opposite signs.
Statement 2: Line L passes through the 4th quadrant.
Key Inference from Statement 1: Line L is a negative sloping line.
Possibility 1: Negative Sloping Line L passes through IV quadrant. Has a positive x-intercept.

 
In this possibility, answer to the question is YES
Possibility 2: Negative Sloping Line L passes through IV quadrant. Has a negative x-intercept

In this possibility, answer to the question is NO
Because both possibilities exist, we are not able to answer the question despite combining the statements.
Statement TOGETHER are NOT sufficient.
Eliminate answer option C.
Choice E is the correct answer.
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Does the line L whose equation is y = mx + c cut the x-axis in the positive direction of x-axis?Statement 1: The intercepts of Line K, perpendicular to L, are of the opposite signs.Statement 2: Line L passes through the 4th quadrant.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;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 are needed.Correct answer is option 'E'. Can you explain this answer?
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Does the line L whose equation is y = mx + c cut the x-axis in the positive direction of x-axis?Statement 1: The intercepts of Line K, perpendicular to L, are of the opposite signs.Statement 2: Line L passes through the 4th quadrant.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;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 are needed.Correct answer is option 'E'. 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 Does the line L whose equation is y = mx + c cut the x-axis in the positive direction of x-axis?Statement 1: The intercepts of Line K, perpendicular to L, are of the opposite signs.Statement 2: Line L passes through the 4th quadrant.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;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 are needed.Correct answer is option 'E'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Does the line L whose equation is y = mx + c cut the x-axis in the positive direction of x-axis?Statement 1: The intercepts of Line K, perpendicular to L, are of the opposite signs.Statement 2: Line L passes through the 4th quadrant.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;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 are needed.Correct answer is option 'E'. Can you explain this answer?.
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