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A straight line L passes through (2,8) and the origin. Find the equation of a line perpendicular to L.
1. The line passes through the origin.
2. The line passes through (2,-0.5).
  • 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 ask
  • 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 'D'. Can you explain this answer?
Verified Answer
A straight line L passes through (2,8) and the origin. Find the equati...
The line L passes through (2,8) and (0,0) hence its slope is
slope = (8 - 0)/(2 - 0) = 4.
Since L is perpendicular to the line in question, the product of their slope is -1. Therefore, the slope of the line in question is -1/4.
In statement 1, the line passes the origin, (0,0) and its slope is -1/4 hence its equation is y = -x/4. The statement is sufficient.
In statement 2, line passes through the (2,0.5) and its slope is -1/4. Thus we have (y + 0.5)/(x - 2) = -1/4
y + 1/2 = -x/4 + 1/2
thus  y = -x/4. The statement is sufficient too.
Thus, EACH statement ALONE is sufficient.
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Most Upvoted Answer
A straight line L passes through (2,8) and the origin. Find the equati...

Statement Analysis:

Statement 1:
- The line passes through the origin.
- Since the line passes through the origin, we know that the y-intercept is 0. This information alone is not enough to determine the equation of a line perpendicular to L.

Statement 2:
- The line passes through (2,-0.5).
- With this point given, we can determine the slope of the line that is perpendicular to L. The slope of the original line L can be found using the points (2,8) and (0,0), which is (8-0)/(2-0) = 4. The perpendicular line would have a slope that is the negative reciprocal of 4, which is -1/4. Using the point (2,-0.5) and the slope -1/4, we can determine the equation of the perpendicular line.

Conclusion:
- Combining both statements, we have the information needed to determine the equation of a line perpendicular to L. Therefore, both statements together are sufficient to answer the question asked.
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A straight line L passes through (2,8) and the origin. Find the equation of a line perpendicular to L.1. The line passes through the origin.2. The line passes through (2,-0.5).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 askd)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 'D'. 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 A straight line L passes through (2,8) and the origin. Find the equation of a line perpendicular to L.1. The line passes through the origin.2. The line passes through (2,-0.5).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 askd)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 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A straight line L passes through (2,8) and the origin. Find the equation of a line perpendicular to L.1. The line passes through the origin.2. The line passes through (2,-0.5).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 askd)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 'D'. Can you explain this answer?.
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