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Line C is a straight line in the coordinate geometry plane defined by the equation y = ax + b, for which a and b are constants. What is the value of a?
(1) Line C is perpendicular to a line with the equation y = −2x + 5
(2) Line C is parallel to a line with the equation y = (1−a)x + b + 2
(2) Line C is parallel to a line with the equation y = (1−a)x + b + 2
- 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
- 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 'D'. Can you explain this answer?
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Most Upvoted Answer
Line C is a straight line in the coordinate geometry plane defined by ...
Statement (1) tells us that Line C is perpendicular to a line with the equation y = -2x + 5. Perpendicular lines have negative reciprocal slopes. The given line has a slope of -2. Therefore, the slope of Line C must be the negative reciprocal of -2, which is 1/2. Hence, from statement (1) alone, we can determine the value of a as 1/2.
Statement (2) tells us that Line C is parallel to a line with the equation y = (1 - a)x + b + 2. Parallel lines have the same slope. In this case, the slope of Line C is equal to the slope of the given line, which is 1 - a. Therefore, from statement (2) alone, we can determine the value of a as 1 - a.
Both statements individually provide enough information to determine the value of a. Statement (1) allows us to directly determine the value of a as 1/2, and statement (2) allows us to determine the value of a as 1 - a. Therefore, each statement alone is sufficient to answer the question.
Hence, the answer is (D): EACH statement ALONE is sufficient to answer the question asked.
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Line C is a straight line in the coordinate geometry plane defined by the equation y = ax + b, for which a and b are constants. What is the value of a?(1) Line C is perpendicular to a line with the equation y = −2x + 5(2) Line C is parallel to a line with the equation y = (1−a)x + b + 2a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'D'. Can you explain this answer?
Question Description
Line C is a straight line in the coordinate geometry plane defined by the equation y = ax + b, for which a and b are constants. What is the value of a?(1) Line C is perpendicular to a line with the equation y = −2x + 5(2) Line C is parallel to a line with the equation y = (1−a)x + b + 2a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'D'. 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 Line C is a straight line in the coordinate geometry plane defined by the equation y = ax + b, for which a and b are constants. What is the value of a?(1) Line C is perpendicular to a line with the equation y = −2x + 5(2) Line C is parallel to a line with the equation y = (1−a)x + b + 2a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Line C is a straight line in the coordinate geometry plane defined by the equation y = ax + b, for which a and b are constants. What is the value of a?(1) Line C is perpendicular to a line with the equation y = −2x + 5(2) Line C is parallel to a line with the equation y = (1−a)x + b + 2a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'D'. Can you explain this answer?.
Line C is a straight line in the coordinate geometry plane defined by the equation y = ax + b, for which a and b are constants. What is the value of a?(1) Line C is perpendicular to a line with the equation y = −2x + 5(2) Line C is parallel to a line with the equation y = (1−a)x + b + 2a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'D'. 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 Line C is a straight line in the coordinate geometry plane defined by the equation y = ax + b, for which a and b are constants. What is the value of a?(1) Line C is perpendicular to a line with the equation y = −2x + 5(2) Line C is parallel to a line with the equation y = (1−a)x + b + 2a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Line C is a straight line in the coordinate geometry plane defined by the equation y = ax + b, for which a and b are constants. What is the value of a?(1) Line C is perpendicular to a line with the equation y = −2x + 5(2) Line C is parallel to a line with the equation y = (1−a)x + b + 2a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'D'. Can you explain this answer?.
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