In the rectangular coordinate system, lines L1 and L2 intersect at point C. Are the lines L1 and L2 perpendicular to each other?(1) The product of the slopes of lines L1 and L2 is at a distance of 1 unit from 0 on the number line.(2) Lines x = 0 and y = 0 are the perpendicular bisectors of lines L1 and L2 respectively.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 'B'. Can you explain this answer?

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In the rectangular coordinate system, lines L₁ and L₂ intersect at point C. Are the lines L₁ and L₂ perpendicular to each other?

(1) The product of the slopes of lines L₁ and L₂ is at a distance of 1 unit from 0 on the number line.

(2) Lines x = 0 and y = 0 are the perpendicular bisectors of lines L₁ and L₂respectively.

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 'B'. Can you explain this answer?

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In the rectangular coordinate system, lines L1 and L2 intersect at poi...

Steps 1 & 2: Understand Question and Draw Inferences

Lines L₁ and L₂ intersect at point C

To Find:

If lines L₁ and L₂ are perpendicular?
- Let’s assume the slopes of lines L₁ and L₂ be m₁ and m₂
- So, we need to find if m₁ * m₂ = -1?

Step 3: Analyze Statement 1 independently

(1) Statement 1 states that: "The product of the slopes of lines L₁ and L₂ is at a distance of 1 unit from 0 on the number line."

Numbers that are at a distance of 1 unit from 0 on the number line:
- 0 + 1 = 1 and
- 0 – 1 = -1
So, as per Statement 1, Product of slopes, that is,= m₁ * m₂ = 1 or -1
If m₁ * m₂ = 1, lines L₁ and L₂are not perpendicular to each other
If m₁ * m₂ = -1, lines L₁ and L₂are perpendicular to each other
Thus, statement 1 is not sufficient to answer.

Step 4: Analyze Statement 2 independently

(2) Statement 2 states that: "Lines x = 0 and y = 0 are the perpendicular bisectors of lines L₁ and L₂respectively."

As x= 0 is the perpendicular bisector of line L_1,L₁is perpendicular to line x= 0 i.e. L₁ is the y –axis
As y = 0 is the perpendicular bisector of line L_2,L₂is perpendicular to line y = 0 i.e. L₂is the x –axis

Since x axis and y-axis are perpendicular to each other, lines L₁ and L₂will also be perpendicular to each other.
Hence, Statement 2 is sufficient to answer the question

Step 5: Analyze Both Statements Together (if needed)

As we have got a unique answer from step-4, this step is not required.

Thus the correct answer is Option B.

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In the rectangular coordinate system, lines L1 and L2 intersect at point C. Are the lines L1 and L2 perpendicular to each other?(1) The product of the slopes of lines L1 and L2 is at a distance of 1 unit from 0 on the number line.(2) Lines x = 0 and y = 0 are the perpendicular bisectors of lines L1 and L2 respectively.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 'B'. Can you explain this answer?

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In the rectangular coordinate system, lines L1 and L2 intersect at point C. Are the lines L1 and L2 perpendicular to each other?(1) The product of the slopes of lines L1 and L2 is at a distance of 1 unit from 0 on the number line.(2) Lines x = 0 and y = 0 are the perpendicular bisectors of lines L1 and L2 respectively.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 'B'. 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 rectangular coordinate system, lines L1 and L2 intersect at point C. Are the lines L1 and L2 perpendicular to each other?(1) The product of the slopes of lines L1 and L2 is at a distance of 1 unit from 0 on the number line.(2) Lines x = 0 and y = 0 are the perpendicular bisectors of lines L1 and L2 respectively.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 'B'. 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 rectangular coordinate system, lines L1 and L2 intersect at point C. Are the lines L1 and L2 perpendicular to each other?(1) The product of the slopes of lines L1 and L2 is at a distance of 1 unit from 0 on the number line.(2) Lines x = 0 and y = 0 are the perpendicular bisectors of lines L1 and L2 respectively.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 'B'. Can you explain this answer?.

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