In the xy-plane, the circle C centered at the origin O is intersected by a line l at two points A and B. A line from O is drawn to AB intersecting AB at point D, such that the product of the slopes of OD and AB is -1. If the line l does not pass through origin and the coordinates of point D are (1, -1), what is the radius of the circle?(1) The x intercept of line l is 2.(2) The product of the x coordinates of points A and B as well as the product of the y coordinates of points A and B is zero.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 'B'. Can you explain this answer?

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(1) The x intercept of line l is 2.
(2) The product of the x coordinates of points A and B as well as the product of the y coordinates of points A and B is zero.

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 xy-plane, the circle C centered at the origin O is intersected ...

Step 1 & 2: Understand Question and Draw Inference

Circle C with center at (0, 0)
Line l intersects the circle at A and B
OD is perpendicular to AB, where D is a point on line segment AB with coordinates (1, -1)
- As OD is a perpendicular from the center of circle C to chord AB, D must be the midpoint of AB

Since the coordinates of point O are (0,0) and of point D are (1, -1), Slope of line OD =
- Slope of line AB * Slope of line OD = -1
- (Slope of line AB)*(-1)= -1
- Slope of line AB = 1
Since we’ve inferred that the slope of line AB is 1, we can write the Equation of line AB as: y = 1*x + c, that is, y = x + c
- As AB passes through (1, -1), we have -1 = 1 + c, i.e. c = -2
- Equation of line AB : y = x – 2
To find: Radius of the circle, say r, That is, the length of OA (or OB)
- To answer this question, we need the coordinates of points A or B so that we can then find the distance between points O(0,0) and points A or B.

Step 3 : Analyze Statement 1 independent

(1) The x intercept of line l is 2.
We know from the equation of the line, that x- intercept of the line is 2. Hence, there is no added information provided.

Insufficient to answer

Step 4 : Analyze Statement 2 independent

(2) The product of the x coordinates of points A and B as well as the product of the y coordinates of points A and B is zero.

Let the coordinates of point A be (x₁, y₁) and coordinates of point B be(x₂ , y₂).
x * x = 0
- Either of x or x or both are zero
y * y = 0
- Either of y or y or both are zero
x and y both cannot be zero, as that would mean that point A is the origin. Similarly x and y cannot be zero at the same time.
So, coordinates of point A and B can be (0, y ) and (x , 0) or vice versa, i.e. they lie on the y-axis and the x-axis respectively.
Now, we know that equation of line AB : y = x – 2.
- Putting coordinates of point A(0, y ) in the equation, we have y = 0 – 2, i.e. y = -2
- So, Coordinates of point A(0, -2)

As we know the coordinate of point A, we can calculate the radius of the circle C.
Sufficient to answer.

Step 5: Analyze Both Statements Together (if needed)

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

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In the xy-plane, the circle C centered at the origin O is intersected by a line l at two points A and B. A line from O is drawn to AB intersecting AB at point D, such that the product of the slopes of OD and AB is -1. If the line l does not pass through origin and the coordinates of point D are (1, -1), what is the radius of the circle?(1) The x intercept of line l is 2.(2) The product of the x coordinates of points A and B as well as the product of the y coordinates of points A and B is zero.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 'B'. Can you explain this answer?

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In the xy-plane, the circle C centered at the origin O is intersected by a line l at two points A and B. A line from O is drawn to AB intersecting AB at point D, such that the product of the slopes of OD and AB is -1. If the line l does not pass through origin and the coordinates of point D are (1, -1), what is the radius of the circle?(1) The x intercept of line l is 2.(2) The product of the x coordinates of points A and B as well as the product of the y coordinates of points A and B is zero.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 '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 xy-plane, the circle C centered at the origin O is intersected by a line l at two points A and B. A line from O is drawn to AB intersecting AB at point D, such that the product of the slopes of OD and AB is -1. If the line l does not pass through origin and the coordinates of point D are (1, -1), what is the radius of the circle?(1) The x intercept of line l is 2.(2) The product of the x coordinates of points A and B as well as the product of the y coordinates of points A and B is zero.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 '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 xy-plane, the circle C centered at the origin O is intersected by a line l at two points A and B. A line from O is drawn to AB intersecting AB at point D, such that the product of the slopes of OD and AB is -1. If the line l does not pass through origin and the coordinates of point D are (1, -1), what is the radius of the circle?(1) The x intercept of line l is 2.(2) The product of the x coordinates of points A and B as well as the product of the y coordinates of points A and B is zero.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 'B'. Can you explain this answer?.

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If the line l does not pass through origin and the coordinates of point D are (1, -1), what is the radius of the circle?(1) The x intercept of line l is 2.(2) The product of the x coordinates of points A and B as well as the product of the y coordinates of points A and B is zero.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 'B'. Can you explain this answer? defined & explained in the simplest way possible. 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If the line l does not pass through origin and the coordinates of point D are (1, -1), what is the radius of the circle?(1) The x intercept of line l is 2.(2) The product of the x coordinates of points A and B as well as the product of the y coordinates of points A and B is zero.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 'B'. 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If the line l does not pass through origin and the coordinates of point D are (1, -1), what is the radius of the circle?(1) The x intercept of line l is 2.(2) The product of the x coordinates of points A and B as well as the product of the y coordinates of points A and B is zero.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 'B'. 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If the line l does not pass through origin and the coordinates of point D are (1, -1), what is the radius of the circle?(1) The x intercept of line l is 2.(2) The product of the x coordinates of points A and B as well as the product of the y coordinates of points A and B is zero.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 'B'. 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If the line l does not pass through origin and the coordinates of point D are (1, -1), what is the radius of the circle?(1) The x intercept of line l is 2.(2) The product of the x coordinates of points A and B as well as the product of the y coordinates of points A and B is zero.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 'B'. Can you explain this answer? tests, examples and also practice GMAT tests.

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