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Is there a point of intersection between the circle (X2 + Y2 = 4)and the Line ( Y = aX + b) ?
(1) a = b2.
(2) The line intersects the X-axis at (40, 0).
(1) a = b2.
(2) The line intersects the X-axis at (40, 0).
- a)Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
- b)Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
- c)Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
- d)Either statement BY ITSELF is sufficient to answer the question.
- e)Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Is there a point of intersection between the circle (X2 + Y2 = 4)and t...
The best answer is C.
From statement (1) we learn that the equation of the line can be written as Y = b2X + b.
From statement (2) we learn that the line goes threw the point (40, 0), from that we can find the equation of the line by posting the coordinate in the equation: 0 = b240 + b.
There is no need to solve it, both statements are sufficient to solve the problem.
From statement (2) we learn that the line goes threw the point (40, 0), from that we can find the equation of the line by posting the coordinate in the equation: 0 = b240 + b.
There is no need to solve it, both statements are sufficient to solve the problem.
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Most Upvoted Answer
Is there a point of intersection between the circle (X2 + Y2 = 4)and t...
Given:
Circle equation: x^2 + y^2 = 4
Line equation: y = ax + b
To find: Is there a point of intersection between the circle and the line?
Statement 1: a = b^2
Statement 2: The line intersects the x-axis at (40, 0)
Let's analyze each statement separately:
Statement 1: a = b^2
This statement provides a relationship between the slope (a) and the y-intercept (b) of the line. However, it does not provide any information about the x-coordinate of the point of intersection. Therefore, statement 1 alone is not sufficient to answer the question.
Statement 2: The line intersects the x-axis at (40, 0)
If the line intersects the x-axis at (40, 0), it means that the y-coordinate of the point of intersection is 0. Substituting this into the line equation, we get:
0 = ax + b
This equation represents the y-coordinate of the point of intersection as a function of the x-coordinate. However, it does not provide any information about the specific value of a or b. Therefore, statement 2 alone is not sufficient to answer the question.
Statements 1 and 2 together:
Using statement 2, we know that the y-coordinate of the point of intersection is 0. Substituting this into the line equation, we get:
0 = ax + b
Using statement 1, we have the relationship a = b^2. Substituting this into the line equation, we get:
0 = bx^2 + b
Now, we have an equation with one variable (b) and the x-coordinate of the point of intersection. By solving this equation, we can find the value of b. Once we have the value of b, we can substitute it back into the equation a = b^2 to find the value of a.
Therefore, statements 1 and 2 together are sufficient to answer the question.
Hence, the correct answer is option (c): Statements (1) and (2) taken together are sufficient to answer the question, even though neither statement by itself is sufficient.
Circle equation: x^2 + y^2 = 4
Line equation: y = ax + b
To find: Is there a point of intersection between the circle and the line?
Statement 1: a = b^2
Statement 2: The line intersects the x-axis at (40, 0)
Let's analyze each statement separately:
Statement 1: a = b^2
This statement provides a relationship between the slope (a) and the y-intercept (b) of the line. However, it does not provide any information about the x-coordinate of the point of intersection. Therefore, statement 1 alone is not sufficient to answer the question.
Statement 2: The line intersects the x-axis at (40, 0)
If the line intersects the x-axis at (40, 0), it means that the y-coordinate of the point of intersection is 0. Substituting this into the line equation, we get:
0 = ax + b
This equation represents the y-coordinate of the point of intersection as a function of the x-coordinate. However, it does not provide any information about the specific value of a or b. Therefore, statement 2 alone is not sufficient to answer the question.
Statements 1 and 2 together:
Using statement 2, we know that the y-coordinate of the point of intersection is 0. Substituting this into the line equation, we get:
0 = ax + b
Using statement 1, we have the relationship a = b^2. Substituting this into the line equation, we get:
0 = bx^2 + b
Now, we have an equation with one variable (b) and the x-coordinate of the point of intersection. By solving this equation, we can find the value of b. Once we have the value of b, we can substitute it back into the equation a = b^2 to find the value of a.
Therefore, statements 1 and 2 together are sufficient to answer the question.
Hence, the correct answer is option (c): Statements (1) and (2) taken together are sufficient to answer the question, even though neither statement by itself is sufficient.
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Is there a point of intersection between the circle (X2 + Y2 = 4)and theLine ( Y = aX + b) ?(1) a = b2.(2) The line intersects the X-axis at (40, 0).a)Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.b)Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.c)Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.d)Either statement BY ITSELF is sufficient to answer the question.e)Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.Correct answer is option 'C'. Can you explain this answer?
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Is there a point of intersection between the circle (X2 + Y2 = 4)and theLine ( Y = aX + b) ?(1) a = b2.(2) The line intersects the X-axis at (40, 0).a)Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.b)Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.c)Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.d)Either statement BY ITSELF is sufficient to answer the question.e)Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.Correct answer is option 'C'. 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 Is there a point of intersection between the circle (X2 + Y2 = 4)and theLine ( Y = aX + b) ?(1) a = b2.(2) The line intersects the X-axis at (40, 0).a)Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.b)Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.c)Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.d)Either statement BY ITSELF is sufficient to answer the question.e)Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Is there a point of intersection between the circle (X2 + Y2 = 4)and theLine ( Y = aX + b) ?(1) a = b2.(2) The line intersects the X-axis at (40, 0).a)Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.b)Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.c)Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.d)Either statement BY ITSELF is sufficient to answer the question.e)Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.Correct answer is option 'C'. Can you explain this answer?.
Is there a point of intersection between the circle (X2 + Y2 = 4)and theLine ( Y = aX + b) ?(1) a = b2.(2) The line intersects the X-axis at (40, 0).a)Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.b)Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.c)Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.d)Either statement BY ITSELF is sufficient to answer the question.e)Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.Correct answer is option 'C'. 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 Is there a point of intersection between the circle (X2 + Y2 = 4)and theLine ( Y = aX + b) ?(1) a = b2.(2) The line intersects the X-axis at (40, 0).a)Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.b)Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.c)Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.d)Either statement BY ITSELF is sufficient to answer the question.e)Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Is there a point of intersection between the circle (X2 + Y2 = 4)and theLine ( Y = aX + b) ?(1) a = b2.(2) The line intersects the X-axis at (40, 0).a)Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.b)Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.c)Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.d)Either statement BY ITSELF is sufficient to answer the question.e)Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.Correct answer is option 'C'. Can you explain this answer?.
Solutions for Is there a point of intersection between the circle (X2 + Y2 = 4)and theLine ( Y = aX + b) ?(1) a = b2.(2) The line intersects the X-axis at (40, 0).a)Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.b)Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.c)Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.d)Either statement BY ITSELF is sufficient to answer the question.e)Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
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Is there a point of intersection between the circle (X2 + Y2 = 4)and theLine ( Y = aX + b) ?(1) a = b2.(2) The line intersects the X-axis at (40, 0).a)Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.b)Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.c)Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.d)Either statement BY ITSELF is sufficient to answer the question.e)Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.Correct answer is option 'C'. Can you explain this answer?, a detailed solution for Is there a point of intersection between the circle (X2 + Y2 = 4)and theLine ( Y = aX + b) ?(1) a = b2.(2) The line intersects the X-axis at (40, 0).a)Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.b)Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.c)Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.d)Either statement BY ITSELF is sufficient to answer the question.e)Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of Is there a point of intersection between the circle (X2 + Y2 = 4)and theLine ( Y = aX + b) ?(1) a = b2.(2) The line intersects the X-axis at (40, 0).a)Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.b)Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.c)Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.d)Either statement BY ITSELF is sufficient to answer the question.e)Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Is there a point of intersection between the circle (X2 + Y2 = 4)and theLine ( Y = aX + b) ?(1) a = b2.(2) The line intersects the X-axis at (40, 0).a)Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.b)Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.c)Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.d)Either statement BY ITSELF is sufficient to answer the question.e)Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice GMAT tests.
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