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There are three circles, with radii 2, 4 and 5, respectively, that lie on a plane. Do any two of these circles intersect with each other?
(1) The centres of the three circles lie on a straight line
(2) The greatest distance between the centres of any two of these circles is 7
  • 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 'E'. Can you explain this answer?
Most Upvoted Answer
There are three circles, with radii 2, 4 and 5, respectively, that lie...
Statement (1) states that the centers of the three circles lie on a straight line. This information alone does not provide any conclusive evidence regarding whether the circles intersect or not. The alignment of the centers on a straight line does not guarantee that the circles will intersect. For example, if the centers are arranged in a collinear manner, with the circle of radius 2 between the circles of radii 4 and 5, the circles will not intersect. On the other hand, if the centers are arranged such that the circle of radius 2 overlaps with one or both of the other circles, they will intersect. Therefore, statement (1) alone is not sufficient to answer the question.
Statement (2) states that the greatest distance between the centers of any two circles is 7. This information also does not provide a definitive answer. While the distance between the centers can give us an idea of their relative positions, it does not provide direct information about the intersection of the circles. For example, if the circle of radius 5 is located at the origin, the circle of radius 4 is centered at (7, 0), and the circle of radius 2 is centered at (-3, 0), the circles will not intersect. However, if the circle of radius 2 is centered at (-7, 0), the circles will intersect. Hence, statement (2) alone is not sufficient to answer the question.
By considering both statements together, we still cannot definitively determine if any two circles intersect. While statement (1) provides information about the alignment of the centers, statement (2) only gives the greatest distance between the centers. Without more precise information about the positions and arrangements of the circles, we cannot determine if they intersect.
Therefore, the correct answer is E: Statements (1) and (2) together are NOT sufficient to answer the question asked, and additional data are needed.
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There are three circles, with radii 2, 4 and 5, respectively, that lie on a plane. Do any two of these circles intersect with each other?(1) The centres of the three circles lie on a straight line(2) The greatest distance between the centres of any two of these circles is 7a)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 'E'. Can you explain this answer?
Question Description
There are three circles, with radii 2, 4 and 5, respectively, that lie on a plane. Do any two of these circles intersect with each other?(1) The centres of the three circles lie on a straight line(2) The greatest distance between the centres of any two of these circles is 7a)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 'E'. 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 There are three circles, with radii 2, 4 and 5, respectively, that lie on a plane. Do any two of these circles intersect with each other?(1) The centres of the three circles lie on a straight line(2) The greatest distance between the centres of any two of these circles is 7a)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 'E'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are three circles, with radii 2, 4 and 5, respectively, that lie on a plane. Do any two of these circles intersect with each other?(1) The centres of the three circles lie on a straight line(2) The greatest distance between the centres of any two of these circles is 7a)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 'E'. Can you explain this answer?.
Solutions for There are three circles, with radii 2, 4 and 5, respectively, that lie on a plane. Do any two of these circles intersect with each other?(1) The centres of the three circles lie on a straight line(2) The greatest distance between the centres of any two of these circles is 7a)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 'E'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT. Download more important topics, notes, lectures and mock test series for GMAT Exam by signing up for free.
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