Three circles with radii of 1, 2, and 3, lie on the same plane. Do any

800score Official Solution:

From Statement (1), we can determine how the circles are positioned relative to each other, because we know the distances between the centers. Therefore, we could establish whether any two of the circles intersect each other or one lies within another. Thus Statement (1) is sufficient. You do NOT need to do any further analysis of Statement (1).

Statement (2) is not sufficient. Imagine the two different situations: all the centers coincide; the centers are the vertices of an equilateral triangle with sides 5.5 . The first situation would answer the original question positively, the second one – negatively. Only if the distance was less than or equaled 5 could we guarantee the positive answer.

Remember that, in Data Sufficiency questions, it is not necessary to solve the problem, it is only necessary to establish whether or not we have sufficient information to do so.

Since Statement (1) is sufficient, and Statement (2) is not, the correct answer is A.

Similar questions to practice:
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Hope it helps.

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