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CAT 1999 | Question: 87

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Answer the question based on the following information.
A rectangle PRSU, is divided into two smaller rectangles PQTU, and QRST by the line TQ. PQ $= 10$ cm. QR $= 5$ cm and RS $= 10$ cm. Points A, B, F are within rectangle PQTU, and points C, D, E are within the rectangle QRST. The closest pair of points among the pairs (A, C), (A, D), (A, E), (F, C), (F, D), (F, E), (B, C), (B, D), (B, E) are $10 \sqrt{3}$ cm apart.
Which of the following statements is necessarily true?

  1. The closest pair of points among the six given points cannot be (F, C)
  2. Distance between A and B is greater than that between F and C.
  3. The closest pair of points among the six given points is (C, D), (D, E), or (C, E).
  4. None of the above

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