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CAT 1999 — QA Question 25

Basics of QuadrilateralsEasy
Passage / Data

Directions : Answer the questions 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 103 cm apart.

AB > AF > BF ; CD > DE >CE ; and BF = 65 cm. Which is the closest pair of points among all the six given points?

Answer & solution

  • A

    B, F

  • B

    C, D

  • C

    A, B

  • None of these

Solution

The maximum possible distance between the pairs (C,D), (D,E) or (C, E) is the length of the diagonal of the rectangle QRST, i.e. 102+52=55 cm.

Since AB > AF > BF = 65 cm, the closest pair of points of the given six points will be from the set (C, D, E). As CD > DE > CE, so (C, E) will be the pair of closest points.
*Note: There is slight inconsistency regarding the information given in the question. If BF = 65 ≈ 13.4 cm, then A, B and F cannot be close to the same vertex as the length of the diagonal of rectangle PQTU is 14 cm approximately. This in turn will contradict the fact the minimum distance between any point of A, B, F and the other from C, D, E is 103 cm.

A likely possibility is that the information regarding minimum distance between any point of (A, B, F) and the other from (C, D, E) is specific to previous question only.

Hence, option (d).

CAT 1999 QA Q25: AB > AF > BF ; CD > DE >CE ; and BF = 6 5 cm. Which is the closest pair of points among all the six given poin — Solution | TheCATExam