Passage

Direction for the following 3 (three) items : Consider the given information and answer the three items that follow. Six boxes A, B, C, D, E and F have been painted with six different colours viz., violet, indigo, blue, green, yellow and orange and arranged from left to right (not necessarily either kept or painted with the colours in the same order). Each box contains a ball of any one of the following six games: cricket, hockey, tennis, golf, football and volleyball (not necessarily in the same order). The golf ball is in violet box and is not in the box D. The box A which contains tennis ball is orange in colour and is at the extreme right. The hockey ball is neither in box D nor in box E. The box C having cricket ball is painted green. The hockey ball is neither in the box painted blue nor in the box painted yellow. The box C is fifth from right and next to box B. The box B contains volleyball. The box containing the hockey ball is between the boxes containing golf ball and volleyball.

Which of the following statements is/are correct ?

(a) D is painted yellow
(b) F is painted indigo ✓ UPSC's answer
(c) B is painted blue
(d) All of the above

Why the answer is (b)

• Balls known directly: A has tennis, C has cricket, B has volleyball; so hockey, golf and football are in D, E and F.

• Hockey is in neither D nor E, so hockey is in F.

• Golf is not in D, so golf is in E, leaving football in D.

• Colours: A orange, C green; golf is in the violet box, so E is violet.

• Hockey's box (F) is neither blue nor yellow, so F is indigo; B and D share blue and yellow, and nothing decides which is which.

• Only 'F is painted indigo' must be true; D yellow and B blue are merely possible.

• Hence option (b).

Why the other options are wrong

(a) D is painted yellow: While D is either Blue or Yellow, there is no information to definitively assign Yellow to D over Blue, making this statement not necessarily correct.
(c) B is painted blue: While B is either Blue or Yellow, there is no information to definitively assign Blue to B over Yellow, making this statement not necessarily correct.
(d) All of the above: Since statements (a) and (c) are not definitively proven by the constraints, 'All of the above' is incorrect.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2016, held on 7 August 2016. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.