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.

The football is in the box of which colour ?

(a) Yellow
(b) Indigo
(c) Cannot be determined as data are inadequate ✓ UPSC's answer
(d) Blue

Why the answer is (c)

• 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.

• Football is in D, whose colour is blue or yellow, so it cannot be fixed.

• Hence option (c).

Why the other options are wrong

(a) Yellow: D may be yellow or blue, so yellow is not certain.
(b) Indigo: Indigo is F's colour, and F holds hockey.
(d) Blue: D may be blue or yellow, so blue is not certain.

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.