UPSC Prelims 2016 CSAT Paper II · Q36 of 79 Comprehension easy

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 ?

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

Why the answer is (c)

• Box A is at the extreme right (Position 6), is Orange, and contains Tennis.

• Box C is 5th from the right (Position 2), is Green, and contains Cricket.

• Box C is next to Box B, so Box B is at Position 1 or 3. Since Box B contains Volleyball, and the Hockey ball is between Golf and Volleyball, we must determine the positions.

• The Golf ball is in the Violet box and is not in Box D. The Hockey ball is not in Box D or E, nor in Blue or Yellow boxes.

• Arranging the sequence: If B is at 1, C is at 2. Hockey is between Golf and Volleyball (B). This implies Golf is at 3. So, Pos 1: B (Volleyball), Pos 2: C (Cricket, Green), Pos 3: Golf (Violet). The box with Golf (Pos 3) is Violet. The box with Hockey is between Golf (Pos 3) and Volleyball (Pos 1), so Hockey is at Pos 2? No, C is at Pos 2 with Cricket. Contradiction. Thus, B cannot be at 1.

• Therefore, Box B is at Position 3. Box C is at Position 2. Box B (Pos 3) has Volleyball. Hockey is between Golf and Volleyball (Pos 3). So Hockey is at Pos 2 or 4. But Pos 2 is C (Cricket). So Hockey must be at Pos 4. This means Golf is at Pos 5. So, Pos 5 has Golf (Violet). Pos 4 has Hockey. Pos 3 is B (Volleyball). Pos 2 is C (Cricket, Green). Pos 6 is A (Tennis, Orange).

• Remaining boxes: D and E are at Pos 1 and Pos 4? No, Pos 4 has Hockey. We know Hockey is not in D or E. So Pos 4 cannot be D or E. Thus Pos 4 must be F. So F is at Pos 4 (Hockey). D and E are at Pos 1 and Pos 5? No, Pos 5 is Golf (Violet). We know Golf is not in D. So Pos 5 is not D. Thus Pos 5 is E. So E is at Pos 5 (Golf, Violet). Then D is at Pos 1.

• Current Status: Pos 1: D, Pos 2: C (Green, Cricket), Pos 3: B (Volleyball), Pos 4: F (Hockey), Pos 5: E (Violet, Golf), Pos 6: A (Orange, Tennis).

• Colors assigned: C=Green, E=Violet, A=Orange. Remaining colors: Indigo, Blue, Yellow for D, B, F.

• Hockey (F, Pos 4) is not in Blue or Yellow. So F must be Indigo.

• Remaining colors for D (Pos 1) and B (Pos 3): Blue and Yellow.

• The remaining ball is Football. It must be in D or B.

• We do not have information to distinguish which of D or B is Blue or Yellow, nor which contains Football. The constraints on Blue/Yellow only apply to Hockey (which is in F). There is no constraint linking Football to a specific color or box among D and B.

• Therefore, the color of the box containing Football cannot be determined.

Why the other options are wrong

(a) Yellow
The football could be in the box painted Blue or Yellow, as the specific assignment of these colors to boxes D and B is not fixed by the given constraints.
(b) Indigo
The football could be in the box painted Blue or Yellow, as the specific assignment of these colors to boxes D and B is not fixed by the given constraints.
(d) Blue
The football could be in the box painted Blue or Yellow, as the specific assignment of these colors to boxes D and B is not fixed by the given constraints.

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.

Reading the answer is not the same as getting it right under a clock. Practise this question with UPSC's negative marking, and anything you miss goes into an error notebook until you get it right twice.

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