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)
• 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.