IAS 2016 — CSAT Reasoning

Correct Option

The correct option is (3) Cannot be determined as data are inadequate.

The problem requires deducing the colour of the box containing the football. Let's systematically arrange the boxes, their contents, and colours based on the given clues:

1. Box A, containing the tennis ball and painted orange, is at the extreme right. This places A at Position 6.
2. Box C, containing the cricket ball and painted green, is fifth from the right, placing it at Position 2.
3. Box B contains the volleyball and is next to Box C. Since C is at Position 2, B must be at Position 1 (extreme left).
4. Current arrangement (from left to right): B (volleyball, ?), C (cricket, green), _, _, _, A (tennis, orange).
5. The hockey ball is neither in Box D nor Box E. This implies the hockey ball is in Box F.
6. The hockey ball is neither in the blue box nor the yellow box.
7. The golf ball is in the violet box and is not in Box D.
8. Combining points 5, 6, and 7: If Box F (hockey) were violet, it would contain the golf ball, which contradicts F containing the hockey ball. Therefore, Box F must be indigo and contains the hockey ball. (F: indigo, hockey).
9. The box containing the hockey ball (F) is between the boxes containing the golf ball and the volleyball (B). Since B (volleyball) is at Position 1, the sequence must be B, F, (Golf/violet box) from left to right.
10. Given C is at Position 2, F cannot be at Position 2. If F were at Position 5, the golf box would need to be to its right, but Position 6 is occupied by A. Thus, F cannot be at Position 5.
11. Therefore, Box F (indigo, hockey) must be at either Position 3 or Position 4.

Scenario 1: F is at Position 3

• Arrangement: B (volleyball, ?), C (cricket, green), F (hockey, indigo), _, _, A (tennis, orange).
• The golf ball (in violet box, not D) must be in Position 4 or 5.
• If the golf ball is at Position 4, it must be Box E (since not D) and be violet. Then Box D (football) is at Position 5.
• If the golf ball is at Position 5, it must be Box E (since not D) and be violet. Then Box D (football) is at Position 4.
• In both sub-scenarios, Box D contains the football. The remaining colours for Box B (volleyball) and Box D (football) are blue and yellow. It is not possible to uniquely assign blue or yellow to Box D.

Scenario 2: F is at Position 4

• Arrangement: B (volleyball, ?), C (cricket, green), _, F (hockey, indigo), _, A (tennis, orange).
• The golf ball (in violet box, not D) must be at Position 5.
• Therefore, Box E is at Position 5 (golf, violet).
• The remaining box, D, must be at Position 3 and contain the football.
• Arrangement: B (volleyball, ?), C (cricket, green), D (football, ?), F (hockey, indigo), E (golf, violet), A (tennis, orange).
• The remaining colours for Box B (volleyball) and Box D (football) are blue and yellow. It is not possible to uniquely assign blue or yellow to Box D.

In both valid scenarios, the colour of the box containing the football (Box D) cannot be uniquely determined, as it could be either blue or yellow. Hence, the data provided is inadequate.

Incorrect Options

Options (1) Yellow, (2) Indigo, and (4) Blue are incorrect because the available information does not definitively assign any single colour to the box containing the football. The deductions show that the box containing the football (Box D) could be either blue or yellow, depending on the final assignment of the remaining colours to Box B and Box D. Therefore, a unique colour cannot be determined.