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Problem 17 - Entrance Test

A man is facing North-West. He turns 90 degrees in the clockwise direction, then 180 degrees in the anti-clockwise direction, and then another 90 degrees in the same (anti-clockwise) direction. In which direction is he facing now?

Correct: C

Let's use degrees clockwise from North (0 degrees). North-West = 315 degrees. 1. Turns 90 degrees clockwise: 315 + 90 = 405 degrees. Since a full circle is 360 degrees, 405 - 360 = 45 degrees. (This is North-East). 2. Turns 180 degrees anti-clockwise: 45 - 180 = -135 degrees. Adding 360 to get a positive angle: -135 + 360 = 225 degrees. (This is South-West). 3. Turns another 90 degrees in the same (anti-clockwise) direction: 225 - 90 = 135 degrees. 135 degrees corresponds to South-East.