Chameli observed that the two hands of a clock were making 110° with each other when she started taking the test. The moment she completed the test, she observed that the angle between the two hands of the clock was still 110° but in a different orientation. Which of the following times (in minutes) cannot be the duration for which she took the test?

The minute hand must move into a new orientation that creates the same 110 degree angle on the opposite side of the clock, meaning it effectively travels 220 degrees or a multiple of 360 plus 220 degrees. Dividing 220 degrees by the minute hand speed of 6 degrees per minute gives 36.66 minutes; similarly, adding 360 degrees gives 416.66 degrees which takes 69.45 minutes, and adding another 360 degrees gives 776.66 degrees which takes 129.45 minutes. The duration 45.45 minutes does not fit this progression, so it cannot be the duration of the test.

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