What is the reflex angle between the hour hand and the minute hand of a clock at 11:35?

Introduction / Context:
This question focuses on finding the reflex angle between the hour and minute hands of a clock at 11:35. Unlike many clock angle problems that ask for the smaller interior angle, this one specifically asks for the reflex angle, which is the larger angle obtained by going the long way around the circle. Understanding the difference between the smaller angle and the reflex angle is important for accurately answering such problems in competitive exams and logical reasoning tests.

Given Data / Assumptions:

- The time is 11:35. - One full circle on the clock face is 360 degrees. - The minute hand moves 6 degrees per minute. - The hour hand moves 0.5 degrees per minute. - The reflex angle is defined as the larger of the two possible angles between the hands.

Concept / Approach:
To find the angle between the hands, we first compute the positions of the hour hand and the minute hand from the 12 o clock position. The minute hand position is straightforward, while the hour hand position accounts for both the hour and the extra minutes. The smaller angle is the absolute difference between these two positions. The reflex angle is then obtained by subtracting this smaller angle from 360 degrees. Our answer must match one of the given choices and be clearly labeled as the reflex angle.

Step-by-Step Solution:
Step 1: At 11:35, the minute hand is at 35 minutes. Step 2: Angle of the minute hand from 12 is 35 * 6 = 210 degrees. Step 3: At 11:00, the hour hand is at 11 * 30 = 330 degrees. Step 4: In 35 minutes, the hour hand moves an additional 35 * 0.5 = 17.5 degrees. Step 5: Therefore, the hour hand angle from 12 at 11:35 is 330 + 17.5 = 347.5 degrees. Step 6: The smaller angle between the hands is |347.5 - 210| = 137.5 degrees. Step 7: The reflex angle is the larger angle, which is 360 - 137.5 = 222.5 degrees.

Verification / Alternative check:
We can check for consistency by visualizing the clock. At 11:35, the minute hand is a little past the 7 mark on the dial, and the hour hand is near but just short of 12. The angle between them if we go the short way is clearly less than 180 degrees, making 137.5 degrees a plausible smaller angle. Subtracting this from 360 degrees gives 222.5 degrees, a reflex angle larger than 180 degrees. This matches one of the options and correctly represents the angle going around the longer side of the dial.

Why Other Options Are Wrong:
137.5 degrees is the smaller angle, not the reflex angle requested by the problem. Values like 192.5 degrees and 330 degrees do not match either the direct difference or 360 minus the difference obtained from the correct hand positions. A value of exactly 180 degrees would mean the hands are in a straight line opposite each other, which does not occur at 11:35. Therefore, only 222.5 degrees is consistent with the definition of the reflex angle at this time.

Common Pitfalls:
One common error is to compute only the smaller angle and then select it without noticing that the question specifies reflex angle. Another pitfall is miscalculating the hour hand position by forgetting that it moves continuously during the 35 minutes after 11:00. Carefully multiplying the minutes by 0.5 degrees and then adding to the base hour position prevents these mistakes. Always double check whether the question wants the smaller angle or the reflex angle before choosing the answer.

Final Answer:
The reflex angle between the clock hands at 11:35 is 222.5 degrees.