Question 26

Mathematics Circle Hard

There are n equally spaced points 1, 2, ...... n marked on the circumference of a circle. If the point 15 is directly opposite to the point 49, then the total number of points is

(A) 50
(B) 68
(C) 66
(D) 70
✓ Correct Answer: Option B Verified Solution

📘 Step-by-Step Solution & Detailed Explanation:

\[ \text{Consider } n \text{ equally spaced points } 1, 2, \dots, 12 \text{ marked on the circumference of a circle.} \] \[ \text{Number of points on Right side} = (\text{Difference of directly opposite points}) - 1 \] \[ = (12-6)-1 = 5 \] \[ \text{Number of points on Left side} = (\text{Difference of directly opposite points}) - 1 \] \[ = (12-6)-1 = 5 \] \[ \text{Total number of points} = \text{Right side points} + \text{Left side points} + \text{Directly opposite points} \] \[ = 5 + 5 + 2 = 12 \text{ points} \] \[ \text{Calculation:} \] \[ \text{Directly opposite points are } 49 \text{ and } 15. \] \[ \text{Difference of directly opposite points} = 49 - 15 = 34 \] \[ \text{Number of points on Right side} = 34 - 1 = 33 \] \[ \text{Number of points on Left side} = 34 - 1 = 33 \] \[ \text{Total number of points} = 33 + 33 + 2 = 68 \]

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