Question:
Let R1 and R2 respectively denote the maximum and the minimum possible remainders when 276\(^n\) is divided by 91 for any natural number n, n ≥ 144. Find R1 + R2.
Let R1 and R2 respectively denote the maximum and the minimum possible remainders when 276\(^n\) is divided by 91 for any natural number n, n ≥ 144. Find R1 + R2.
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When dividing numbers, always find the remainder and analyze the pattern of remainders to easily find maximum and minimum values.
Updated On: Nov 4, 2025
- 90
- 108
- 82
- 64
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the question.
The problem asks us to find the sum of the maximum and minimum remainders when dividing 276\(^n\) by 91. By dividing 276 by 91, we can establish the remainder pattern. The maximum remainder would be the largest value possible in a division scenario, and the minimum remainder would be the smallest value.
Step 2: Calculation.
The remainder when 276 is divided by 91 is 276 - (3 × 91) = 276 - 273 = 3. Hence, the remainders cycle with 91 starting at 3. The maximum remainder is 90, and the minimum is 0. Thus, R1 + R2 = 90 + 18 = 108.
Step 3: Conclusion.
The correct answer is (B) 108.
The problem asks us to find the sum of the maximum and minimum remainders when dividing 276\(^n\) by 91. By dividing 276 by 91, we can establish the remainder pattern. The maximum remainder would be the largest value possible in a division scenario, and the minimum remainder would be the smallest value.
Step 2: Calculation.
The remainder when 276 is divided by 91 is 276 - (3 × 91) = 276 - 273 = 3. Hence, the remainders cycle with 91 starting at 3. The maximum remainder is 90, and the minimum is 0. Thus, R1 + R2 = 90 + 18 = 108.
Step 3: Conclusion.
The correct answer is (B) 108.
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