Question:
The sum of all two digit positive numbers which when divided by 7 yield 2 or 5 as remainder is -
The sum of all two digit positive numbers which when divided by 7 yield 2 or 5 as remainder is -
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Two arithmetic progressions with common difference 7: remainder 2 and remainder 5.
Updated On: Nov 5, 2026
- 1356
- 1256
- 1365
- 1465
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The Correct Option is A
Solution and Explanation
Remainder 2: \(16,23,\ldots,93\): \(n=\frac{93-16}{7}+1=12\); sum \(=\frac{12}{2}(16+93)=654\).
Remainder 5: \(12,19,\ldots,96\): \(n=\frac{96-12}{7}+1=13\); sum \(=\frac{13}{2}(12+96)=702\).
Total \(=654+702=1356\).
Answer: (1) 1356
Remainder 5: \(12,19,\ldots,96\): \(n=\frac{96-12}{7}+1=13\); sum \(=\frac{13}{2}(12+96)=702\).
Total \(=654+702=1356\).
Answer: (1) 1356
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