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JEE Main 2019 · 10 Jan · Shift I

JEE Main 2019 Mathematics question on Sequences and Series

The sum of all two digit positive numbers which when divided by 7 yield 2 or 5 as remainder is
  1. A.
    1256
  2. B.
    1465
  3. C.
    1356
  4. D.
    1365
Show answer and solution

Correct option: C

Solution

Numbers leaving remainder 2 when divided by 7: 16, 23, 30, ..., 93
First term 16, last term 93, common difference 7
Count = (93-16)/7 + 1 = 12
Sum = (12/2)(16+93) = 6 × 109 = 654

Numbers leaving remainder 5 when divided by 7: 12, 19, 26, ..., 96
First term 12, last term 96, common difference 7
Count = (96-12)/7 + 1 = 13
Sum = (13/2)(12+96) = (13/2)(108) = 702

Total = 654 + 702 = 1356

[JEE Main 2019 · 10 Jan · Shift I]

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