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      Question

      Find the sum of all the numbers between 2150 and 3780

      which are divisible by 9 as well as 6.
      A 265410 Correct Answer Incorrect Answer
      B 266490 Correct Answer Incorrect Answer
      C 269100 Correct Answer Incorrect Answer
      D 271260 Correct Answer Incorrect Answer

      Solution

      For a number to be divisible by 9 as well as 6, it must be divisible by 18. So, the numbers between 2150 and 3780 which are divisible by 18 are 2160, 2178, ......., 3762, which forms AP with common difference = 18 To find the number of terms in AP, we have formula = an = a + (n – 1) × d So, n = (an – a)/d + 1 Therefore, total number of terms between 2150 and 3780 which are divisible by 18 = (3762 – 2160)/18 + 1 = 89 + 1 = 90 Sum of AP formula = n/2 × [a + l], where a and l are first and last term, respectively Desired sum = 90/2 × (2160 + 3762) = 45 × 5922 = 266490

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