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Q: Let x be the least number divisible by 13, such that when x is divided by 4,5,6,7,8 and 12, the remainder in each case is 2. The sum of the digits of x is:
  • A. 8
  • B. 10
  • C. 11
  • D. 9
Correct Answer: Option C - L.C.M of 4, 5, 6, 7, 8 and 12 · 840 Hence, x = 840 k + 2 ∵ The number is exactly divisible by 13. On putting k = 3, So the required number · 840 x 3 + 2 = 2522 ∴ Sum of digits = 2+5+2+2 = 11
C. L.C.M of 4, 5, 6, 7, 8 and 12 · 840 Hence, x = 840 k + 2 ∵ The number is exactly divisible by 13. On putting k = 3, So the required number · 840 x 3 + 2 = 2522 ∴ Sum of digits = 2+5+2+2 = 11

Explanations:

L.C.M of 4, 5, 6, 7, 8 and 12 · 840 Hence, x = 840 k + 2 ∵ The number is exactly divisible by 13. On putting k = 3, So the required number · 840 x 3 + 2 = 2522 ∴ Sum of digits = 2+5+2+2 = 11