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Q: Suppose x be the least number which when divided by 15, 18, 20 and 27, the remainder in each case is 10 and x is a multiple of 31. What least number should be added to x to make it a perfect square?
  • A. 36
  • B. 39
  • C. 37
  • D. 43
Correct Answer: Option B - ∵ LCM of 15, 18, 20, 27 = 540 ∴ x = (540 K + 10) On putting K = 4, x = 540  4 + 10 = 2170 Hence, it's nearest square = 47  47 = 2209 ∴ The number to be added to make x a perfect square = 2209–2170 = 39
B. ∵ LCM of 15, 18, 20, 27 = 540 ∴ x = (540 K + 10) On putting K = 4, x = 540  4 + 10 = 2170 Hence, it's nearest square = 47  47 = 2209 ∴ The number to be added to make x a perfect square = 2209–2170 = 39

Explanations:

∵ LCM of 15, 18, 20, 27 = 540 ∴ x = (540 K + 10) On putting K = 4, x = 540  4 + 10 = 2170 Hence, it's nearest square = 47  47 = 2209 ∴ The number to be added to make x a perfect square = 2209–2170 = 39