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Dhruva • 4.38K Points
Extraordinary Math 

Q. The greatest number for four digits which when divided by 12, 16 and 24 leave remainder 2,6 and 14 respectively is = ?

  • (A) 9974
  • (B) 9970
  • (C) 9807
  • (D) 9998
Correct Answer - Option(A)
Explanation by: Dhruva 
12 - 2 = 10
16 - 6 = 10
24 - 14 = 10
LCM of (12, 16, 24) = 6 × 2 × 4 × 1 = 48
Greatest number of four digits = 9999
∴ When it is divided by 48 we get remainder = 15
⇒ The greatest number of 4 digits which completely divides the given number is = 9999 - 15 = 9984
∴ Number is = 9984 - 10 = 9974

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