Multiple choice

Let x be the greatest number of 4 digits which when divided by 15, 20 and 28 leaves, in each case, the remainder 2. The sum of digits of x is

  1. 19

  2. 21

  3. 23

  4. 25
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C Correct answer
Explanation

The LCM of 15, 20, 28 is 420. The greatest 4-digit number is 9999. Dividing 9999 by 420 gives a quotient of 23 and remainder 339. The number x is 420 * 23 + 2 = 9662. The sum of digits is 9 + 6 + 6 + 2 = 23.

AI explanation

We first find the least common multiple of 15, 20, and 28, which is 420. The greatest 4-digit number is 9999, and dividing it by 420 gives a quotient of 23 and a remainder of 339. Subtracting the remainder gives 9660, and adding the required remainder of 2 gives 9662. The sum of the digits of 9662 is 23.

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