Let X be the least number divisible by 13 such that when X divided by 4, 5, 6, 7, 8, and 12 the remainder in each case is 2. Sum of the digits of X is?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 11
| Application |
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x = K × LCM(4,5,6,7,8,12) + 2 Here the value of k is decided such that the resultant number is divisible by 13. We will first evaluate LCM(4,5,6,7,8,12) So LCM (4,5,6,7,8,12) = 840 Hence , x = 840k + 2 By hit & trial, find the value of k such that the resultant number is divisible by 13. Put k = 3 x = 840 × 3 = 2522 + 2, which is divisible by 13 So sum of digits of 2522 = 2 + 5 + 2 + 2 = 11 |