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:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 11
LCM of 4, 5, 6, 7, 8, and 12 = 840
so the number = 840k + 2, which is divisible by 13.
now,
if k = 1 ⇒ number = 842, not divisible by 13
if k = 2 ⇒ number = 1682, not divisible by 13
if k = 3 ⇒ number = 2522, divisible by 13
⇒ sum of digits = 2 + 5 + 2 + 2 = 11