Question : Let $x$ be the least number of 4 digits that when divided by 2, 3, 4, 5, 6 and 7 leaves a remainder of 1 in each case. If $x$ lies between 2000 and 2500, then what is the sum of the digits of $x$?
Option 1: 4
Option 2: 15
Option 3: 9
Option 4: 10
Correct Answer: 4
Solution :
LCM of 2, 3, 4, 5, 6 and 7 is 420. The number should be between 2000 and 2500. So, the number is = 420 × 5 = 2100 The remainder will be 1 in each case so the number = 2100 + 1 = 2101 Sum of digit of the number 2101 is = 2 + 1 + 0 + 1 = 4 Hence, the correct answer is 4.
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