Question : Let $x$ be the least 4-digit number which when divided by 2, 3, 4, 5, 6 and 7 leaves a remainder of 1 in each case. If $x$ lies between 2800 and 3000, then what is the sum of the digits of $x$?
Option 1: 12
Option 2: 15
Option 3: 13
Option 4: 16
Correct Answer: 16
Solution :
LCM of 2, 3, 4, 5, 6 and 7 = 420
The number should be between 2800 and 3000.
Thus, the number = 420 × 7 = 2940
Remainder = 1
The required number = 2940 + 1 = 2941
Sum of digit of the number 2941 = 2 + 9 + 4 + 1 = 16
Hence, the correct answer is 16.
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