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?
Show answer & explanation
Correct answer: D
Explanation
Correct Answer is option 4 i.e. 4
|
Understanding |
Application |
|
First, we need to find the LCM of 2, 3, 4, 5, 6 and 7 |
So, LCM = 2 × 3 × 2 × 5 × 7 = 420 |
|
The number ‘x’ will be in the form: 420a + 1 |
Since x lies between 2000 and 2500: Possible number of the form 420a + 1 will be = 420 × 5 + 1 = 2101 |
|
|
Hence, Sum of digits = 2 + 1 + 1 = 4 |