A number when divided by 3,4,5,6,7 gives remainders 2,3,4,5,6 respectively. The

Question

A number when divided by 3,4,5,6,7 gives remainders 2,3,4,5,6 respectively. The smallest such 5 digit number is?

Options:

A . 10019

B . 10076

C . 11079

D . 10079

Answer: Option D
:
D
Take the LCM of the numbers 3,4,5,6,7. First number to satisfy the given conditions will be LCM-1 = 420-1 = 419
Numbers will fall in an AP with a common difference = LCM

2^{n d}

number = 419+420 = 839

3^{r d}

= 839+420 = 1259 and so on.
First 5 digit number = 10080-1 = 10079.

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