Question

How many numbers are there from 1 to 1000 which when successively divided by 5, 6, 7 give remainders 2, 4, 5.

• A. 1
• B. 3
• C. 4
• D. 6

Answer 1

The correct option is C 4

The first number in this AP can be found as given below.

The first term $=\left(\right(\left(\right(5\times 6)+4)\times 5)+2)$

Common difference $=5\times 6\times 7=210$

General form of the AP is therefore $172+210k,$

So the numbers will be 172, 382, 592 and 802.