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jeev

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· 1 Months ago

regarding the least possible number for the given condition (Question:616884.0)

In the solution it is given that 586 is the least possible number for the given condition i.e. when divided by 7, 11 and 13 it should leave reminders 5,6 and 7 respectively.
But when 586 is divided by 11 and 13 reminders are 3 and 1 respectively. Can you please explain how the given condition satisfies here.

Question:
How many numbers lie between 100 and 10000 which when successively divided by 7, 11 and 13 leaves the respective remainders of 5, 6 and 7?
Options:
A) 5
B) 8
C) 10
D) None of these
Solution:
Ans (c) The least possible number can be obtained as

(((7x11)+6)7+5)=((77+6)7+5) 
=(83x7+5)=(581+ 5)=586
The general form for the higher numbers is 
(7x11 x13)m + 586=(1001)m + 586 
So, the numbers can be obtained by considering m= 0, 1, 2, 3... so the first number is 586 and the last number is 9595 which can be attained at m = 9. So there are total 10 such numbers lying between 100 and 10000.

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