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?

Answer 1

Answer:

10 Number exists

586 , 1587 , 2588  , 3589 , 4590 , 5591 , 6592 , 7593 , 8594 , 9595

Step-by-step explanation:

Let say  Number = A

A  = 7B  + 5  

B  = 11C + 6  

C = 13D + 7  

B = 11 (13D + 7) + 6 = 143D + 83

A = 7(143D + 83) + 5  = 1001D + 586

Number = 1001D + 586

  100 < 1001D + 586  < 10000

=> -486 < 1001D  < 9414

=>   0 ≤ D ≤ 9

Total numbers of D = 10  ( 0 to 9)

So such 10 Number exists

586 , 1587 , 2588  , 3589 , 4590 , 5591 , 6592 , 7593 , 8594 , 9595