Replace the interrogation marks in the following statements by appropriate digits (0 to 9) to make these statements valid:

D1: 34?561? is exactly divisible by 45
D2: 68??37 is exactly divisible by 99
D3: 9???057 is equal to 417 times ?1???
D3: 70??34? is exactly divisible by 792
D4: 4?18? is exactly divisible by 101
D5: 6?80?8??51 is exactly divisible by 73*137

710ab34c is exactly divisible by 792

792=8*99

34c is divisible by 8 so c=4

a+b=9 to permit divisibility by 9

7+a+3+4-0-b-4=0 mod11 to permit divisibility by 11

a-b=1mod11 so a=5, b=4

 

Posted by xdog on 2011-06-06 19:37:45