integer problem

(100A+10B+C-100C-10B-A) is divisible by 7. Hence (99A-99C) is divisible by 7 or 99(A-C) is divisible by 7. The possibilities are A=9 and C=2 along with C=9 and A=2 or A=8 and C=1 along with A=1 and C=8. There are four numbers and nine possibilities for(A-C) turning into 0, i.e. 4+9=13 possibilities.
With (A-C)=0 we have one divisor (factor) and with (A-C)=2 we may have the following options: 9B2-2B9=693 has one factor 99. The same with every other number, e.g. 2B9-9B2=-693 has one factor -99. Hence total makes (4+1)=5 divisors (factors) out of which only 3 divisors will be different 0,99,-99

gopinathhyd wrote:1. If A, B and C are all positive integers. and three digit number ABC - CBA is divisible by 7. How many different numbers are possible divisors for 7.

pemdas wrote:(100A+10B+C-100C-10B-A) is divisible by 7. Hence (99A-99C) is divisible by 7 or 99(A-C) is divisible by 7. The possibilities are A=9 and C=2 along with C=9 and A=2 or A=8 and C=1 along with A=1 and C=8. There are four numbers and nine possibilities for(A-C) turning into 0, i.e. 4+9=13 possibilities.

gopinathhyd wrote:1. If A, B and C are all positive integers. and three digit number ABC - CBA is divisible by 7. How many different numbers are possible divisors for 7.

I understand the 4 different numbers and I understand the 9 possiblities that give 0 but what does the zeros have to do with being divisible by 7? So I dont understand why its not just 4 but 13

just updated: three different divisors 0,99,-99

1. If A, B and C are all positive integers. and three digit number ABC - CBA is divisible by 7. How many different numbers are possible divisors for 7.

I reached till this step: 99 X (A - C)/7

this means that (A-C) has to be divisible by 7 as 99 is not divisible by 7

Hence 7 is a factor of (A - C).

Also A-C can be any number multiple of 7...

I did not understand beyond this step....

Guyzzz kindly help...

gopinathhyd!! please post the question properly with all the options just as the question is presented in the test...

We all are seriously studying these sums with the timer...

Thank You...