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integer problem

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by gopinathhyd » Sun Mar 18, 2012 6:12 am
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.


(Can any one suggest me good material for practice, which has more venn diagrams and tables.)
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by pemdas » Sun Mar 18, 2012 2:19 pm
(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.
Last edited by pemdas on Sun Mar 18, 2012 2:29 pm, edited 1 time in total.
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by seal4913 » Sun Mar 18, 2012 2:28 pm
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
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by pemdas » Sun Mar 18, 2012 2:30 pm
just updated: three different divisors 0,99,-99
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by [email protected] » Wed Mar 21, 2012 11:24 pm
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...
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by [email protected] » Wed Mar 21, 2012 11:25 pm
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...
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