A symmetric number of an another one is a number where the

Should be 9 because the difference will always be a multiple of 9.

For example,

xyz = 100x+10y+z
zyx= 100z+10y+x

(zyx) - (xyz) = 99(z-x)

which si always divisible by 9 or 11. Therefore the answer choice is E.

I like your solution as it taught me a new way of doing this problem. But I tried another way and was wondering if I am correct in my approach.

Can we not use the divisibility property of nine here? Any number is divisible by nine if the sum of its digits is equal to nine. A number symmetrical to the original number will still have the sum of its digit equal to nine. Hence, 9 is the answer.

Hi Forsaken...i guess you are assuming here that the digits taken as example are delebrately taken which are already divisble by 9...

As usual Brunel's explanation is really awasome and teaches new ways...

For example lets take 21 and its reverse is 12....and we are asking if the difference between them is divisble by 9....indeed it is..but if you observe the numbers 21 and 12 are not divisble by 9..

hopefully this answers your question
[/quote]Can we not use the divisibility property of nine here? [/quote]
that we cannot assume it that way

for this question, we could also quickly pick 2 numbers and see what we get. 100 & 1 => diff of 99, 20 & 2=> diff of 18, 9 is the largest common number.

i am totally agree with your solution but the question is asking about "the number and difference must be divisible".
can you please expleain

The questions asks: the difference of a number and its symmetrical must be divisible by which of the following...

Hi All,

This question is actually based on a 'math truism' of a sort. If you've ever taken an accounting class, then you might have learned about "transpositional errors" - errors that happen when you put the same digits in the wrong "order." While this question focuses on symmetrical numbers, the issue is exactly the same and works in any variation.

Putting a set of digits in a different order will ALWAYS lead to a difference that is divisible by 9.

23 and 32 is a difference of 9, which is divisible by 9
147 and 714 is a difference of 567, which is divisible by 9
34567 and 56374 is a difference of 21,807 which is divisible by 9

It goes to show that some of the concepts that you're going to learn for the GMAT have some value even after you're done with the Test.

GMAT assassins aren't born, they're made,
Rich

Dear Moderator,
Found this " Arithmetic" question under " work/rate problems ", hope you will look into this. Thank you.

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Fixed. Thank you.