enigma123 wrote:

10^25 – 560 is divisible by all of the following EXCEPT:

a)11

b)8

c)5

d)4

e) 3

Guys any idea what concept has been Tested over here and what will be the answer?

I have started doing it this way but got stuck. So can someone please help?

I have started from

10^5 - 560 = 99,440 i.e. it has two 9s followed by 440.

.

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10^10 - 560 = 99,99,440 ------------------------------> Am I doing it right this way?

Yes, you were on a right track.

10^(25) is a 26 digit number: 1 with 25 zeros. 10^(25)-560 will be 25 digit number: 22 9's and 440 in the end: 9,999,999,999,999,999,999,999,440 (you don't really need to write down the number to get the final answer). From this point you can spot that all 9's add up to some multiple of 3 (naturally) and 440 add up to 8 which is not a multiple of 3. So, the sum of all the digits is not divisible by 3 which means that the number itself is not divisible by 3.

Answer: E.

You can also quickly spot that the given number is definitely divisible:

By 2 as the last digit is even;

By 4 as the last two digits are divisible by 4;

By 8 as the last three digits are divisible by 8;

By 11 as 11 99's as well as 440 have no reminder upon division by 11 (or by applying divisibility by 11 rule).

Check Divisibility Rules chapter of Number Theory:

math-number-theory-88376.htmlThank you Bunuel. I used this tactic after seeing you reference it in other posts. I learned this before but had not committed it to memory until now. Great explanation as always