few tricky questions on divisibility

Today's concept...few tricky questions on divisibility


concepts...


a^n - b^n is always divisible by a-b

a^n - b^n is divisible by a+b when n is even.

a^n + b ^n is divisible by a+b when n is odd.

a^n + b^n + c^n +... is divisible by a+b+c+.... when n is odd.

when last n digits of a no. are divided by 2^n, the remainder is same as the remainder when the entire no. is divided by 2^n.





Answers to yesterday's questions.

1. smallest no. that must be added to 1000 so that the resultant no. leaves remainders 2,3,4,5 with 5,6,7,11 respectivelt----667

2. smallest no. that leaves remainders 1,2,5,6, when divided successively by 2,3,4,23.----such a no. doesnt exist as 5 rem with aint possible.

3. smallest no. that leaves remainders 4 everytime when successively divided by 7,5,10,13 respectively.----872

4. a no. leaves remainders 2,5,3,7 when successively divided by 3,7,6,9. what is the remainder when this no. is divided by 126?----80

5.find the largest no. that leaves same remainder when it divides 2345,7645,9845,6595 and 10095.----50

6.a no. when divided 88 leaves remainder 3. what is the remainder when its divided by 11? ----3

7.a no. when divided by 391 leaves rem. of 49. find the remainder when its divided by 39...options 29,10,none of these,cannot be determined.---cannot be detrmnd

kudos to rockeezee who got most of them right!



questions for today...

1. 32^23 + 17^23 is definetly divisible by....

a. 49 b. 15 c. 49 & 15 d. none of these.


2. 32^23 - 17^23 is definetly divisible by....

a. 49 b. 15 c. 49 & 15 d. none of these.


3. 32^232 + 17^232 is definetly divisible by....

a. 49 b. 15 c. 49 & 15 d. none of these.


4. 32^232 - 17^232 is definetly divisible by....

a. 49 b. 15 c. 49 & 15 d. none of these.


5. 32^2321 + 17^2321 + 13^2321 + 18^2321 is definetly divisible by....

a. 40 b. 20 c. 80 d. all of these. e. none of these.


what is the remainder when 42527152653425416242624272427215287 is divided by :

6. 16

7. 32

8. 64