Question

(10^25)-7 is divisible by

a) 2 b)3 c)9 d) both 2 & 3

Answer 1

b) 3

Answer 2

this will be and odd so wont be divisible by 2
it will consist of 24 9's and end in 3
so it is divisible by 3

Answer 3

please explain i can't understand

Answer 4

10^2 - 7 = 100 - 7 = 93 one 1 nine followed by 3
10^3 - 7 = 1000 - 7 = 993 2 nines followed by 3
10^4 - 7 = 10000 - 7 = 9993 3 nines followed by 3

following the above pattern we find that 10^25 - 7 will have 24 nines with 3 at the end

so it will be an odd no so 2 is ruled out
so a) 2 and d) both 2 & 3 are ruled out

for 3 and 9 we have to find sum of all the digits
it will b (9x24) + 3 = 219 and 219 is only divisible by 3 and not by 9
so correct ans is b)3


hope it is clear now ☺

Answer 5

10^25-7=(10^25-1)-6
the no 10^25-1 =999.....99 (25 digits) is divisible by 3 & 9
therefore (10^25-1)-6=(24 nines & unit digit is 3) i.e. 999......93
this number is only divisible by 3.