Elitmus
Exam
Numerical Ability
Number System
Find numbers of n for which (100^n- (112^2)) divisible by 3?
Read Solution (Total 24)
-
- The min value of n have to be 3... So have to be => 3...
- 10 years agoHelpfull: Yes(15) No(2)
- least value be 3
expl=when n=3
x=1000000
112^2=12544
so y=1000000-12544 = 987456
divisiblity rule for 3 is 9+8+7+4+5+6=39
987456 is divisible be 3 - 10 years agoHelpfull: Yes(9) No(3)
- Least value will be n=6
let x = ((100^n)-(112^2))
As 1oo^6 = 1000000000000
And 112^2 = 12544
therefore
x = 1000000000000 - 12544
=> x =999999987546
now to check whether number is divisible by 3 , check whether summation of its digits is divisible by 3 or not
as 9+9+9+9+9+9+9+8+7+5+4+6 is equal to 93
so, 999999987546 is divisible by 3.
like wise for each n>=6,
number will be divisible by 3
but least value will be 6.
After subtraction - 10 years agoHelpfull: Yes(4) No(2)
- 2,3,4,5,6,7,8,9,........................(from 2 all positive integer)
- 10 years agoHelpfull: Yes(3) No(4)
- all positive numbers...1,2,3.........
- 10 years agoHelpfull: Yes(3) No(8)
- n value should be 3 and above.......as we subtract 1000000-12544...only then we get positive answer....
- 10 years agoHelpfull: Yes(3) No(0)
- nd 1 more conditon n
- 10 years agoHelpfull: Yes(1) No(1)
- n is greater than 6 (n>6)
options;-
a. 6
b.17
c.16
d.8 - 10 years agoHelpfull: Yes(1) No(0)
- If n=1 100^1/3=Reminder is 3
if 3/3=1
then 1-(112^2)/3=1-(1/3)
=1-1=0
IF n=2 then
(100^2-(112^2)=(1^2)-(1^2)=1-1=0
Then we can clearly say then N =Any Positive Integer number.....
Ans:=1,2,3,..............................................+Infinity - 10 years agoHelpfull: Yes(1) No(0)
- hey how to post a question here in e litmus page of m4 maths
- 10 years agoHelpfull: Yes(0) No(0)
- Given n
- 10 years agoHelpfull: Yes(0) No(0)
- Given n
- 10 years agoHelpfull: Yes(0) No(0)
- here question is 100^n-112^2 is positive and n
- 10 years agoHelpfull: Yes(0) No(0)
- this question is incomplete ....
- 10 years agoHelpfull: Yes(0) No(0)
- for all positive numbers from 1,2,3...............of n
- 10 years agoHelpfull: Yes(0) No(0)
- n can be anything....because
consider it (100)^n/3-112^2/3 then
(99+1)^n/3 gives modules 1
112^2/3 gives modules 1
so 1^n-1 wil gives 0...
so n value can be any postive integer - 10 years agoHelpfull: Yes(0) No(0)
- the condition will satisfy for all n>=3
- 10 years agoHelpfull: Yes(0) No(1)
- 112^2=12544 100^3=1000000-12544=987456 add all digit 9+8+7+4+5+6=39 and 39 is divisible by 3 so n=3
- 10 years agoHelpfull: Yes(0) No(0)
- any no greater or equal to 1 here it is not given in question that number should positive.
- 9 years agoHelpfull: Yes(0) No(0)
- It is not necessary for the result of subtraction to be +ve . Even -ve nos are divisible by 3
So for n = 1
100 - 12544 = 12444 is divisible by 3
Hence for n = 1,2 3, 4,..... - 9 years agoHelpfull: Yes(0) No(0)
- for all values of n=0,1,2,3,...
because its not mentioned that the answer must be +ve - 9 years agoHelpfull: Yes(0) No(0)
- given number = 3
let n=3
then 100 pow 3 = 1000000
x=1000000
112 pow 3 = 12544
now
x= 1000000-12544
we get 987456
now divisibility rule of 3
9+8+7+4+5+6=39 and 39 vl be divisible by 3
so 987456 will be divisible by 3
- 9 years agoHelpfull: Yes(0) No(0)
- n=3 becoz 112^2=12544 and 1000000-12544=987456 which is divisible to 3
- 8 years agoHelpfull: Yes(0) No(0)
- 112^2/3 will give remainder 1 ad 100/3 remainder 1/3 so 1^n/3 always gives remainder 1 so
1-1=0 n=1,2,3... but we cant take 1 and 2 because i ll become negative thats y
n>=3 - 7 years agoHelpfull: Yes(0) No(0)
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