Latest Elitmus Aptitude Question SOLUTION: X pow 100 = 31digit then find x pow 1000= how many digits

• Placement Papers
• /
• Elitmus
• /
• Numerical Ability
• /
• Number System

Elitmus Question Papers:

(#M40039347) ELITMUS Numerical Ability question no of digit Keep an EYE

X pow 100 = 31digit then find x pow 1000= how many digits

Asked In Elitmus Abhishek Mishra (9 years ago)

Unsolved Read Solution (11)

Is this Puzzle helpful?   (7)   (2) Submit Your Solution Number System

Read Solution (11) :

SUDHAKAR SRIVASTAVA  (9 years ago)

ans- 301

1- 10^1=2 digits

10^2=3 digits......anso on

thf: 10^30=31 digits

now...10^30=x^100

applying log both sides

30 log 10=100 log x

multiply both side by 10

300 log 10=1000 log x

again removing the log from both sides

10^300=x^1000

10^300=301 digits....

Is this solution Helpfull? Yes (40) | No (3)  

DILIP KUMAR YADAV  (9 years ago)

x^100=31 digit
we know that,
10^1=10
10^2=100,means three digits
10^3-1=3 digit
10^31-1=x^100
10^30=x^100
30 log10=100 logx
now,suppose that
10^y-1=x^1000
(y-1)log10=1000 logx
y-1=10*100 logx
y-1=300
y=301

Is this solution Helpfull? Yes (7) | No (4)  

vamsi  (9 years ago)

301 digits..
for power 100 characterstic is 30
so..for 1000 it will be 300..
number of digits will be 301..

Is this solution Helpfull? Yes (4) | No (1)  

ankit gupta  (9 years ago)

Ans:- 302

here X=2

So,

100log2 + 1= 31.103

1000log2 +1= 302.03

Is this solution Helpfull? Yes (4) | No (3)  

avinash jha  (9 years ago)

x^100=31 digit number
X^1000 can be written as (X^100)^10
which can again be converted to 10 log(x^100) = 10*31 = 310 digit number.
so ans is 310.

Is this solution Helpfull? Yes (2) | No   

moumita ghose  (9 years ago)

302 digits

Is this solution Helpfull? Yes (1) | No (1)  

Abhishek Mishra  (9 years ago)

Rakesh please solve this

Is this solution Helpfull? Yes (1) | No   

Moumita Das  (9 years ago)

How @Moumita ??

Is this solution Helpfull? Yes | No   

SHASHIKANT  (9 years ago)

ans is 110

Is this solution Helpfull? Yes | No (1)  

ANKUSH MONGA  (9 years ago)

3 digit number lies between 10^2 to 10^3.Similarly,
31 digit means the number lies between 10^30 to 10^31.
(10^30)=< X^100 < 10^31 where =< represents less than or equal to.
(10^30)^10 =< (X^100)^10 < (10^31)^10
10^300 =< X^1000 < 10^310.-------(1)
If a number lies between 10^2 to 10^3 then it has 3 digit(eg-777 lies between 10^2 to 10^3 and it has 3 digit).
Similarly, eqn (1) will have 301 to 310 digits.

Is this solution Helpfull? Yes | No (1)  

Saikat Guin  (9 years ago)

10^2=3 digit
10^3=4 digit
10^4=5 digit
10^30=31 digit=x^100(as given in question)
or, 10^31=x^100
=> log 10^31= log x^100(applying log)
=> 31 log 10=100 log x
=>310 log 10= 1000 log x(multiply with 10 both side)
=> 10^310=x^1000
now we know, 10^300= 301 digit
so, x^1000= 301 digit

Is this solution Helpfull? Yes | No   

Please Login to Read Solution.