Latest Elitmus Aptitude Question SOLUTION: If x^100 has 31 digit,then x^1000 will have how many digits?

• Placement Papers
• /
• Elitmus
• /
• Logical Reasoning
• /
• Decision Making and Problem Solving

Elitmus Question Papers:

(#M40018614) ELITMUS Logical Reasoning question number Keep an EYE

If x^100 has 31 digit,then x^1000 will have how many digits?

Asked In Elitmus shash (11 years ago)

Unsolved Read Solution (11)

Is this Puzzle helpful?   (15)   (2) Submit Your Solution Decision Making and Problem Solving

Read Solution (11) :

shailesh  (11 years ago)

10^1 has 2 digits = 10
10^2 has 3 digits = 100
10^3 has 4 digits = 1000
similarly 10^y-1 has y digits
if we have y digits in x^100 that means
10^(y-1)=x^100
10^(31-1)=x^100
taking log both side
30 log 10 = 100 log x
30 = 100 log x
now,
10^(y-1)= x^1000
y-1=1000 log x
y-1=10*100 log x
put value of 100 log x in this equation
we get y-1=10*30
y=301
Ans=301

Is this solution Helpfull? Yes (96) | No (3)  

Sandeep S Hegde  (11 years ago)

31-1=100 log x solve this, we wil get x=2
so
2^1000 has (1000 log 2)+1=302
ANS: 302

Is this solution Helpfull? Yes (13) | No (6)  

pavan  (11 years ago)

302 digits

Is this solution Helpfull? Yes (7) | No (9)  

Umesh Yadav  (10 years ago)

10^1=(1+1)=2 digit
10^2=(2+1)=3 digit
.
.
.
10^30=(30+1)=31 digits
therefore, 10^30=x^100
30=100 log x
multiplaying both side by 10
30*10=10*100 log x
300= 1000 log x = 300+1=301

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

Sneha Agarwal  (11 years ago)

@pavan pls explain

Is this solution Helpfull? Yes (3) | No   

Deepak Chaudhari  (9 years ago)

The same question is repeated on 21st jun delhi center....and ans is 301.

Is this solution Helpfull? Yes (2) | No (1)  

tech  (10 years ago)

i think 8 is wrong .......
answer is 12 ...
(team) (matches played) (win) (lose)
1 14 11 3
2 14 11 3
3 14 11 3
4 14 11 3
5 14 11 3
6 14 1 13
7 14 0 14
8 14 0 14

Is this solution Helpfull? Yes (1) | No   

Tarun Sharma  (9 years ago)

taking log so 100log(x)=30.abcd...(a belong to {0-9})
so log(x)=.30abcd...
so 1000 log(x)=30a.bcd
so no of digits [30a.bcd] +1 i.e 30a+1 so it can be 301 to 310

Is this solution Helpfull? Yes (1) | No   

Prateek Sancheti  (11 years ago)

@ Pavan can you please explain the answer?

Is this solution Helpfull? Yes | No   

SAMBIT KUMAR GHOSH  (11 years ago)

please explain the soln...

Is this solution Helpfull? Yes | No   

mohini gupta  (9 years ago)

302
solve using log

Is this solution Helpfull? Yes | No   

Please Login to Read Solution.