Verbal Reasoning - Arithmetic Reasoning - Discussion
Discussion Forum : Arithmetic Reasoning - Section 2 (Q.No. 30)
30.
A printer numbers the pages of a book starting with 1 and uses 3189 digits in all. How many pages does the book have ?
Answer: Option
Explanation:
No. of digits in 1-digit page nos. = 1x9 = 9.
No. of digits in 2-digit page nos. = 2 x 90 = 180.
No. of digits in 3-digit page nos. = 3 x 900 = 2700.
No. of digits in 4-digit page nos. = 3189 - (9 + 180 + 2700) = 3189 - 2889 = 300.
Therefore No. of pages with 4-digit page nos. = (300/4) = 75.
Hence, total number of pages = (999 + 75) = 1074.
Discussion:
16 comments Page 1 of 2.
Dileep kumar said:
3 years ago
@Najmi.
Here is the answer.
1 to 9 = 9.
10 to 99 = 90.
The remaining 2736-(180+9) = 2547 (all these digits as printed as 3 digit numbers).
100 to x = 2547/3 = 849.
total pages = 9 +90 + 849 = 948 pages.
Here is the answer.
1 to 9 = 9.
10 to 99 = 90.
The remaining 2736-(180+9) = 2547 (all these digits as printed as 3 digit numbers).
100 to x = 2547/3 = 849.
total pages = 9 +90 + 849 = 948 pages.
Dileep said:
3 years ago
@All.
Know the difference between digit and number before solving this question.
Hope the below example helps you.
Consider a book of 5 pages, then the total number of digits of all pages is 5 i.e. 1, 2, 3, 4, 5 (1+1+1+1+1=5).
Now, consider a book of 10 pages, then the total number of digits of all pages is 11 i.e.1, 2, 3, 4. 10 (1+1+1+1+1+1+1+1+1+2=11) since the number 10 has 2 digits.
Now, coming to the question. The total digits the printer uses is 3189 (not numbers, just digits).
No Of 1 digit pages =9 (1 to 9) , digits =9.
No Of 2 digit pages = 90 (10 to 99) , digits = 180 (since each number has 2 digits).
No Of 3 digit pages = 900 (100 to 999) , digits = 2700.
Now, to calculate the no. Of 4 digit pages, calculate the remaining digits.
3189 - (9 + 180 + 2700) = 3189 - 2889 = 300.
These 300 are digits for 4-digit pages. That means the printer will print 4 digits on each page.
No Of 4 digit pages = 300/4 = 75 (each page has a 4 digit number).
Now, total no. Of pages = 9 + 90 + 900 + 75 = 1075.
Know the difference between digit and number before solving this question.
Hope the below example helps you.
Consider a book of 5 pages, then the total number of digits of all pages is 5 i.e. 1, 2, 3, 4, 5 (1+1+1+1+1=5).
Now, consider a book of 10 pages, then the total number of digits of all pages is 11 i.e.1, 2, 3, 4. 10 (1+1+1+1+1+1+1+1+1+2=11) since the number 10 has 2 digits.
Now, coming to the question. The total digits the printer uses is 3189 (not numbers, just digits).
No Of 1 digit pages =9 (1 to 9) , digits =9.
No Of 2 digit pages = 90 (10 to 99) , digits = 180 (since each number has 2 digits).
No Of 3 digit pages = 900 (100 to 999) , digits = 2700.
Now, to calculate the no. Of 4 digit pages, calculate the remaining digits.
3189 - (9 + 180 + 2700) = 3189 - 2889 = 300.
These 300 are digits for 4-digit pages. That means the printer will print 4 digits on each page.
No Of 4 digit pages = 300/4 = 75 (each page has a 4 digit number).
Now, total no. Of pages = 9 + 90 + 900 + 75 = 1075.
(2)
Basant bhatt said:
4 years ago
Why do we divide 300 by 4? I don't understand. Please explain.
Payal said:
7 years ago
Why do we divide 300 by 4? Please explain.
Zarith said:
8 years ago
Why do we divide 300 by 4? I don't understand. Please explain it.
Abid ali said:
8 years ago
Because 1 digt page no. is 9 and 2 digts pages no. is 90 and 3 digits pages no. is 900.
So, total number page digits 1,2&3 are 2889.
Then, rest pages will be 4 digits these are 300.
Thus we calculate 300/4 and get 75 pages.
So, total number page digits 1,2&3 are 2889.
Then, rest pages will be 4 digits these are 300.
Thus we calculate 300/4 and get 75 pages.
(1)
Sam_91 said:
9 years ago
I did not understand from this step.
Number of digits in 4-digit page nos.
Why don't we calculate 4 digits from 1000 to 3189?
Number of digits in 4-digit page nos.
Why don't we calculate 4 digits from 1000 to 3189?
Najmi said:
9 years ago
If there is 2736 digits used in all then what is the number of pages?
Dilip Kumar Das said:
9 years ago
Per page 1 digit cover in 1-9 pg no. = 9 digits covered.
Per page 2 digit cover in 10-99 pg no. = 90*2 = 180 digits covered.
Per page 3 digit cover in 100-999 pg no. = 1242 - (9 + 180) = 1053 digit.
Then, 9 digit covered = 9 page.
180 digit covered = 90 page.
1053 digit covered = 1053/3 = 351 page.
Total = 9+90+351 = 450 pages.
Per page 2 digit cover in 10-99 pg no. = 90*2 = 180 digits covered.
Per page 3 digit cover in 100-999 pg no. = 1242 - (9 + 180) = 1053 digit.
Then, 9 digit covered = 9 page.
180 digit covered = 90 page.
1053 digit covered = 1053/3 = 351 page.
Total = 9+90+351 = 450 pages.
VENKY said:
9 years ago
Excellent.
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