Verbal Reasoning - Arithmetic Reasoning - Discussion

@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.

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.

9 digits covered in 1-9 pg no.

90*2 = 180 digits covered in 10-99 pg no.

900*3 = 2700 digits covered in 100-999 pg no.

Now 3189-(9+180+2700) = 300 digits will cover in 4 digits pg no.

So 300/4 pages will take to cover 300 nos.

i.e 75. Now total pages will be 999+75 = 1074 pages.

No of pages with 1-digit page no=9/1 = 9.

No of pages with 2-digit page no=180/2 = 90.

No of pages with 3-digit page no=2700/3 = 900.

Total no of pages with 1-digit, 2-digit and 3-digit numbers = 9+90+900 = 999.

Required no of pages = 999+75 = 1074.

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.

@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.

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?

I did not understand the procedure from 2nd step. Why did he take 90 in 2nd step?

If there is 2736 digits used in all then what is the number of pages?

@Sowmya.

Because from 10 -99 there are 90 pages with two digits.