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If a book has 252 pages, how many digits have been used to number the

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Bunuel
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If a book has 252 pages, how many digits have been used to number the [#permalink] New post   21 Feb 2020, 02:07
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If a book has 252 pages, how many digits have been used to number the pages?

A. 648
B. 650
C. 660
D. 661
E. 662

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Re: If a book has 252 pages, how many digits have been used to number the [#permalink] New post   21 Feb 2020, 02:21
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Quote:
If a book has 252 pages, how many digits have been used to number the pages?

A. 648
B. 650
C. 660
D. 661
E. 662


To answer the question, we need to calculate the total digits used in writing numbers from 1 to 252

Single Digit numbers = 9 (1 to 9)
So, Digits used in Single-digit numbers = 1*9 = 9

Two Digit numbers = 90 (10 to 99)
So, Digits used in Two digit numbers = 2*90 = 180

Three-digit Numbers = 153 (100 to 252)
So, Digits used in Three digit numbers = 3*153 = 459

Total Digits used = 9+180+459 = 648

Answer: Option A
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Re: If a book has 252 pages, how many digits have been used to number the [#permalink] New post   21 Feb 2020, 05:08
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Digits for pages 1-9 => 9
Digits used for pages 10-99 => 99-10+1 = 90*2 = 180
Digits used for pages 100-252 =. 252-100+1 = 153*3 = 459

Adding we get Total number of digits used to page the numbers = 648 - Answer - A
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Re: If a book has 252 pages, how many digits have been used to number the [#permalink] New post   21 Feb 2020, 05:40
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The question asks us how many digits are used to write numbers from 1 to 252.

There are 252 units digits.
252 - 9 = 243 tens digits (because first 9 numbers don't have tens digits)
and 252 - 99 = 153 hundreds digits (because first 99 numbers don't have hundreds digits)

Total = 252 + 243 + 153 = 648

Answer (A)
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Re: If a book has 252 pages, how many digits have been used to number the [#permalink] New post   21 Feb 2020, 07:19
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Quote:
If a book has 252 pages, how many digits have been used to number the pages?

A. 648
B. 650
C. 660
D. 661
E. 662


1 digit pages: 1 to 9 = 9 numbers * 1 digit = 9
2 digit pages: 10 to 99 = 90 numbers * 2 digits = 180
3 digit pages: 100 to 252 = 153 numbers * 3 digits = 459
total digits: 459+180+9 = 648

Ans (A)
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Re: If a book has 252 pages, how many digits have been used to number the [#permalink] New post   21 Feb 2020, 07:36
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648

(252-100+1)*3 + (99-10+1)*2 +9

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Re: If a book has 252 pages, how many digits have been used to number the [#permalink] New post   21 Feb 2020, 10:06
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Numbering the pages and digits used for each section of pages

1- 9: 1*9
10-99: 90*2
100-199: 100*3
200-249: 50*3
250-252: 3*3

Total Digits = 9 + 180 + 300 + 150 + 9 = 648
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Re: If a book has 252 pages, how many digits have been used to number the [#permalink] New post   21 Feb 2020, 10:08
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PAGE 1-9 --> 9 page*1=9 digits
PAGE 10-99 --> 90 page*2= 180 digits
PAGE 100-252 --> 153 page*3= 459 digits
Total digits that have been used to number the pages = 9 +180 +459 = 648

FINAL ANSWER IS (A) 648
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Re: If a book has 252 pages, how many digits have been used to number the [#permalink] New post   21 Feb 2020, 12:04
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If a book has 252 pages, how many digits have been used to number the pages?

A. 648
B. 650
C. 660
D. 661
E. 662

From 1 to 9 , there are 9 digits
From 10 to 99 , there are 99-10+1 = 90 pages. Number of digits in 90 pages = 90*2 = 180.
From 10 to 99 , there are 252-100+1 = 153 pages. Number of digits in 153 pages = 153*3 = 459.
Total number of digits = 9 + 180 + 459 = 648
Answer:648(A)
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Re: If a book has 252 pages, how many digits have been used to number the [#permalink] New post   21 Feb 2020, 13:44
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If a book has 252 pages, how many digits have been used to number the pages?

—> from 1 to 9 —9 digits
—> from 10 to 99 — 90*2 = 180 digits
—> from 100 to 252 —153*3 = 459 digits

In total, 9+ 180 + 459= 648 digits

The answer is A.

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Re: If a book has 252 pages, how many digits have been used to number the [#permalink] New post   21 Feb 2020, 22:03
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No.of digits from
1-9 = 9
10-99 = 90*2= 180
100-252 = 153*3= 459
Total no.of digits= 9+180+459=648

OA:A

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Re: If a book has 252 pages, how many digits have been used to number the [#permalink] New post   22 Feb 2020, 06:16
total no of digits
0-9 ; 9 digits
from
10-99 ; 90*2 ; 180 digits
from 100 to 252 ; 153*3 ; 459 digits
total 459+180+9 ; 648
IMO A


If a book has 252 pages, how many digits have been used to number the pages?

A. 648
B. 650
C. 660
D. 661
E. 662
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Re: If a book has 252 pages, how many digits have been used to number the [#permalink] New post   22 Feb 2020, 08:09
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If a book has 252 pages, how many digits have been used to number the pages?

A. 648
B. 650
C. 660
D. 661
E. 662

Number of digits at ones place = 252
Number of digits at tens place = 252 - 9 = 243
Number of digits at hundreds lace = 252 - 99 = 153

Total = 252 + 243 + 153 = 648

Answer A.
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Re: If a book has 252 pages, how many digits have been used to number the [#permalink] New post   22 Feb 2020, 08:18
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1-9 -> 9 digits
10-99-> 3*90 = 180 digits
100-252-> 3*153 = 549 digits

Total digits used = 9 + 180 + 549 = 648

IMO A

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Re: If a book has 252 pages, how many digits have been used to number the [#permalink] New post   18 Nov 2023, 12:22
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