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# A book has 1000 pages numbered 1, 2, 3, …, and so on. How many times d

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42
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A book has 1000 pages numbered 1, 2, 3, …, and so on. How many times d  [#permalink]

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07 May 2019, 01:03
00:00

Difficulty:

55% (hard)

Question Stats:

56% (02:00) correct 44% (02:01) wrong based on 48 sessions

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[GMAT math practice question]

A book has 1000 pages numbered 1, 2, 3, …, and so on. How many times does the digit 2 appear on the page numbers?

A. 200
B. 250
C. 300
D. 400
E. 500

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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Intern Joined: 06 Jan 2018 Posts: 7 Re: A book has 1000 pages numbered 1, 2, 3, …, and so on. How many times d [#permalink] ### Show Tags 07 May 2019, 01:26 From 1 to 100 total 2s=20 Hence frm 1 to 1000 2s=20×10=200 imo option A Posted from my mobile device Senior Manager Joined: 13 Feb 2018 Posts: 451 GMAT 1: 640 Q48 V28 Re: A book has 1000 pages numbered 1, 2, 3, …, and so on. How many times d [#permalink] ### Show Tags 07 May 2019, 02:57 Hope in real GMAT I wont face question like that because I have no idea how to solve it in even 4 minutes Happy learning to you all Senior Manager Joined: 04 Aug 2010 Posts: 474 Schools: Dartmouth College Re: A book has 1000 pages numbered 1, 2, 3, …, and so on. How many times d [#permalink] ### Show Tags 07 May 2019, 03:35 MathRevolution wrote: [GMAT math practice question] A book has 1000 pages numbered 1, 2, 3, …, and so on. How many times does the digit 2 appear on the page numbers? A. 200 B. 250 C. 300 D. 400 E. 500 Ignore page 1000, since it does not include the digit 2. To make the calculation easier, consider the remaining pages numbered as 3-digit integers, beginning with 000 and ending with 999: 000, 001, 002...997, 998, 999 There are 1000 options between 000 to 999, inclusive. Since each option is composed of 3 digits, the total number of digits = 3*1000 = 3000. The probability that 2 will appear in any given position is the same as the probability that 3 will appear in any given position. Implication: Each of the 10 digits 0 through 9 will appear the SAME NUMBER OF TIMES. Thus, the number of times that 2 will appear $$= \frac{3000}{10} = 300$$. _________________ GMAT and GRE Tutor Over 1800 followers GMATGuruNY@gmail.com New York, NY If you find one of my posts helpful, please take a moment to click on the "Kudos" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. GMAT Club Legend Joined: 18 Aug 2017 Posts: 4998 Location: India Concentration: Sustainability, Marketing GPA: 4 WE: Marketing (Energy and Utilities) Re: A book has 1000 pages numbered 1, 2, 3, …, and so on. How many times d [#permalink] ### Show Tags 07 May 2019, 09:03 3 MathRevolution wrote: [GMAT math practice question] A book has 1000 pages numbered 1, 2, 3, …, and so on. How many times does the digit 2 appear on the page numbers? A. 200 B. 250 C. 300 D. 400 E. 500 from 1 to 100 ; 2 will come ; 20 times so except 200 to 299 series ; we get 20*9 ; 180 times for 200 to 299 series two will come in hundreds place; 100 times tens place ; 220-229 ; 10 times units place ; 202-292 ; 10 times so total 180+100+10+10; 300 IMO C Intern Joined: 09 Apr 2019 Posts: 8 Location: Brazil Schools: Wharton, Kellogg, Booth GPA: 3.45 Re: A book has 1000 pages numbered 1, 2, 3, …, and so on. How many times d [#permalink] ### Show Tags 07 May 2019, 15:38 1 MathRevolution wrote: [GMAT math practice question] A book has 1000 pages numbered 1, 2, 3, …, and so on. How many times does the digit 2 appear on the page numbers? A. 200 B. 250 C. 300 D. 400 E. 500 In my humble opinion, the best approach is to analyze the probability for each digit class. First of all, let's eliminate the thousands class since there are no 2's in this class. We are left with: Ones: 1 out of 10 (numbers in the xx2 form), so $$\frac{1}{10} * 1000 = 100$$ Tens: 10 out of 100 (numbers in the x2x form), so $$\frac{10}{100} * 1000 = 100$$ Hundreds: 100 out of 1000 (numbers from 200 to 299), so $$\frac{100}{1000} * 1000 = 100$$ Which will give us: $$100 + 100 + 100 = 300$$ Answer: C _________________ Hope some of my posts may help you. If that was the case, please hit +1 KUDOS. Thank you! "Perfection is not attainable, but if we chase perfection we can catch excellence" Vince Lombardi Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8007 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: A book has 1000 pages numbered 1, 2, 3, …, and so on. How many times d [#permalink] ### Show Tags 09 May 2019, 02:44 => The page numbers $$2, 12, 20, 21, 22, … , 29, 32, 42, … , 92$$ contain $$19+1 = 20$$ copies of the digit, $$2$$. The page numbers $$102, 112, 120, 121, … , 129, 132, 142, … , 192$$ similarly contain $$20$$ copies of the digit $$2$$. The page numbers $$200, 201, … , 299$$ contain $$120$$ copies of the digit, $$2$$. Page numbers $$302, 312, 320, 321, … , 329, 332, 342, … , 392$$ contain $$20$$ copies of the digit, $$2$$. Page numbers $$902, 912, 920, 921, 922, … , 929, 932, 942, … , 992$$ contain $$20$$ copies of the digit, $$2$$. The total number of copies of the digit, $$2$$ printed on the pages is $$9*20 + 120 = 300.$$ Therefore, the answer is C. Answer: C _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Re: A book has 1000 pages numbered 1, 2, 3, …, and so on. How many times d   [#permalink] 09 May 2019, 02:44
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