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# How many whole numbers between 100 and 400, inclusive, contain the dig

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8011
GMAT 1: 760 Q51 V42
GPA: 3.82
How many whole numbers between 100 and 400, inclusive, contain the dig  [#permalink]

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27 Feb 2019, 05:27
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Difficulty:

45% (medium)

Question Stats:

62% (01:42) correct 38% (02:07) wrong based on 42 sessions

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How many whole numbers between 100 and 400, inclusive, contain the digit 2?

A. 100
B. 125
C. 138
D. 145
E. 150

_________________
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" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" GMAT Club Legend Joined: 18 Aug 2017 Posts: 5008 Location: India Concentration: Sustainability, Marketing GPA: 4 WE: Marketing (Energy and Utilities) Re: How many whole numbers between 100 and 400, inclusive, contain the dig [#permalink] ### Show Tags 27 Feb 2019, 05:40 MathRevolution wrote: How many whole numbers between 100 and 400, inclusive, contain the digit 2? A. 100 B. 125 C. 138 D. 145 E. 150 total digits = 301 and digits not containing 2 ; 2*9*9 ; 162 + 1; 163 of '400 ' so digits containing 2 ; 301-163 ; 138 IMO C Senior Manager Joined: 04 Aug 2010 Posts: 474 Schools: Dartmouth College Re: How many whole numbers between 100 and 400, inclusive, contain the dig [#permalink] ### Show Tags 27 Feb 2019, 05:42 1 MathRevolution wrote: How many whole numbers between 100 and 400, inclusive, contain the digit 2? A. 100 B. 125 C. 138 D. 145 E. 150 (integers with the digit 2) = (all integers between 100 and 399, inclusive) - (integers without the digit 2) All integers between 100 and 399, inclusive: For any set of consecutive integers, count = biggest - smallest + 1. In this case: count = 399-100+1 = 300 Integers without the digit 2: Number of options for the hundreds digit = 2. (1 or 3) Number of options for the tens digit = 9. (Any digit but 2) Number of options for the units digit = 9. (Any digit but 2) To combine these options, we multiply: 2*9*9 = 162 Integers with the digit 2: 300-162 = 138 _________________ 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. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8011 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: How many whole numbers between 100 and 400, inclusive, contain the dig [#permalink] ### Show Tags 01 Mar 2019, 00:57 => There are $$19$$ such numbers with hundreds digit $$1: 102, 112, 120, 121, …, 129, 132, 142, …, 192.$$ There are $$100$$ such numbers with hundreds digit $$2: 200, 201, 202, 203, …, 299.$$ There are $$19$$ such numbers with hundreds digit $$3: 302, 312, 320, 321, …, 329, 332, 342, …, 392.$$ Thus, there are a total of $$19 + 100 + 19 = 138$$ such numbers. 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: How many whole numbers between 100 and 400, inclusive, contain the dig   [#permalink] 01 Mar 2019, 00:57
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