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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## How many whole numbers between 100 and 400, inclusive, conta ##### This topic has 3 expert replies and 0 member replies ### GMAT/MBA Expert ## How many whole numbers between 100 and 400, inclusive, conta ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult How many whole numbers between 100 and 400, inclusive, contain the digit 2? A. 100 B. 125 C. 138 D. 145 E. 150 _________________ Math Revolution Finish GMAT Quant Section with 10 minutes to spare. The one-and-only Worldâ€™s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. Only$149 for 3 month Online Course
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Max@Math Revolution 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

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There are 19 such numbers with hundreds digit 1: 102, 112, 120, 121, â€¦, 129, 132, 142, â€¦, 192.
There are 100 such numbers with hundreds digit 2: 200, 201, 202, 203, â€¦, 299.
There are 19 such numbers with hundreds digit 3: 302, 312, 320, 321, â€¦, 329, 332, 342, â€¦, 392.

Thus, there are a total of 19 + 100 + 19 = 138 such numbers.

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Only $149 for 3 month Online Course Free Resources-30 day online access & Diagnostic Test Unlimited Access to over 120 free video lessons-try it yourself Email to : info@mathrevolution.com ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2791 messages Followed by: 18 members Upvotes: 43 Max@Math Revolution wrote: How many whole numbers between 100 and 400, inclusive, contain the digit 2? A. 100 B. 125 C. 138 D. 145 E. 150 From 100 to 199, we have 10 instances of 2 from 120 to 129 and 9 instances of 2 in the ones place of all numbers from 100 to 199, not counting 122, since we already counted it. Thus, there are 19 instances of a number with 2 from 100 to 199. From 200 to 299, we have 100 instances of numbers with a 2. From 300 to 399, we have another 19 instances, just like from 100 to 199. Thus, the total number of numbers from 100 to 400, inclusive, containing a digit of 2 is 19 + 100 + 19 = 138. Answer: C _________________ Scott Woodbury-Stewart Founder and CEO scott@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews • Award-winning private GMAT tutoring Register now and save up to$200

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