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

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

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New post 27 Feb 2019, 05:27
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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

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Re: How many whole numbers between 100 and 400, inclusive, contain the dig  [#permalink]

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New post 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
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Re: How many whole numbers between 100 and 400, inclusive, contain the dig  [#permalink]

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New post 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


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Re: How many whole numbers between 100 and 400, inclusive, contain the dig  [#permalink]

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New post 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
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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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