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
The correct answer is
C.
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