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How many whole numbers between 100 and 400, inclusive, conta

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by Max@Math Revolution » Wed Feb 27, 2019 4:14 am
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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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by GMATGuruNY » Wed Feb 27, 2019 4:29 am
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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by Max@Math Revolution » Thu Feb 28, 2019 11:39 pm
=>

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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by Scott@TargetTestPrep » Sat Mar 02, 2019 8:01 am
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

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