Difference between revisions of "1985 AJHSME Problem 15"
Coolmath34 (talk | contribs) (Created page with "== Problem == How many whole numbers between <math>100</math> and <math>400</math> contain the digit <math>2</math>? <math>\text{(A)}\ 100 \qquad \text{(B)}\ 120 \qquad \tex...") |
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How many whole numbers between <math>100</math> and <math>400</math> contain the digit <math>2</math>? | How many whole numbers between <math>100</math> and <math>400</math> contain the digit <math>2</math>? | ||
− | <math>\text{(A)}\ 100 \qquad \text{(B)}\ 120 \qquad \text{(C)}\ | + | <math>\text{(A)}\ 100 \qquad \text{(B)}\ 120 \qquad \text{(C)}\ 137 \qquad \text{(D)}\ 140 \qquad \text{(E)}\ 148</math> |
== Solution == | == Solution == | ||
− | There are <math>100</math> numbers from 200 to 299 that have the number 2. In addition, there are 20 numbers that have a units digit of 2 and 20 numbers that have a tens digit of 2. However, we overcounted | + | There are <math>100</math> numbers from 200 to 299 that have the number 2. In addition, there are 20 numbers that have a units digit of 2 and 20 numbers that have a tens digit of 2. However, we overcounted three numbers, 122,222 and 322. |
− | Our final count is <math>100 + 20 + 20 - | + | Our final count is <math>100 + 20 + 20 - 3 = \boxed{\text{(C)}\ 137}</math> numbers that contain the digit <math>2.</math> |
Latest revision as of 06:51, 21 April 2025
Problem
How many whole numbers between and
contain the digit
?
Solution
There are numbers from 200 to 299 that have the number 2. In addition, there are 20 numbers that have a units digit of 2 and 20 numbers that have a tens digit of 2. However, we overcounted three numbers, 122,222 and 322.
Our final count is numbers that contain the digit