What percent of the integers between 200 and 999, inclusive, end with the digits "03"?
Show Hint
- 1%
- 2.5%
- 3%
- 4%
- 5%
The Correct Option is A
Solution and Explanation
This question asks us to find a percentage, which requires calculating the number of items that meet a specific criterion and dividing it by the total number of items in the set.
Step 2: Detailed Explanation:
1. Find the total number of integers in the range.
The range is from 200 to 999, inclusive. The total number of integers is:
\[ \text{Total Count} = \text{Last} - \text{First} + 1 = 999 - 200 + 1 = 800 \] There are 800 integers in this range.
2. Find the number of integers that end with "03".
We are looking for numbers of the form `X03`, where `X` is the hundreds digit. The range of integers is from 200 to 999.
The possible values for the hundreds digit `X` are 2, 3, 4, 5, 6, 7, 8, and 9.
The numbers are: 203, 303, 403, 503, 603, 703, 803, 903.
Counting these numbers, we find there are 8 such integers.
3. Calculate the percentage.
\[ \text{Percentage} = \left( \frac{\text{Number of matching integers}}{\text{Total number of integers}} \right) \times 100% \] \[ \text{Percentage} = \left( \frac{8}{800} \right) \times 100% = \left( \frac{1}{100} \right) \times 100% = 1% \] Step 3: Final Answer:
1 percent of the integers between 200 and 999, inclusive, end with the digits "03".
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