How many numbers between 200 and 400 meet one or both of the conditions given in the statements below?

Statement 1: The number begins with 3

Statement 2: The number ends with 3

There are 100 numbers that begin with 3. In the other 200, there are effectively a tenth ending in 3. That is, 120 total numbers.

Answered by Anonymous | 2024-06-10

There are 116 numbers between 200 and 400 that meet one or both of the given conditions; 100 numbers start with 3, and 20 end with 3, but 4 numbers are counted in both and must be subtracted to avoid double-counting.
To find how many numbers between 200 and 400 meet one or both of the conditions given in the statements, we'll look at each statement individually and then combine results while accounting for any overlap.
Statement 1: The number begins with 3
All numbers between 300 and 399 meet this condition. There are 100 numbers that start with 3.
Statement 2: The number ends with 3
Numbers between 200 and 300 that end with 3 are: 203, 213, 223, ..., 293. The same pattern applies for numbers between 300 and 400: 303, 313, 323, ..., 393. Each set has 10 numbers, so there's a total of 20 numbers that end with 3.
However, four numbers (303, 313, 323, 333) are counted in both sets, so we have to subtract these from the total to avoid double-counting.
The total number fulfilling one or both conditions without double-counting is 100 (from statement 1) + 20 (from statement 2) - 4 (overlap) = 116.

Answered by AakanshaB | 2024-06-24

There are 119 total numbers between 200 and 400 that either start with a 3 or end with a 3. This includes 100 numbers that start with 3 and 20 numbers that end with 3, with one overlap at 303. Therefore, applying the inclusion-exclusion principle gives us 119 unique numbers.
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Answered by Anonymous | 2025-01-08