Maths Olympiad Prep

Track / Stage 3 / 28 of 260 #28 of 1964

Problem 28

AMC 10/12, early questions
Number theory Difficulty 3.1 Multiple choice

Among the following numbers, the largest one is:

Pick one

Official solution

To compare the given numbers and find the largest one, we analyze them in the context of their values on the number line:

- We know that π\pi is approximately 3.143.14, which is a positive number.
- The fraction 12023\frac{1}{2023}, while positive, is significantly smaller than 11, and thus, also smaller than π\pi.
- The number 00 is neutral, meaning it is less than any positive number, including both π\pi and 12023\frac{1}{2023}.
- Lastly, 2π-2\pi is a negative number, and since π\pi is positive, 2π-2\pi is less than 00, making it the smallest among the given options.

Putting these observations in order, we get:
π>12023>0>2π\pi > \frac{1}{2023} > 0 > -2\pi

Therefore, the largest number among the given options is π\pi.

Thus, the correct answer is B\boxed{B}.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.