Maths Olympiad Prep

Track / Stage 3 / 64 of 260 #64 of 1964

Problem 64

AMC 10/12, early questions
Number theory Difficulty 3.2 Find the answer

Starting from 400,000, counting by increments of 50 up to 500,000 requires counting \_\_\_\_\_\_ times.

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

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Official solution

First, calculate the difference between 500,000 and 400,000:
500,000400,000=100,000500,000 - 400,000 = 100,000

Then, divide the difference by 50 to find the number of times:
100,00050=2,000 times\frac{100,000}{50} = 2,000 \text{ times}

Therefore, the answer is: 2000\boxed{2000}.

Starting from 400,000 and counting by increments of 50, which means each time you count, the number increases by 50 until it reaches 500,000. By calculating 500,000400,000=100,000500,000 - 400,000 = 100,000 and then dividing 100,000100,000 by 5050, we find it takes 2,0002,000 times; this is how the problem is solved.

This question is prone to errors. It should be clear that counting starts from 400,000, meaning that 400,050 is counted as the first time.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.