Each of the even numbers 2, 4, 6, $\dots$ , 50 is divided by 7. The remainders are recorded. Which histogram displays the number of times each remainder occurs?
A. Histogram A (counts for remainders 0-6: 3, 4, 4, 3, 4, 3, 4)
B. Histogram B (counts for remainders 0-6: 3, 4, 4, 4, 3, 3, 4)
C. Histogram C (counts for remainders 0-6: 3, 4, 4, 4, 4, 3, 3)
D. Histogram D (counts for remainders 0-6: 4, 3, 4, 3, 4, 3, 4)
E. Histogram E (counts for remainders 0-6: 4, 4, 3, 4, 3, 4, 3)

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Worked solution

1. 2025 AMC 8 官方解析

Answer (A): There are 25 numbers in all. The table below shows the first few numbers and their remainders when divided by 7.

number	2	4	6	8	10	12	14	16	18	20	22	24	$\dots$
remainder	2	4	6	1	3	5	0	2	4	6	1	3	$\dots$

The remainders follow a repeating pattern of 2, 4, 6, 1, 3, 5, 0. This pattern will repeat with each remainder occurring 3 times over the first 21 even numbers. Then the first 4 remainders, 2, 4, 6, and 1 will each occur a fourth time. This corresponds to histogram (A).

Answer

A. Histogram A (counts for remainders 0-6: 3, 4, 4, 3, 4, 3, 4)

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