AMC8 2004

AMC8 2004 · Q19

AMC8 2004 · Q19. It mainly tests GCD & LCM, Remainders & modular arithmetic.

A whole number larger than 2 leaves a remainder of 2 when divided by each of the numbers 3, 4, 5 and 6. The smallest such number lies between which two numbers?

一个大于2的整数，除以3、4、5、6各数时余数均为2。最小这样的数在哪两个数之间？

(A) 40 and 49 40 and 49

(B) 60 and 79 60 and 79

(D) 210 and 249 210 and 249

(E) 320 and 369 320 and 369

Answer

Correct choice: (B)

正确答案：（B）

Solution

(B) The numbers that leave a remainder of 2 when divided by 4 and 5 are 22, 42, 62 and so on. Checking these numbers for a remainder of 2 when divided by both 3 and 6 yields 62 as the smallest.

（B）当被 4 和 5 除时余 2 的数是 22、42、62 等等。检验这些数在被 3 和 6 同时除时是否也余 2，可得最小的是 62。

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