AMC10 2012 B

AMC10 2012 B · Q4

AMC10 2012 B · Q4. It mainly tests GCD & LCM, Remainders & modular arithmetic.

When Ringo places his marbles into bags with 6 marbles per bag, he has 4 marbles left over. When Paul does the same with his marbles, he has 3 marbles left over. Ringo and Paul pool their marbles and place them into as many bags as possible, with 6 marbles per bag. How many marbles will be left over?

Ringo 把他的弹珠装入每袋 6 个的袋子时，剩下 4 个。Paul 这样做时剩下 3 个。Ringo 和 Paul 把弹珠合在一起，尽可能装入每袋 6 个的袋子。会剩下多少弹珠？

(A) 1 1

(B) 2 2

(D) 4 4

(E) 5 5

Answer

Correct choice: (A)

正确答案：（A）

Solution

Answer (A): The 7 marbles left over will fill one more bag of 6 marbles leaving 1 marble left over.

答案（A）：剩下的 7 颗弹珠可以再装满一袋（每袋 6 颗），并且还会剩下 1 颗弹珠。

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