AMC8 2001

AMC8 2001 · Q2

AMC8 2001 · Q2. It mainly tests Word problems (algebra), Divisibility & factors.

I'm thinking of two whole numbers. Their product is 24 and their sum is 11. What is the larger number?

我在想两个整数。它们的乘积是24，它们的和是11。较大的数是多少？

(A) 3 3

(B) 4 4

(D) 8 8

(E) 12 12

Answer

Correct choice: (D)

正确答案：（D）

Solution

Since their sum is to be 11, only positive factors need to be considered. Number pairs whose product is 24 are $(1, 24)$, $(2, 12)$, $(3, 8)$ and $(4, 6)$. The sum of the third pair is 11, so the numbers are 3 and 8. The larger one is 8.

因为它们的和是11，只需考虑正因数即可。乘积为24的数对是 $(1, 24)$、$(2, 12)$、$(3, 8)$ 和 $(4, 6)$。第三对的和是11，所以这些数是3和8。较大的是8。

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