AMC10 2024 B

AMC10 2024 B · Q2

AMC10 2024 B · Q2. It mainly tests Exponents & radicals.

What is $10! - 7! \cdot 1!$ ?

$10! - 7! \cdot 1!$ 等于多少？

(A) 2021 2021

(B) 2022 2022

(D) 2024 2024

(E) 2025 2025

Answer

Correct choice: (A)

正确答案：（A）

Solution

$10! = 10 \cdot 9 \cdot 8 \cdot 7! = 720 \cdot 7!$ $6! \cdot 7! = 720 \cdot 7!$ Therefore, the equation is equal to $720 \cdot 7! - 720 \cdot 7! = (B)\ 0$ [ONLY FOR CERTAIN CHINESE TESTPAPERS] $0 - 5! = (A)\ -120$

$10! = 10 \cdot 9 \cdot 8 \cdot 7! = 720 \cdot 7!$ $6! \cdot 7! = 720 \cdot 7!$ 因此，该式等于 $720 \cdot 7! - 720 \cdot 7! = (B)\ 0$ [仅适用于某些中国试卷] $0 - 5! = (A)\ -120$

Topics

AL.008 Exponents & radicals