6. In the expression 5 * 4* 3* 2* 1, * is chosen from +, -, × each at most two times. What is the smallest non-negative value of the expression?

1. A. 3
2. B. 2
3. C. 1

Answer: D

Explanation

We need to find the smallest non-negative value for the expression 5 * 4 * 3 * 2 * 1, using the operators +, -, ×, with each operator used at most twice. The smallest non-negative integer is 0. Let’s try to achieve 0. Consider the arrangement: 5 – 4 – 3 + 2 × 1. Following the order of operations (multiplication first): 2 × 1 = 2. Then, proceeding from left to right: 5 – 4 = 1, 1 – 3 = -2, -2 + 2 = 0. This combination uses ‘-‘ twice, ‘+’ once, and ‘×’ once, which satisfies the condition that each operator is used at most two times. Since 0 is a possible value and it is the smallest non-negative integer, it is the correct answer. This question tests logical reasoning and basic arithmetic skills.