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Problem 353

Algebra Difficulty 2.4 Find the answer CEMC Cayley

What is the greatest possible value of $n$ if Juliana chooses three different numbers from the set $\{-6,-4,-2,0,1,3,5,7\}$ and multiplies them together to obtain the integer $n$ ?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Official solution

Since $3 \times 5 \times 7=105$ , then the greatest possible value of $n$ is at least 105. For the product of three numbers to be positive, either all three numbers are positive or one number is positive and two numbers are negative. If all three numbers are positive, the greatest possible value of $n$ is $3 \times 5 \times 7=105$ . If one number is positive and two numbers are negative, the greatest possible value of $n$ is $7 \times(-4) \times(-6)=7 \times 24=168$ . Combining the two cases, we see that the greatest possible value of $n$ is 168.

Source: Omni-MATH, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.