Question

the least quotient that can be formed by using two numbers chosen from the set ${-48, -3, 2, 12, 50, 90}$ is $m$. what is $|m|$?
answer:

Explanation:

Step1: Identify goal: find smallest quotient

To get the least quotient, we need the most negative value (since negative numbers are smaller than positive ones). We can achieve this by dividing the largest positive number by the smallest negative number, or the smallest negative number by the largest positive number? Wait, no: largest positive divided by smallest negative gives most negative.
Set: $\{-48, -3, 2, 12, 50, 90\}$
Largest positive number: $90$
Smallest negative number: $-3$

Step2: Calculate the least quotient

Compute quotient of largest positive and smallest negative:
$\frac{90}{-3} = -30$
This is the smallest possible quotient (other combinations give less negative or positive values, e.g., $\frac{-48}{2}=-24$, which is larger than $-30$; positive quotients are all larger than negative ones). So $m=-30$.

Step3: Compute absolute value of m

Calculate $|m|$:
$|m| = |-30| = 30$

Answer:

30