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Sample Question 7:
Step 1: We aim to achieve a positive product. To do this, we can either select three positive numbers or one positive number and two negative numbers from the set.
Step 2: The set does not contain three positive numbers, therefore choosing three positive numbers is not possible.
Step 3: For the second case, to get the largest product we need to select the numbers with the largest absolute values. Therefore, we choose \(5\) (the largest positive number), \(-3\) and \(-2\) (the two negative numbers).
Step 4: Multiplying these three numbers \(5 \times -3 \times -2\) gives us \(30\).
Therefore, the answer is \(\boxed{\text{C}}\).
When three different numbers from the set \(\{ -3, -2, -1, 4, 5 \}\) are multiplied, the largest possible product is
\(\text{(A)}\ 10 \qquad \text{(B)}\ 20 \qquad \text{(C)}\ 30 \qquad \text{(D)}\ 40 \qquad \text{(E)}\ 60\)
Answer Keys
Question 7: CSolutions
Question 7Step 1: We aim to achieve a positive product. To do this, we can either select three positive numbers or one positive number and two negative numbers from the set.
Step 2: The set does not contain three positive numbers, therefore choosing three positive numbers is not possible.
Step 3: For the second case, to get the largest product we need to select the numbers with the largest absolute values. Therefore, we choose \(5\) (the largest positive number), \(-3\) and \(-2\) (the two negative numbers).
Step 4: Multiplying these three numbers \(5 \times -3 \times -2\) gives us \(30\).
Therefore, the answer is \(\boxed{\text{C}}\).