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Sample Question 6:
Step 1: Remember that the problem is asking for the unit's digit of the product (multiplication results) of any six consecutive positive whole numbers.
Step 2: Understand that within any group of six consecutive integers, there must be both a number that has a factor of \(5\) and another even integer with a factor of \(2\).
Step 3: Realize that when a number which has a factor of \(5\) and an even number with a factor of \(2\) are multiplied together, the product is a multiple of \(10\).
Step 4: Notably, any number that is a multiple of \(10\) ends with a zero. Therefore, for the given conditions, the unit's digit in the multiplication results is always \(0\).
Step 5: Hence, the answer is \(\boxed{\text{(A)}\ 0}\).
The unit's digit (one's digit) of the product of any six consecutive positive whole numbers is
\(\text{(A)}\ 0 \qquad \text{(B)}\ 2 \qquad \text{(C)}\ 4 \qquad \text{(D)}\ 6 \qquad \text{(E)}\ 8\)
Answer Keys
Question 6: ASolutions
Question 6Step 1: Remember that the problem is asking for the unit's digit of the product (multiplication results) of any six consecutive positive whole numbers.
Step 2: Understand that within any group of six consecutive integers, there must be both a number that has a factor of \(5\) and another even integer with a factor of \(2\).
Step 3: Realize that when a number which has a factor of \(5\) and an even number with a factor of \(2\) are multiplied together, the product is a multiple of \(10\).
Step 4: Notably, any number that is a multiple of \(10\) ends with a zero. Therefore, for the given conditions, the unit's digit in the multiplication results is always \(0\).
Step 5: Hence, the answer is \(\boxed{\text{(A)}\ 0}\).