How many such sequences of five consecutive integers are possible?
Consider the following for the next two (02) items that follow:<br><br>Collect all the sequences of five consecutive integers such that their product is equal to one of these integers. Let X be the collection of all possible such sequences. Let P be the smallest integer and Q be the largest integer occurring in these sequences.
- A. One
- B. Two
- C. Three
- D. Five ✓
Correct Answer: D. Five
Explanation
For the product of five consecutive integers to equal one of them, the product must be 0 (otherwise the absolute product grows too large). Thus, 0 must be one of the integers. There are exactly 5 such sequences where 0 is included (e.g., from \{-4, -3, -2, -1, 0\} up to \{0, 1, 2, 3, 4\}).
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