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Lisa completed the table to describe the product of a mystery one-digit factor and each number.



× 1 2 3 4 5


? even even even even even



Part A Give all of the possible numbers that could be Lisa’s mystery one-digit factor.



Part B Explain how you know that you have selected all of the correct possibilities.

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Answer:

  • A: {0, 2, 4, 6, 8}
  • B: that is all the one-digit even numbers there are

Step-by-step explanation:

Part A.

We're only told that the product of the mystery factor and the number shown is even. This is true when the number shown is odd as well as even, hence the mystery factor is even.

There are no other conditions on the product that might limit the value of the mystery factor (non-zero, or < 10, for example).

Hence, the mystery factor could be any single-digit even number. In our base-10 number system, there are 5 of them: {0, 2, 4, 6, 8}.

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Part B.

There are only 5 even single-digit numbers in our base-10 number system, so by choosing 5, I know I have all of them.