A certain tour company bought canoes kayaks and life jackets for a total of $3279. If the company paid $65 for each canoe $40 for each kayak and $2 for each life jacket then the company must have bought which of the following? I. An odd number of canoes II. An even number of kayaks III. An even number of life jackets

Rationale

An odd number of canoes.

To find the correct answer, we can analyze the total cost of the items purchased by the tour company. The total cost can be expressed as a linear equation based on the number of canoes, kayaks, and life jackets.

A (I only) CORRECT

The total spent on canoes is $65 times the number of canoes. For the total cost of $3279 to be odd, the number of canoes must be odd. Since $65 is an odd number, multiplying it by an odd number will yield an odd product, which aligns with our total.

B (II only) YOUR ANSWER

The total cost of kayaks is $40 times the number of kayaks, where $40 is an even number. Therefore, regardless of whether the number of kayaks is odd or even, the total cost contributed by kayaks will always be even, leaving no restriction on the total cost being odd. Thus, we cannot conclude that the number of kayaks is even based solely on the total.

C (III only) YOUR ANSWER

The total cost of life jackets is $2 times the number of life jackets. Since $2 is an even number, multiplying it by any whole number (even or odd) will always yield an even product. Hence, we cannot assert the number of life jackets must be even just from the total cost.

D (I and III only) YOUR ANSWER

Although it's true that the number of canoes must be odd, the statement about the life jackets does not hold since their total cost does not impose any condition of being even, making this option incorrect.

E (I II and III) YOUR ANSWER

This choice incorrectly assumes both the number of kayaks and life jackets must meet specific conditions, which we have established are not true.

Conclusion

The analysis shows that only the number of canoes must be odd to satisfy the condition of the total cost being odd. The conditions for kayaks and life jackets do not restrict their counts in the manner described, confirming that the only verified statement is I, making option A the correct answer.

An odd number of canoes.

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