2009 Grade 8 CEMC Gauss Problems/Problem 3

Problem

This page has been proposed for deletion. Reason: moved


Note to sysops: Before deleting, please review: • What links hereDiscussion pageEdit history

Jack has a $3$ litre jug of water. What is the maximum number of $0.5$ litre bottles that he can completely fill?

$\text{ (A) }\ 3 \qquad\text{ (B) }\ 1.5 \qquad\text{ (C) }\ 6 \qquad\text{ (D) }\ 12 \qquad\text{ (E) }\ 15$

Solution 1

To find the maximum number, we can see how many times $0.5$ goes into $3$. To do this, we can divide $3$ by $0.5$, and round the result down if the result is a decimal:

$\frac{3}{0.5} = \frac{3}{\frac12} = \frac{3 \times 2}{\frac12 \times 2} = \frac{6}{1} = 6$

Since the result is not a decimal, we do not have to round it down. This also means that our answer is $\boxed {\textbf {(C) } 6}$.

~anabel.disher

Solution 2 (answer choices)

We can multiply answer choices by $0.5$ to see if they fit the amount of water that can be held by the jug. We can ignore answer choice B because the number of bottles cannot be a decimal.

$6 \times 0.5 = 6 \times \frac12 = 3$, which happens to be exactly the number of litres that can be held by the jug, so the answer is $\boxed {\textbf {(C) } 6}$.

~anabel.disher

Solution 3 (answer choices)

We can notice that the result must be an even number, since $0.5 = \frac12$, eliminating answer choices A, B, and E.

Using answer choice D, we get:

$12 \times \frac12 = 6$, which is not equal to the number of litres that can be held by the jug, meaning D is not the answer.

Since all other answer choices have been eliminated, the answer is $\boxed {\textbf {(C) } 6}$.

~anabel.disher