2009 Grade 8 CEMC Gauss Problems/Problem 3
Problem
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Jack has a litre jug of water. What is the maximum number of
litre bottles that he can completely fill?
Solution 1
To find the maximum number, we can see how many times goes into
. To do this, we can divide
by
, and round the result down if the result is a decimal:
Since the result is not a decimal, we do not have to round it down. This also means that our answer is .
~anabel.disher
Solution 2 (answer choices)
We can multiply answer choices by 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.
, which happens to be exactly the number of litres that can be held by the jug, so the answer is
.
~anabel.disher
Solution 3 (answer choices)
We can notice that the result must be an even number, since , eliminating answer choices A, B, and E.
Using answer choice D, we get:
, 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 .
~anabel.disher