Practice Math Kangaroo Problems 11 to 15, Level 0304
Problem Kangur_2002_0304_11 (4 pts) http://www.mathkangaroo.org
This picture below is a sketch of a castle. Which of the lines below does not belong to the sketch?
Solution: Answer: C. This is a somewhat tricky image/shape recognition problem in which you need to test each of the solutions one by one and see if you can find it in a bigger castle image.
Problem Kangur_2002_0304_12 (4 pts) http://www.mathkangaroo.org
We add 17 to the smallest two-digit number and then we divide the sum by the largest one-digit number.
What is the result?
Solution: Answer: A. The trick here is to figure what numbers are being manipulated with. The smallest two-digit (integer) number is 10, adding 17 to it yields 27, the largest one digit integer is 9, so the result of division is 3.
Problem Kangur_2002_0304_13 (4 pts) http://www.mathkangaroo.org
In a certain ancient country the numbers: one, ten, and sixty were expressed with the following symbols:
Using those symbols people were writing down other numbers, for example the number 22 was written as
Which of the following notations represents the number 124 ?
Solution: Answer: E. Notice that in the example provided for 22, two symbols for tens add up to 20 and all symbols for ones add up to 2. Two symbols for sixty add up to 120, and 4 ones give us 124 in E.
Problem Kangur_2002_0304_14 (4 pts) http://www.mathkangaroo.org
A face of a clock was divided into four parts. The sums of the numbers in each of those parts are consecutive
E numbers. Which of the following pictures satisfies this rule?
Solution: Answer: B. It is quite important to understand what they are asking here. For each of possible solutions, they are splitting the numbers between 1 and 12 into 4 groups, and then add them up for each group. We want to have a solution with sums being 4 consecutive integers. Clearly, this means that as soon as we find 2 sums more than 3 apart from one another, we can throw this answer out and move to the next one. Solution A) thus can be thrown out because of 19 and 15 sums. B is the one we want luckily pretty fast (19, 20, 21, 22 are the 4 sums)
Problem Kangur_2002_0304_15 (4 pts) http://www.mathkangaroo.org
Klara and Zosia had 60 matches altogether. Klara took as many matches as she needed to build a triangle, each side 6 matches long. Zosia used the remaining matches to build a rectangle, which had one side equal to 6 matches. How many matches long is each of the longer sides of this rectangle?
Solution: Answer: C. Lets figure out first how many matches Klara used up for her triangle: 3 sides x 6 matches per side = 18 matches total. Hence 42 matches are left for Zosia. The perimeter of her rectangle is thus 42 (she will use up all matches), and 12 matches will go on two opposite sides of it with 6 matches each, hence 30 is left for the remaining two, and 15 is the answer. Note that it is crucially essential to read what they ask exactly as most of the numbers we used in our solution are present in multiple choice.
Problem copyright www.mathkangaroo.org,
Solution copyright Darya and Dmitry Pavlov