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1.A bread recipe uses flour and sugar in the ratio 5 to 3. The two together weigh 320 grams. How much of that is flour?[3]
A120 g
B160 g
C200 g
D192 g
E64 g
2.In a triangle, one angle measures 30 degrees. Of the other two angles, one is exactly twice the other. What is the largest angle in the triangle?[3]
A50 degrees
B75 degrees
C100 degrees
D150 degrees
E90 degrees
3.A jacket costs 80 pounds. In January the price rises by 20 percent. In February the new price falls by 20 percent. What is the price at the end of February?[3]
A80 pounds
B76.80 pounds
C64 pounds
D83.20 pounds
E96 pounds
4.In a class of 30 students, 18 play football and 15 play chess. Exactly 7 students do both. How many students play neither?[4]
A4
B26
C3
D11
E7
5.A photograph measures 8 cm by 12 cm. It is enlarged so that the shorter side becomes 20 cm, and the shape is not distorted. How long is the longer side of the enlargement?[4]
A24 cm
B30 cm
C32 cm
D4.8 cm
E18 cm
6.A pattern is built in rows. The first figure has 1 row, the second has 2 rows, and so on. In every figure, the first row has 1 dot, the second has 3 dots, the third has 5 dots, and each row after has 2 more dots than the one above it. How many dots are in the eighth figure?[4]
A64
B15
C36
D72
E81
7.A drawer holds 12 red socks, 10 blue socks and 8 green socks, all mixed up. You take socks out one at a time in the dark. What is the smallest number of socks you must take to be certain of having three of the same colour?[5]
A4
B7
C9
D13
E3
8.What is the last digit of 3 multiplied by itself 2026 times, that is, of 3 to the power 2026?[5]
A3
B9
C7
D1
E6
9.One tap fills a tank in 6 hours. A second tap fills the same tank in 4 hours. Both taps are opened together on an empty tank. How long does it take to fill?[5]
A2 hours 24 minutes
B5 hours
C10 hours
D2 hours
E1 hour 12 minutes
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Answer key — Math Kangaroo practice
Each wrong choice carries the thinking that produces it. When a student picks C, this is what they were doing.
1.C — 200 gKA-0151Ratio as parts of a whole
AI worked out the part size correctly and then answered for the sugar instead of the flour.
BI split the 320 grams into two halves instead of into eight equal parts.
DI took three fifths of 320 rather than five eighths, using the ratio numbers as a fraction of each other.
EI divided 320 by the 5 in the ratio and stopped, treating 5 as the number of parts.
2.C — 100 degreesKA-0152Angles on lines, in triangles, in polygons
AI found the smaller of the two unknown angles and stopped before doubling it.
BI split the remaining 150 degrees into two equal halves instead of a one-to-two split.
DI split the remainder evenly into 75 and 75, then doubled one of them.
EI assumed that the largest angle in a triangle like this must be a right angle.
3.B — 76.80 poundsKA-0153Percentages and simple discounts
AI assumed a 20 percent rise and a 20 percent fall must cancel because the percentages match.
CI applied only the fall and forgot the rise.
DI got the size of the change right but the direction wrong.
EI applied only the rise and forgot the fall.
4.A — 4KA-0154Inclusion–exclusion with two sets
BI found how many students play at least one of the two and answered with that instead.
CI added 18 and 15 to get 33, subtracted the 30 in the class, and used the 3 left over.
DI removed the 7 from both groups and subtracted 11 and 8 from 30, taking the overlap away twice.
EI answered with the number who play both, which is what the question gave me rather than what it asked for.
5.B — 30 cmKA-0155Scaling and similar figures
AI kept the difference of 4 cm between the two sides instead of keeping their ratio.
CI added 20 to 12 rather than scaling 12.
DI used the scale factor upside down and multiplied 12 by 8/20 instead of 20/8.
EI multiplied 12 by 1.5, the ratio between the original sides, instead of by the enlargement factor.
6.A — 64KA-0156Growth patterns and figurate numbers
BI gave the number of dots in the eighth ROW instead of the whole figure.
CI added the row numbers 1 through 8 instead of the odd numbers of dots.
DI multiplied 8 rows by 9, using a rough average row that is one too large.
EI counted the rows starting from zero and used the ninth square number.
7.B — 7KA-0157The pigeonhole principle
AI thought that one more than the number of colours must give three of a kind, which only guarantees a PAIR.
CI got to two of each colour, then added one more for each colour instead of one more in total.
DI assumed the worst case meant emptying the largest pile of 12 reds first.
EI answered with the number of socks I want rather than the number I must take to be sure of them.
8.B — 9KA-0158Last-digit behavior of products and powers
AI used the first entry of the cycle because 2026 is even, without working out where in the cycle it lands.
CI counted the cycle starting from zero, so a remainder of 2 put me one place too far along.
DI assumed a power that large must end in 1.
EI multiplied 3 by 2 and used the last digit of that.
9.A — 2 hours 24 minutesKA-0159Combined work rates
BI averaged the two times, but two taps together must be faster than either one alone.
CI added the two times, which would be right for filling two tanks one after the other.
DI halved the smaller of the two times, guessing that two taps must simply be twice as fast as one.
EI found 2 hours 24 minutes correctly and then halved it a second time.