Pick what you want, print the page. The answer key comes with it, on its own sheet, and it tells you the mistake behind every wrong choice — not just which letter is right.
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1.Today is Tuesday. What day of the week will it be in 100 days?[3]
AMonday
BTuesday
CWednesday
DThursday
EFriday
2.A jacket costs 80 euros. Its price is reduced by 25%. What is the new price?[3]
A20
B40
C45
D55
E60
3.One bus leaves every 12 minutes and another every 18 minutes. They leave together at 9:00. When do they next leave together?[3]
A9:06
B9:30
C9:36
D9:54
E12:36
4.In the number 4073, what is the value of the digit 7?[3]
A3
B7
C70
D700
E4000
5.What is 1 + 2 + 3 + ... + 20?[3]
A190
B200
C210
D220
E420
6.Each shape stands for a whole number. A triangle plus a triangle plus a triangle is 12, and a triangle plus a square is 9. What is the square?[3]
A3
B4
C5
D6
E8
7.Which of these fractions lies between one third and one half?[3]
A1/5
B1/4
C2/5
D3/5
E2/3
8.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
9.What is the remainder when 2 to the power 50 is divided by 7?[3]
A1
B2
C4
D6
E0
10.What is the remainder when 7 to the power 100 is divided by 5?[3]
A1
B2
C3
D4
E0
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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.D — ThursdayKA-0021Remainders and modular cycles
AI found the remainder 2 but counted the two days starting from today rather than starting from tomorrow.
BI divided 100 by 7 and used the quotient of 14, treating the leftover days as if there were none.
CI remembered there was a remainder but used a remainder of 1 instead of working it out.
EI counted 100 divided by 7 as 14 remainder 3 instead of remainder 2.
2.E — 60KA-0026Percentages and simple discounts
AI worked out the size of the discount and gave that as the new price instead of subtracting it.
BI treated a quarter off as half off and took the price down to 40.
CI applied the 25% reduction twice, taking 80 down to 60 and then 60 down to 45.
DI subtracted 25 euros rather than 25 percent, treating the percentage as an amount of money.
3.C — 9:36KA-0041Factors, multiples, LCM and GCD by listing
AI found the greatest common divisor of 12 and 18 instead of the least common multiple.
BI added the two intervals together rather than looking for a time that is a multiple of both.
DI found a common multiple but not the least one, landing on a later coincidence.
EI multiplied the two intervals together instead of finding their least common multiple.
4.C — 70KA-0055Place value and digit positions
AI gave the last digit of the number instead of looking at the 7 at all.
BI gave the digit itself rather than what it is worth in the position it sits in.
DI counted the positions from the left, so I read the 7 as being in the hundreds place.
EI gave the value of the largest digit instead of the value of the 7.
5.C — 210KA-0057Clever regrouping (pair to round numbers)
AI paired the numbers from the outside in but left the 20 out of every pair, so I added only up to 19.
BI estimated the total as a round number instead of working it out.
DI used eleven pairs of 20 instead of ten pairs of 21.
EI multiplied 20 by 21 and forgot that pairing counts every number twice.
6.C — 5KA-0061Operation puzzles and cryptarithms
AI solved for the triangle and gave that instead of the square.
BI found the triangle is 4 and gave that number, without going on to the second equation.
DI halved the 12 instead of dividing it by the three triangles.
EI subtracted the wrong way round, taking 9 from a number instead of taking the triangle from 9.
7.C — 2/5KA-0141Number lines and betweenness
AI compared the bottom numbers and assumed a bigger denominator means a bigger fraction.
BI saw that 4 lies between 3 and 2 and assumed one quarter therefore lies between the two fractions.
DI checked that it is bigger than one third but never checked it against one half.
EI compared the top numbers only and ignored what the bottoms do to the size.
8.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.
9.C — 4KA-0161Remainders and modular cycles
AI assumed the cycle ends on 1 at every exponent that is a multiple of 2.
BI used a remainder of 1 rather than 2 when dividing 50 by 3.
DI doubled my way to 2 cubed = 8 and used 8 minus 2.
EI assumed a large power of 2 must eventually be divisible by 7.
10.A — 1KA-0169Remainders and modular cycles
BI reduced 7 to 2 correctly but then used a remainder of 1 when dividing 100 by 4.
CI read the cycle backwards and landed on the entry before the right one.
DI used 100 divided by 4 giving 25 and read off the 25th entry as if the cycle had length 25.
EI assumed a power that large must be divisible by 5.