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1.On the number line shown, the marks are equally spaced. What number does the arrow point to?[3]
Text description of the figure
A number line with equally spaced tick marks. The leftmost tick is labelled 0 and the rightmost is labelled 60, with five unlabelled ticks evenly spaced between them. An arrow points to the fourth tick from the left.
A4
B24
C30
D40
E50
2.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
3.In the number 4073, what is the value of the digit 7?[3]
A3
B7
C70
D700
E4000
4.What is 1 + 2 + 3 + ... + 20?[3]
A190
B200
C210
D220
E420
5.Which of these fractions lies between one third and one half?[3]
A1/5
B1/4
C2/5
D3/5
E2/3
6.The mean of five numbers is 12. One of the numbers is removed and the mean of the remaining four is 11. What number was removed?[4]
A1
B11
C12
D16
E23
7.What is the remainder when 2 to the power 30 is divided by 7?[4]
A1
B2
C4
D5
E6
8.The two digits of a number are swapped and the number gets bigger by 36. Which of these could be the number?[4]
A13
B15
C24
D41
E62
9.What is 2 + 4 + 6 + ... + 100?[4]
A1275
B2450
C2500
D2550
E5100
10.A and B are different digits. The two-digit number AB added to the two-digit number BA gives 132. What is A + B?[5]
A3
B6
C11
D12
E13
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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 — 30KA-0006Number lines and betweenness
AI counted the tick marks and gave the position number instead of reading the value on the scale.
BI worked out that each gap is worth 10 but then counted only as far as the tick before the arrow.
DI counted the tick marks rather than the gaps between them, so every gap came out one step too small.
EI counted the gaps from the right-hand end instead of from zero.
2.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.
3.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.
4.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.
5.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.
6.D — 16KA-0033Means, and working backwards from a mean
AI subtracted the two means from each other and gave the difference as the removed number.
BI assumed the removed number must be the new mean, since the mean dropped to 11.
CI assumed removing a number equal to the old mean is what changes the mean.
EI added the two totals instead of subtracting one from the other.
7.A — 1KA-0053Remainders and modular cycles
BI found the cycle 2, 4, 1 but read the remainder of 30 divided by 3 as one instead of zero.
CI counted the cycle positions from zero, which shifted my answer one step along.
DI divided 30 by 7 and used that remainder rather than the remainder of the powers.
EI assumed the remainder would be one less than the divisor because the power is large.
8.B — 15KA-0056Place value and digit positions
AI checked that the digits differ and stopped, without working out how much the swap actually changes the number.
CI saw a difference of 2 between the digits and expected that to give a change of 36.
DI ignored the direction: swapping this number makes it smaller, not bigger.
EI picked a number whose digits differ by 4 without noticing that the larger digit is already in front.
9.D — 2550KA-0058Clever regrouping (pair to round numbers)
AI found the sum of 1 to 50 and forgot that every term here is twice as big.
BI used 49 pairs instead of 25, losing one pair from the count.
CI estimated the answer as a round number rather than pairing properly.
EI paired the terms but forgot that pairing counts every number twice, so I never halved.
10.D — 12KA-0060Operation puzzles and cryptarithms
AI added the digits of 132 instead of working out what A and B must be.
BI found A + B correctly and then halved it, as if the question wanted one digit.
CI spotted the 11 in the working and gave that instead of the sum it multiplies.
EI found a pair of digits by trial and misadded them by one.