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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.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
2.A photograph is enlarged so that each side becomes 3 times as long. How many times bigger is its area?[4]
A3 times
B6 times
C9 times
D12 times
E27 times
3.One tap fills a tank in 6 hours and another fills it in 3 hours. With both running, how long does the tank take to fill?[4]
A1 hour
B2 hours
C4.5 hours
D9 hours
E3 hours
4.A square of side 6 cm is cut along a midline into two identical rectangles. What is the perimeter of one of them?[4]
A12
B15
C18
D24
E36
5.A sequence starts at 3. Each term after that is double the one before it, minus 1. What is the sixth term?[4]
A17
B33
C65
D96
E129
6.Dots are arranged in triangles: 1 dot, then 3, then 6, then 10, and so on. How many dots does the tenth triangle have?[4]
A36
B45
C55
D66
E100
7.A train covers 150 km at a steady 60 km per hour. How many minutes does the journey take?[4]
A25
B90
C150
D210
E9000
8.Two circles touch on the outside. One has a radius of 3 cm and the other a radius of 5 cm. How many centimetres apart are their centres?[4]
A2
B4
C8
D15
E16
9.What is the smaller angle between the hands of a clock at exactly 4 o'clock?[4]
A30
B60
C90
D120
E240
10.What is the units digit of 3 multiplied by itself 100 times, that is 3 to the power 100?[4]
A1
B3
C7
D9
Eit cannot be found without a calculator
Math Kangaroo Star · https://kangaroo-atlas.vercel.app · seed 2 · CC BY-NC-SA 4.0 · Independent project, not affiliated with Math Kangaroo in USA, NFP.
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 — 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.
2.C — 9 timesKA-0042Scaling and similar figures
AI applied the length scale factor straight to the area.
BI doubled the scale factor because area involves two dimensions, instead of squaring it.
DI multiplied the scale factor by four, as though area scaled with the number of sides.
EI cubed the scale factor, which is the rule for volume rather than area.
3.B — 2 hoursKA-0044Combined work rates
AI subtracted the two times from each other rather than adding the rates.
CI averaged the two times, which would only be right if the taps took turns instead of running together.
DI added the two times together, which makes the tank slower with two taps than with one.
EI used the faster tap's time alone and ignored the contribution of the slower one.
4.C — 18KA-0084Area by dissection and rearrangement
AI added the two different side lengths without doubling for the opposite pair.
BI halved the square's perimeter of 24 and adjusted by three, treating the cut as if it removed length.
DI gave the perimeter of the whole square instead of one of the pieces.
EI gave the area of the square rather than the perimeter of a piece.
5.C — 65KA-0103Recursive rules
AI stopped at the fourth term, counting the starting number as the first step rather than the first term.
BI generated one term too few, giving the fifth term instead of the sixth.
DI doubled six times and subtracted 1 only once at the end.
EI generated one term too many, giving the seventh instead of the sixth.
6.C — 55KA-0107Growth patterns and figurate numbers
AI stopped at the eighth triangle, losing count while adding the rows.
BI gave the ninth triangle instead of the tenth, being one row short.
DI gave the eleventh triangle, adding one row too many.
EI squared the position number, which describes square patterns rather than triangular ones.
7.C — 150KA-0117Rate, time, distance
AI divided 150 by 60 and read the answer as minutes rather than hours.
BI used 1.5 hours instead of 2.5, dividing 90 by 60 rather than 150.
DI converted 2.5 hours as two hours and fifty minutes.
EI multiplied the distance by 60 instead of dividing, then converted.
8.C — 8KA-0147Circles: radius, diameter, and touching circles
AI subtracted the radii, which is the answer when one circle sits inside the other.
BI averaged the two radii instead of adding them.
DI multiplied the radii together rather than adding them.
EI added the two diameters instead of the two radii.
9.D — 120KA-0148Clock geometry: hands, angles, times
AI gave the angle for a single hour mark rather than the four marks between the hands.
BI counted two hour marks instead of four.
CI assumed any gap of a few hours is a right angle, as it is at three o'clock.
EI measured the angle the long way round the clock face instead of the smaller one.
10.A — 1KA-0149Last-digit behavior of products and powers
BI assumed every power of 3 ends in 3.
CI found the cycle 3, 9, 7, 1 but counted its positions from zero, landing one step early.
DI used a remainder of 2 instead of 0 when dividing 100 by the cycle length of 4.
EI assumed a number this large has no reachable last digit, rather than looking for a repeat.