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1.A sequence begins 7, 11, 15, 19, and continues with the same constant step. What is the 30th term?[3]
A123
B127
C120
D119
E137
2.What is the remainder when 2 to the power 50 is divided by 7?[3]
A1
B2
C4
D6
E0
3.Two towns are 300 km apart. A car leaves each town at the same moment driving toward the other, one at 60 km/h and the other at 90 km/h. How long until they meet?[3]
A2 hours
B3 hours 20 minutes
C4 hours
D5 hours
E1 hour
4.A club has 8 members. In how many ways can a group of 3 be chosen to attend a conference, if the three places are all the same?[4]
A56
B336
C24
D112
E28
5.Two triangles are similar. The sides of the smaller are 3/5 as long as the matching sides of the larger. The smaller triangle has area 18 square cm. What is the area of the larger triangle?[4]
A30 sq cm
B50 sq cm
C45 sq cm
D10.8 sq cm
E90 sq cm
6.Four litres of a solution that is 25 percent acid are mixed with six litres of a solution that is 50 percent acid. What percentage of the mixture is acid?[4]
A40 percent
B37.5 percent
C75 percent
D35 percent
E30 percent
7.Six friends sit around a circular table. Two seatings count as the same if one can be turned into the other by rotating the table. How many genuinely different seatings are there?[5]
A120
B720
C36
D60
E24
8.The numbers 1 to 10 are written on a board. You repeatedly rub out any two of them and write down their positive difference instead, until a single number is left. What can be said about that final number?[5]
AIt is always odd
BIt is always even
CIt can be either odd or even
DIt is always zero
EIt is always 1
9.An ordinary six-sided die is rolled three times. What is the probability that at least one roll shows a six?[5]
A91/216
B1/2
C125/216
D3/216
E1/6
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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.A — 123KA-0160Arithmetic sequences and the nth term
BI multiplied the step by 30 instead of by 29, forgetting that the first term needs no steps.
CI used 4 times 30 and forgot to add the starting value.
DI added 28 steps instead of 29, counting the gaps one short.
EI treated the first term as the step and used 7 times 30 minus something close.
2.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.
3.A — 2 hoursKA-0162Rate, time, distance
BI used only the slower car's speed and divided 300 by 90 the wrong way round.
CI averaged the two speeds to 75 km/h and divided 300 by it, which ignores that both cars move at once.
DI divided 300 by 60, using only the slower car.
EI halved the distance to 150 and then divided by 150, applying the closing speed twice.
4.A — 56KA-0163Selections of a few objects
BI counted ordered selections, so I counted the same three people once for every order they could stand in.
CI multiplied the 8 members by the 3 places, which counts something quite different from a selection.
DI divided the 336 ordered selections by 3 instead of by 3 factorial.
EI chose 2 people rather than 3.
5.B — 50 sq cmKA-0164Scaling and similar figures
AI scaled the area by 5/3, using the side ratio directly instead of its square.
CI multiplied the area by 2.5, halfway between the side ratio and its square.
DI scaled by 3/5 instead of 5/3, making the larger triangle smaller.
EI multiplied by 5 and ignored the 3 in the ratio entirely.
6.A — 40 percentKA-0165Mixtures and weighted averages
BI averaged 25 and 50 without weighting by how much of each solution there was.
CI added the two percentages together, which cannot be right because a mixture can never be stronger than its strongest ingredient.
DI weighted the percentages by the wrong volumes, giving the 25 percent solution the larger share.
EI used only the acid from the weaker solution and spread it over all ten litres.
7.A — 120KA-0166Counting up to symmetry
BI counted every arrangement in a row, so each circular seating got counted once for every rotation.
CI divided 720 by 20 or some other number instead of by the 6 rotations.
DI divided by 12, treating reflections as identical too, though the question only allows rotations.
EI fixed two people rather than one, dividing by an extra factor.
8.A — It is always oddKA-0167Parity arguments
BI checked the parity of the count of numbers rather than of their sum.
CI tried two examples, got different answers, and concluded nothing is forced.
DI assumed differences must shrink all the way to nothing.
EI found one sequence of moves ending at 1 and assumed every sequence must.
9.A — 91/216KA-0168Complementary counting
BI added 1/6 three times, which counts the overlapping cases more than once and would exceed 1 for seven rolls.
CI worked out the probability of NO six and forgot to subtract it from 1.
DI found the probability of three sixes instead of at least one.
EI gave the probability for a single roll and ignored that there are three.