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1. A rectangle has a perimeter of 20 cm. One of its sides is 6 cm. What is its area in square centimetres?[3]
2. A pattern of tiles repeats: black, black, white. What colour is the 100th tile?[3]
A blackB whiteC it depends where you start countingD grey, because the pattern breaksE there is no 100th tile3. Two apples balance three pears. One apple weighs 90 grams. How many grams does one pear weigh?[4]
4. Ana says: "Bo and I are both liars." Each child is either always truthful or always a liar. Who is telling the truth?[4]
A Ana onlyB Bo onlyC both of themD neither of themE it cannot be decided5. A code uses the letters A, B and C, each exactly once. How many codes do not start with A?[5]
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1. B — 24 KA-0083 Perimeter and area of rectilinear shapes
A I subtracted 6 from 20 and gave that, which is neither a side nor an area.C I took the other side to be 20 minus 6 divided by 2, forgetting there are two sides of each length.D I multiplied the perimeter by half the known side instead of finding the missing side first.E I used 16 as the other side, taking 20 minus 6 plus 2 rather than working from the perimeter properly.2. A — black KA-0108 Repeating cycles and position mod n
B I got a remainder of 1 but read the last colour of the repeat rather than the first.C I thought the pattern had no fixed first tile, even though tile one is given.D I assumed a repeating pattern must eventually change.E I assumed the pattern runs only for as many tiles as one repeat contains.3. B — 60 KA-0093 Weighing and balance puzzles
A I halved the apple's weight, as if one apple balanced two pears.C I assumed a pear must weigh the same as an apple because the two sides balance.D I multiplied the apple's weight by three halves the wrong way round, making the pear heavier.E I gave the total weight of the two apples rather than the weight of one pear.4. B — Bo only KA-0096 Truth-tellers and liars
A I took Ana's statement at face value without checking whether a truthful person could say it.C I decided nobody was lying without testing Ana's statement against that assumption.D I believed Ana's statement even after concluding she was a liar, which is what a liar's statement cannot be.E I gave up when Ana's statement looked circular, instead of testing one assumption all the way through.5. C — 4 KA-0140 The multiplication principle
A I counted the codes that do start with A rather than the ones that do not.B I counted the letters available for the first position instead of counting whole codes.D I counted every arrangement of the three letters and forgot the restriction.E I allowed letters to repeat, which the words each exactly once rule out.