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1. Toma spent 4 euros, then spent half of what was left, and now has 6 euros. How much did she start with?[3]
2. Two apples balance three pears. One apple weighs 90 grams. How many grams does one pear weigh?[4]
3. All the red boxes are heavy. Box X is not heavy. What must be true?[4]
A Box X is redB Box X is not redC Box X is blueD Some red boxes are lightE Nothing can be said about box X4. Cards numbered 1 to 10 lie face up. You take any six of them. Must two of your cards add up to 11?[4]
A Yes, alwaysB Yes, but only if you take the card numbered 1C No, six cards can be chosen that avoid itD Only if the six numbers are consecutiveE It cannot be decided without knowing the cards5. Ana says "Bo is lying." Bo says "Cal is lying." Cal says "Ana and Bo are both lying." How many of the three are telling the truth?[5]
A 0B 1C 2D 3E it cannot be decidedKangaroo Atlas · https://kangaroo-atlas.vercel.app · seed 1 · CC BY-NC-SA 4.0 · Independent project, not affiliated with Math Kangaroo in USA, NFP.
1. C — 16 KA-0050 Working backwards
A I added the 4 and the 6 and stopped, forgetting to undo the halving.B I doubled the 6 first and then added the 4, reversing the steps in the wrong order.D I doubled the total at the end rather than doubling only the amount left after the first spend.E I doubled twice because spending half felt like it needed undoing more than once.2. 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.3. B — Box X is not red KA-0099 Reading a logical statement precisely
A I read the rule backwards, as if being heavy were what makes a box red.C I assumed not red must mean one particular other colour, when the rule says nothing about which.D I contradicted the rule I was given rather than applying it to box X.E I decided one fact could not settle anything, without testing what would follow if X were red.4. A — Yes, always KA-0102 Informal proof by contradiction
B I found one pair that works and assumed the argument depended on that particular card.C I tried a couple of selections, did not find a pair, and stopped looking.D I looked for a pattern in the numbers rather than at how many pairs there are to avoid.E I thought the answer depended on which six were taken, when the counting settles it for every choice.5. B — 1 KA-0017 Truth-tellers and liars
A I assumed everyone could be lying at once without checking that Cal's statement would then be true.C I found one consistent truth-teller and added another without testing whether both could hold together.D I assumed everyone was telling the truth without noticing that Ana's statement then contradicts Bo's.E I gave up after one assumption led to a contradiction, instead of trying the other assumption.