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1. In a triangle, one angle is 90 degrees and another is 35 degrees. What is the third angle?[3]
A 35 degreesB 45 degreesC 55 degreesD 65 degreesE 145 degrees2. A jacket costs 80 euros. Its price is reduced by 25%. What is the new price?[3]
3. Eight people meet and everyone shakes hands with everyone else exactly once. How many handshakes take place?[3]
4. One bus leaves every 12 minutes and another every 18 minutes. They leave together at 9:00. When do they next leave together?[3]
A 9:06B 9:30C 9:36D 9:54E 12:365. Three angles of a quadrilateral are 80, 95 and 110 degrees. What is the fourth angle?[3]
6. A bag of flour holds 2.5 kg. 1750 g are used. How many grams are left?[3]
7. Which of these fractions lies between one third and one half?[3]
8. Three more than twice a number is 19. What is the number?[3]
9. A counter sits at the point (3, 5) on a grid. It moves 4 squares right and 2 squares down. Where is it now?[3]
A (1, 3)B (1, 7)C (5, 3)D (7, 7)E (7, 3)10. Suppose it is true that some birds cannot fly. Which of these must also be true?[3]
A No birds can flyB All birds can flyC Most birds cannot flyD Exactly one bird cannot flyE Not all birds can flyKangaroo 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 — 55 degrees KA-0022 Angles on lines, in triangles, in polygons
A I assumed the triangle was isosceles because it had a right angle, so I repeated the 35.B I assumed a right-angled triangle always has two 45 degree angles.D I subtracted 35 from 100 instead of from 90, mixing the angle sum up with a round number.E I subtracted only the 35 from 180 and forgot to take off the right angle as well.2. E — 60 KA-0026 Percentages and simple discounts
A I worked out the size of the discount and gave that as the new price instead of subtracting it.B I treated a quarter off as half off and took the price down to 40.C I applied the 25% reduction twice, taking 80 down to 60 and then 60 down to 45.D I subtracted 25 euros rather than 25 percent, treating the percentage as an amount of money.3. B — 28 KA-0035 Handshakes and pairs
A I doubled the number of people, as if each person made two handshakes in total.C I let each person shake hands with all eight people including themselves before halving.D I multiplied 8 by 7 and forgot that each handshake was counted from both sides.E I multiplied 8 by 8, counting every ordered pair including a person with themselves.4. C — 9:36 KA-0041 Factors, multiples, LCM and GCD by listing
A I found the greatest common divisor of 12 and 18 instead of the least common multiple.B I added the two intervals together rather than looking for a time that is a multiple of both.D I found a common multiple but not the least one, landing on a later coincidence.E I multiplied the two intervals together instead of finding their least common multiple.5. B — 75 KA-0088 Angles on lines, in triangles, in polygons
A I added the three angles wrongly, getting 295 instead of 285.C I used an angle sum of 370, mis-remembering the total for a quadrilateral.D I repeated one of the given angles instead of computing the missing one.E I used the triangle's 180 degrees and then adjusted, rather than the quadrilateral's 360.6. C — 750 KA-0113 Unit conversion
A I worked in kilograms and gave the answer in kilograms when grams were asked for.B I converted 2.5 kg to 250 g rather than 2500 g.D I subtracted 1750 from 3000, mis-converting 2.5 kg as three thousand grams.E I subtracted without converting at all, taking 2.5 away from 1750.7. C — 2/5 KA-0141 Number lines and betweenness
A I compared the bottom numbers and assumed a bigger denominator means a bigger fraction.B I saw that 4 lies between 3 and 2 and assumed one quarter therefore lies between the two fractions.D I checked that it is bigger than one third but never checked it against one half.E I compared the top numbers only and ignored what the bottoms do to the size.8. A — 8 KA-0144 Translating a sentence into an equation
B I subtracted 8 from 19 rather than working the two steps backwards.C I subtracted the 3 from 19 and gave that without halving it.D I added the 3 to 19 instead of subtracting it.E I doubled 19 and added 3, applying the machine forwards instead of undoing it.9. E — (7, 3) KA-0145 Grid coordinates and lattice reasoning
A I moved left instead of right, subtracting the 4 rather than adding it.B I moved left and up, reversing both directions.C I swapped the two coordinates round before moving.D I moved up instead of down, adding the 2 rather than subtracting it.10. E — Not all birds can fly KA-0146 Reading a logical statement precisely
A I read some cannot as meaning none can, which is a far stronger claim.B I chose a statement that directly contradicts the one I was given.C I read some as meaning a majority, when it only guarantees at least one.D I read some as meaning exactly one, when it means at least one.