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1. A jacket costs 80 euros. Its price is reduced by 25%. What is the new price?[3]
2. A sequence begins 7, 11, 15, 19, and continues with the same constant step. What is the 30th term?[3]
3. Two students are chosen from a group of six to represent the class. How many different pairs are possible?[4]
4. What is the units digit of 7 multiplied by itself 2026 times, that is 7 to the power 2026?[5]
A it cannot be found without a calculatorB 1C 3D 7E 95. You are 20 minutes into a 75-minute paper of 30 questions, still on question 9, and four minutes in with no progress. What is the best move?[5]
A Keep going — four minutes are already investedB Answer it with your best guess, mark it, and move onC Skip it, leave it blank, and come back at the endD Go back and re-check questions 1 to 8E Jump to question 30 and work backwardsKangaroo 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. 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.2. A — 123 KA-0160 Arithmetic sequences and the nth term
B I multiplied the step by 30 instead of by 29, forgetting that the first term needs no steps.C I used 4 times 30 and forgot to add the starting value.D I added 28 steps instead of 29, counting the gaps one short.E I treated the first term as the step and used 7 times 30 minus something close.3. B — 15 KA-0074 Selections of a few objects
A I doubled the group size instead of counting pairs.C I allowed a student to be paired with themselves, adding six impossible pairs.D I counted each pair twice, once in each order, and forgot to halve.E I multiplied 6 by 6, counting every ordered pair including a student with themselves.4. E — 9 KA-0037 Last-digit behavior of products and powers
A I assumed a number this large has no reachable last digit and gave up on the cycle.B I found the cycle 7, 9, 3, 1 but used a remainder of 0 when the remainder is actually 2.C I found the cycle but counted its positions starting at zero, shifting my answer along by one.D I assumed the units digit of any power of 7 is always 7.5. B — Answer it with your best guess, mark it, and move on KA-0126 Time triage: now, later, or guess
A I let the time already spent decide, but that time is gone whatever I do next.C I moved on but left a blank, which scores nothing if I never get back to it.D I spent time re-reading work I had no reason to doubt, while 21 unseen questions waited.E I assumed the hardest questions are the best use of time, when the unseen easy ones are worth the same each.