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1. A number is 4 more than a third of itself. Which of the choices is that number?[5]
2. What is the value of (1 - 1/2) x (1 - 1/3) x (1 - 1/4) x ... x (1 - 1/10)?[5]
3. 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 backwards4. You reach the ten 5-point questions with 18 minutes left. What is the best plan?[5]
A Start at the first and work through in order until time runs outB Read all ten quickly, pick the two or three that look most doable, and fill in every answer before the endC Spend the whole time on the last question, since it is the hardestD Answer the ones with the shortest statementsE Divide the time evenly, about 1.8 minutes eachKangaroo 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. B — 6 KA-0045 Back-solve from the answer choices
A I tested the smallest choice first and stopped at the first one that felt about right.C I read a third of itself as three times itself and solved the wrong equation.D I reversed the comparison, finding a number whose third is 4 less than itself in the wrong direction.E I picked the largest choice because dividing by three made me expect a big starting number.2. A — 1/10 KA-0125 Spot the trick vs. decide to grind
B I cancelled the chain but stopped one factor early, leaving a 9 on the bottom.C I worked out the first bracket and assumed the rest made no difference.D I gave the last bracket on its own instead of the whole product.E I assumed everything cancels completely, leaving nothing behind.3. 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.4. B — Read all ten quickly, pick the two or three that look most doable, and fill in every answer before the end KA-0130 Managing the 5-point block
A I worked in order, so a hard early question could eat the time meant for easier later ones.C I assumed the hardest question is worth the most, but every question in this block scores the same.D I used length as a proxy for difficulty, which is not reliable in this block.E I spread the time equally, which is too little for the questions I could do and wasted on the ones I could not.