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Problem solving

Problem solving

Selecting methods, combining information, troubleshooting, and reaching practical solutions.

Lesson

Start with the shared skill lesson — objectives, worked examples, and glossary.

Open skill lesson

Diagnostic practice

100 questions published across 10 sections. Every question is written for this skill specifically — no universal or borrowed bank is substituted. Answers are checked on this device only, and the result is an educational practice band for that exercise, never a clinical, diagnostic, or IQ-style score.

Choose a section

This bank has 10 themed sections and 100 questions in total, ordered so the earlier sections are the gentler ones. Sit a single section, or work through the whole bank in one go. Nothing here is timed — the minutes are only a guide.

  1. 1. Multi-step foundations10 questions · about 6 min, untimed
  2. 2. Rates, ratios and fair shares10 questions · about 6 min, untimed
  3. 3. Working backwards10 questions · about 6 min, untimed
  4. 4. Constraints and elimination10 questions · about 6 min, untimed
  5. 5. Finding the rule10 questions · about 6 min, untimed
  6. 6. Planning and scheduling10 questions · about 6 min, untimed
  7. 7. Trade-offs and best choices10 questions · about 6 min, untimed
  8. 8. Multi-stage processes10 questions · about 6 min, untimed
  9. 9. Arrangements, counting and chance10 questions · about 6 min, untimed
  10. 10. Integrated challenge problems10 questions · about 6 min, untimed

Section 1: Multi-step foundations

Warm up by combining two or three simple facts into a single answer.

1. Three coworkers restock shared printer paper on different cycles: every 2 days, every 3 days, and every 4 days. All three restocked together today. In how many days will all three restock on the same day again?
2. A delivery van can carry either 40 small boxes or 25 large boxes (space scales proportionally by count). It currently carries 16 small boxes. How many large boxes can it still fit?
3. A 4-character password uses only the digits 1, 2, 3, and 4, with no digit repeated. How many different passwords are possible?
4. Item A sells 8 units per day from a 40-unit stock; Item B sells 5 units per day from a 40-unit stock. Assuming no restocking, which item runs out first, and by how many days sooner?
5. A task force needs exactly one representative from each of three departments. Sales has 4 possible reps, Engineering has 3, and Support has 2. How many different three-person task forces are possible?
6. Four friends — Sam, Priya, Marcus, and Yuki — sit in a row of four seats numbered 1 to 4, left to right. Priya is not at either end. Sam is immediately to the left of Priya. Marcus is in seat 4. Yuki is not in seat 1. Which seat is Yuki in?
7. A cinema ticket costs £9 and a snack combo costs £6. Ana buys 2 tickets and 1 combo, paying with £30. How much change does she receive?
8. A lift can carry at most 600 kg. Four crates weigh 150 kg, 180 kg, 120 kg, and 200 kg. Which single crate should be left behind so the other three weigh as much as possible without exceeding the limit?
9. Tea bags come in boxes of 40. The office uses 25 tea bags per week. How many full weeks will 2 boxes last?
10. A bus departs every 15 minutes starting at 09:00. Leo arrives at the stop at 09:50. How long must he wait for the next bus?

0 of 10 answered

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