problem-solving-s01-q01
The next joint restock day is the least common multiple of 2, 3, and 4, which is 12.
This is untimed educational practice for one cognitive skill. It is not a clinical, diagnostic, employment, or professionally recognized assessment, and it does not produce an IQ score or credential.
The next joint restock day is the least common multiple of 2, 3, and 4, which is 12.
16 of 40 small boxes uses 40% of the space, leaving 60% free: 60% of 25 large boxes = 15.
With 4 distinct digits and no repeats, this is 4! = 24 arrangements.
Item A lasts 40 ÷ 8 = 5 days; Item B lasts 40 ÷ 5 = 8 days. A runs out 3 days sooner.
Multiply the independent choices: 4 × 3 × 2 = 24.
Priya must be in seat 2 or 3. If Priya were in seat 3, Sam would be in seat 2, forcing Yuki into seat 1, which is excluded. So Priya is in seat 2, Sam in seat 1, Marcus in seat 4, and Yuki in seat 3.
Work out the total first: 2 × £9 + £6 = £24. Then subtract from the payment: £30 − £24 = £6.
All four crates total 650 kg: 50 kg over the limit. Removing the lightest crate that clears the excess (120 kg) leaves 530 kg, the heaviest legal load.
Two boxes hold 80 tea bags, and 80 ÷ 25 = 3.2, so only 3 complete weeks are covered before the supply runs short.
List the departures: 09:00, 09:15, 09:30, 09:45, 10:00. Arriving at 09:50, the next bus is at 10:00. A 10-minute wait.
The ratio has 2 + 3 + 4 = 9 parts, so one part is £45 ÷ 9 = £5. The middle share is 3 parts: £15.
Divide the total by the rate: 300 ÷ 12 = 25 minutes.
The mix has 1 + 4 = 5 equal parts, so each part is 2,000 ÷ 5 = 400 ml, and concentrate is exactly one part.
Halving the workforce doubles the time when rates are equal: 6 × 2 = 12 hours.
250 km is 2.5 blocks of 100 km, so fuel scales the same way: 6 × 2.5 = 15 litres.
Standard pay is 35 × £14 = £490. The overtime rate is £21 per hour, adding 4 × £21 = £84, for £574 in total.
6 cm × 50,000 = 300,000 cm. Converting units step by step: 300,000 cm = 3,000 m = 3 km.
Find the per-person amount first: 300 ÷ 4 = 75 g. Then scale up: 75 × 10 = 750 g.
A 2 : 1 split makes 3 equal parts of £40 each; the younger grandchild gets one part.
The rate is 90 ÷ 45 = 2 litres per minute, so 30 minutes delivers 60 litres, leaving 90 − 60 = 30 litres to go.
Reverse the steps in reverse order: subtract 7 (31 − 7 = 24), then halve (24 ÷ 2 = 12).
Undo the last step first: before the coffee he had £6 + £4 = £10, which was half his money, so he started with £20.
Reverse each operation: add 5 back (7 + 5 = 12), then multiply by 3 (12 × 3 = 36).
The sale price is 80% of the original, so divide rather than add: £48 ÷ 0.8 = £60. Adding 20% of £48 back is the classic trap. Percentages of different bases are not interchangeable.
Work backwards by halving: half covered on day 11, a quarter covered on day 10.
Cara's 6 sweets were what remained after two halvings, i.e. a quarter of the jar, so the jar held 6 × 4 = 24.
Subtract the journey from the arrival: 14:20 − 2:45 = 11:35 actual departure. It left 10 minutes late, so the schedule said 11:25.
The new salary is 110% of the old one, so divide: £22,000 ÷ 1.1 = £20,000. Subtracting 10% of the new figure gives the wrong base.
Double once per round going backwards: 4 → 8 → 16 → 32 teams at the start.
Total pages printed = 340 + 340 + 195 = 875. Undo the day's printing: 5,230 − 875 = 4,355.
With lockers 2 and 3 assigned, elimination leaves only locker 1 for Finn.
Chain the clues into one order: Fatima before Dev before Eli, with Gus last, so the full order is Fatima, Dev, Eli, Gus.
One constraint removes rye and another removes white, leaving brown as the only workable option.
The violin is taken by Raj and the drums are ruled out for Kim, so the piano is the only instrument left for her.
Apply the clues in order: the second digit is 3, so the first is 6, and the third is 6 + 3 = 9, giving 639.
Number 5 is at the end of the lane, so its only neighbour is number 4. The red house must be there.
Linking the comparisons gives one chain: Tara, Uma, Vik, Wren from oldest to youngest. Uma sits second.
Starting with 4 eliminates 2144 and 1442; needing an odd final digit then eliminates 4412, leaving 4421.
With the cookbook fixed in position 4, the atlas–dictionary pair fits at positions 1–2 or 2–3. The second option forces the biography into position 1, which is forbidden, so the atlas is first.
Test each possibility against the 'exactly one true statement' condition. Only if Carl is responsible is a single statement true (Ben's denial); every other candidate makes two or more statements true.
Each term is double the previous term plus 1, so the next is 47 × 2 + 1 = 95.
Doubling 24 should give 48, not 45, and doubling 48 would correctly give 96, confirming 45 is the misfit.
Track whose turn it is: the last step was a subtraction, so the next is an addition, 11 + 4 = 15.
Each letter shifts forward by one place in the alphabet, so L, E, M, O, N become M, F, N, P, O.
These are the square numbers 1², 2², 3², …, the missing term is 5² = 25.
Apply the stated rule to the last two terms: 18 + 29 = 47.
The cycle has length 4, and 11 = 4 × 2 + 3, so the 11th shape matches the 3rd in the cycle: moon.
Each output is double the input plus 3 (check: 2 × 6 + 3 = 15), so 12 maps to 2 × 12 + 3 = 27.
The gaps grow by one each time: +1, +2, +3, +4, +5. The next gap is +6, giving 18 + 6 = 24.
Applying the rule to 9 gives 18 − (1 + 8) = 9 again, so 9 is a fixed point. Once reached, the sequence never changes.
Add the work and the break together: 3 hours 20 minutes after 15:30 is 18:50.
The stages are strictly sequential: 50 + 70 = 120 minutes, and two hours after 10:15 is 12:15.
Chop for 10 minutes, then start the 30-minute simmer and boil the pasta during it. Only the chopping and simmering lie on the critical path: 10 + 30 = 40 minutes.
A ends at 09:45; adding the 15-minute changeover lets B start at 10:00 and finish 45 minutes later, at 10:45.
From 08:00 to 18:00 is 600 minutes, which holds 600 ÷ 40 = 15 gaps between crossings, but counting both endpoints gives 15 + 1 = 16 crossings.
Drafting occupies this week's Tuesday, so the earliest available review slot is the following Tuesday, and publishing takes the day after, Wednesday of the following week.
Combine the walk and the margin: 35 minutes before 17:12 is 16:37.
They coincide at the least common multiple of 8 and 12 minutes, which is 24, so at 09:24.
After P's 3 days, Q and R run in parallel, so only the longer of the two matters: 3 + max(2, 4) = 7 days.
The morning block (09:00–12:00) is 180 minutes, fitting 9 appointments; the afternoon block (12:30–14:30) is 120 minutes, fitting 6, a total of 15.
Convert both to a unit price: £1.50 ÷ 6 = 25p per egg against £2.30 ÷ 10 = 23p per egg. Shop B wins.
Set the costs equal: £12 + £2 per GB matches £20 when the data charge is £8, i.e. at 4 GB.
Hourly parking costs £7.50 for 3 hours but £10 for 4 hours, so from 4 hours onward the £9 day ticket is cheaper.
Check each total against the limit: 9 + 7 = 16 kg uses the capacity exactly, while 7 + 6 + 4 = 17 kg is over and the rest carry less.
Work out each saving on the actual order value: 15% of £70 is £10.50, which beats the flat £10.
All the options use the same perimeter, so compare areas: the closer the sides are to equal, the larger the area, and 6 × 6 = 36 m² beats 35, 32, and 20.
Apply the hard constraint before comparing costs: only driving arrives within 45 minutes, so cost never comes into play.
Match the quantities first: 800 pages needs two singles at £36, so the £30 twin pack saves £6.
Use the deal as many times as possible: two 3-for-£2 bundles cover 6 cupcakes for £4, plus one single at 80p makes £4.80.
Count the gaps as well as the talks: 4 × 20 = 80 minutes of talks plus 3 × 5 = 15 minutes of breaks totals 95 minutes, 5 more than the slot allows.
Each unit takes 2 + 3 + 1 = 6 minutes from start to finish, so 5 units take 5 × 6 = 30 minutes.
Work with the net rate: 8 − 3 = 5 litres per minute, so 100 ÷ 5 = 20 minutes.
Three approvals take 3 × 2 = 6 days, and there are only 2 handovers between 3 approvers, adding 2 more days: 8 in total.
Apply fee then doubling, twice: (30 − 10) × 2 = 40, then (40 − 10) × 2 = 60. The order of operations within each level matters.
Take the percentages of the surviving quantity each time: 200 → 180 after the first check, then 5% of 180 (9 parts) fail, leaving 171.
Year one: £100 × 1.05 = £105. Year two starts with £105 + £100 = £205, which grows to £205 × 1.05 = £215.25: interest compounds on the running balance, not just the deposits.
Chain the percentages: 60% of 400 kg is 240 kg of paper, and 75% of that survives contamination checks, 0.75 × 240 = 180 kg.
The first two legs total exactly 4 minutes (1:55 + 2:05), leaving anything under 2 minutes for the final leg.
Follow the funnel stage by stage: 1,000 → 400 opens → 60 clicks → 30 sign-ups. Each percentage applies to the previous stage's result, not the original total.
Running 08:00–10:00 gives 60 widgets, then cleaning lasts until 10:15. From 10:15 to 12:00 is 105 minutes at 2 minutes per widget, 52 complete widgets, for 112 in total.
Independent choices multiply rather than add: 3 × 4 = 12 different lunches.
Three positions filled by three distinct letters gives 3 × 2 × 1 = 6 arrangements.
Plan for the worst case: the first two socks could be one of each colour, but a third sock must match one of them. There are only two colours.
List the outcomes that satisfy both conditions: 4, 6, and 8: three of the eight equally likely sectors, so 3/8.
Each of the 4 people shakes 3 hands, but that counts every handshake twice: 4 × 3 ÷ 2 = 6.
There are 5 × 4 = 20 ordered picks, but a committee ignores order, so halve it: 10 distinct pairs.
Use the complement: the chance of green is 3/10, so the chance of not-green is 1 − 3/10 = 7/10.
Fill the positions one at a time: 4 choices, then 3, then 2, giving 4 × 3 × 2 = 24 numbers.
Count ordered outcomes over the 36 possible rolls: 1+3, 2+2, and 3+1 give a total of 4, so the probability is 3/36 = 1/12.
Each floor contributes an independent two-way choice, so the possibilities multiply: 2 × 2 × 2 × 2 = 16 distinct groups.
Group the books in sixes: three groups cover 18 books while paying for only 15, and the last 2 books are paid in full, 17 paid × £8 = £136.
When two movers approach each other their speeds add: the gap closes at 30 km/h, so 60 km takes 2 hours.
Split the job into phases: the first 20 minutes drain 80 litres, leaving 160; the combined rate of 10 litres per minute then takes 16 more minutes, for 36 in total.
Avoid double-counting the overlap: coffee or tea drinkers number 22 + 17 − 9 = 30, so 40 − 30 = 10 drink neither.
By 10:30 the first train is 45 km ahead. The second closes that gap at 120 − 90 = 30 km/h, taking 1.5 hours, so it catches up at 12:00.
Let the son's age be s, so Anya is 3s. In 12 years: 3s + 12 = 2(s + 12), which solves to s = 12.
Reversing changes the value by 9 times the digit difference, so the digits differ by 27 ÷ 9 = 3. Together with a digit sum of 9, the digits are 3 and 6, and the reversal must grow, so the number is 36.
Express everyone in terms of Lee's share x: Kai pays 2x and Jo pays 2x + 60, so 5x + 60 = 900 gives x = £168, and Kai pays 2 × £168 = £336.
Pack to the limit: the lorry plus two cars is exactly 5 + 1.5 + 1.5 = 8 tonnes for crossing one, leaving the van and the last car (4 tonnes) for crossing two.
With r correct answers there are 20 − r wrong ones, so 4r − (20 − r) = 55. That simplifies to 5r = 75, giving r = 15.