AICE Thinking Skills: Paper 1: Practice Questions
PS6 Sample question (Suggesting Hypotheses) Tina is a part-time teacher. She teaches her lessons during the day and, when she has finished her last lesson, she leaves the school and goes to the bus stop to get a bus home. All lessons start on the hour, or at quarter past, half past or quarter to the hour and each lasts 45 minutes. It takes her 15 minutes from the end of a lesson to reach the bus stop. She doesn't know what the bus timetable is, but she notices that she always has to wait either 5 minutes or 20 minutes for a bus. Which of the following explains the times she has to wait? A The buses run every 15 minutes at 5, 20, 35 and 50 minutes past the hour B The buses run every half hour at 5 and 35 minutes past the hour C The buses run every 20 minutes at 0, 20 and 40 minutes past the hour D In the morning the buses run every hour at 5 minutes past the hour; in the afternoon they run every hour at 20 minutes past the hour
Key B Stimulus Type Words Justification She always arrives at the bus stop on an exact quarter hour - on the hour or quarter past, half past or quarter to the hour (the lessons start on a quarter hour, take ¾ hour and she takes 15 min to get to the bus stop). If she arrives at the bus stop at the hour or half past, she waits five minutes. If she arrives at quarter past or quarter to, she waits 20 minutes. The buses are at 5 and 35 minutes past the hour. B explains this. The skill is in matching the verbal stimulus to one of the verbal explanations.
PS10 Sample question (Choices and Decisions) I have none of my nephew's favourite biscuits left. My nephew visits me, without fail, at least 3 times a week, though never more than five times. On each visit I know he will eat at least 6 biscuits but I won't let him have more than 8. Packets of biscuits can contain as few as 10 biscuits, or as many as 12. How many packets of biscuits must I buy to make sure I do not run out within the next two weeks? A 4 B 5 C 6 D 8
Key D Stimulus Type Verbal Justification A decision on how many to buy is made by dividing my nephew's maximum requirement by the minimum number of biscuits in a pack. This is the only way of ensuring there are enough. The most biscuits my nephew will eat in two weeks is 2 (weeks) × 5 (maximum visits per week) × 8 (maximum number of biscuits per visit) = 80. The minimum number of biscuits in a pack is 10, so 8 packets will be required. D is correct.
PS8 Sample question (Data Necessity and Sufficiency) Bill and Colin are twin brothers. They plan to meet at a hotel between their houses to exchange birthday presents. Bill's journey is on motorways and he travels at an average 120 km/hr. Colin's journey is on minor roads and he travels at 80 km/hr. Bill leaves at 10 am. They expect to arrive at the hotel at the same time. Which one of the following further pieces of information would be sufficient to determine at what time they will meet? A Colin's journey time B Colin's travel distance C Colin's departure time D Bill's travel distance
Key D Stimulus Type Verbal Justification In order to find the meeting time, from information on either journey, the following calculation has to be carried out: Meeting time = departure time + travel distance / average speed. For Bill, we have two of the values on the right hand side (departure time and average speed), for Colin we have only one (average speed). Thus, the only single piece of information which would allow us to calculate the meeting time, would be Bill's travel distance, so D is correct.
PS3 Sample question (Finding a Procedure) Each of two identical cars can carry enough fuel to travel 100 miles only. To make a longer journey over a deserted area, they set out together and then at some stage the first car transfers fuel to the other and returns home. The second car travels on. What, approximately, is the furthest distance from home that the second car can travel? A 125 miles B 133 miles C 150 miles D 167 miles
Key B Stimulus Type Words Justification A method must be developed to solve this problem - it cannot be done just using extraction or processing. One way is by trial and error. For example, if the two cars travel 50 miles together, it would be possible to transfer 50 miles worth of fuel from one to another but then the car donating the fuel would be empty so this is clearly too far. Similarly, at 25 miles only 25 miles worth could be transferred so the donor car would have 25 miles left when it reaches home. It becomes clear that the donor car must divide its fuel into 3 - 1/3 for the outward journey, 1/3 to transfer to the other car, and 1/3 to return. At 33 miles the car which is continuing is completely refilled and would have enough for another 100 miles, making 133 miles in total.
PS4 Sample question (Searching) A private mail delivery company makes the following charges for delivering letters and packages: Weight up to 60 g 25 pence Each extra 10 g or part thereof 5 pence A woman wishes to use this company to send a manuscript either as a single package of weight 138 g or two or more packages with a total weight of 138 g. What is the lowest cost of postage with this company? A 59 pence B 60 pence C 64 pence D 65 pence
Key B Stimulus Type Words/Table Justification The skill is in performing a search of the options on splitting up the package to find how many pieces, and of what weights, is most effective. As a single package it would cost 25p for the first 60 g and 8 × 5p for the remaining 78 g, or 65p in total. If sent as two packages, it is most economical to have both at 60 g or more, as the first 60 g is pro-rata cheaper than the remaining weight. Thus 60 g + 78 g is as effective as any other split: this costs 25p + (25p + 2 × 5p) = 60p. If sent as three packages, once again it is best to keep as many as possible at 60 g or more. They would then divide as 60 g + 60 g + 18 g at 3 × 25p = 75p. The two package option is the best at 60p.
PS1 Sample question (Data Extraction) The cost of sending letters from the United Kingdom to continental Europe is shown below: Not over £ p Not over £ p Not over £ p 20 g=0.22 250 g=1.06 500 g=2.02 60 g=0.37 300 g=1.25 750 g=2.77 100=g 0.53 350 g=1.44 1000 g=3.52 150g=0.70 400 g=1.64 1250 g=4.07 200 g=0.88 450 g=1.83 1500 g=4.62 A firm in London wishes to send two letters to separate clients in continental Europe. The letters weigh 75 g and 215 g. What is the total cost of sending the two letters? A £1.25 B £1.41 C £1.43 D £1.59
Key D Stimulus Type: Table Justification: The 75 g letter will cost 53p to post (over 60 g but under 100 g) and the 215 g letter will cost £1.06p (over 200 g but under 250 g). The total cost is 53p + £1.06p = £1.59p. Candidates are expected to select the two correct values from the table, given the weights of the parcels, and add these together. The primary skill is extraction with a small amount of processing.
PS2 Sample question (Data Processing) We had 76 people wanting coffee at a conference. The caterers provided enough coffee for each of 80 people to have an 8 fluid ounce cup three-quarters full. We carefully filled each cup to exactly three-quarters full as we handed them out, but failed to notice that they had given us 10 fluid ounce cups. How many people went without? A 0 B 4 C 8 D 12
KeyD Stimulus Type Words Justification The amount of coffee provided by the caterers was 80 (people) × 8 (fluid ounce cups) × ¾ (full) = 480 fl oz. The amount of coffee in one of the larger cups is 10 (fluid ounces) × ¾ (full) = 7.5 fl oz. The number of people that can be catered for is 480 (the amount of coffee provided) / 7.5 (in each cup) = 64. There are 76 people so 76 - 64 = 12 people will go without. The candidate must use the data correctly (all the data is relevant so the only extraction skill is to use the correct numbers at the correct time). The skill is processing. Finding a method is a minor part of the answer, as the method of solution is straightforward.
