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Question 1Academic and Quantitative Literacy (AQL)

In the sentence "The committee's terse reply gave no reasons and offered no apology," the word "terse" most nearly means:

  1. carefully worded
  2. brief and to the point Correct answer.
  3. openly hostile
  4. deliberately misleading

Explanation

"Terse" describes language that is brief and to the point, often to the point of seeming curt. The sentence contrasts a very short reply with the absence of reasons or apology, which supports the idea of brevity.

Question 2Academic and Quantitative Literacy (AQL)

Read the passage and answer the question. Many people assume that the human brain stops changing after childhood. In fact, the brain rewires itself throughout life: London taxi drivers, who memorise complex street routes, develop a larger hippocampus than average, and musicians show enlarged brain areas for hearing and hand control. Which statement best expresses the main idea of the passage?

  1. Brain growth stops earlier than most scientists once believed.
  2. Musical training is the most effective way to change the brain.
  3. London taxi drivers are more intelligent than the general population.
  4. The adult brain is physically altered by repeated activity. Correct answer.

Explanation

The passage's central claim is that experience physically reshapes the adult brain, with taxi drivers and musicians given as illustrations. The examples support that general claim rather than being the point in themselves.

Question 3Academic and Quantitative Literacy (AQL)

A shirt priced at R240 is reduced by 15% in a sale. What is the sale price?

  1. R180
  2. R204 Correct answer.
  3. R216
  4. R225

Explanation

A 15% reduction removes 15% of R240, which is R36, leaving R204. Equivalently, the sale price is 85% of R240, that is 0.85 × 240 = 204.

Question 4Academic and Quantitative Literacy (AQL)

A clinic recorded the number of patients it treated on four days: Monday 48, Tuesday 36, Wednesday 60, Thursday 52. How many more patients were treated on the busiest day than on the quietest day?

  1. 18
  2. 20
  3. 12
  4. 24 Correct answer.

Explanation

The busiest day is Wednesday with 60 patients and the quietest is Tuesday with 36. Subtracting gives 60 − 36 = 24 patients.

Question 5Academic and Quantitative Literacy (AQL)

A tap delivers water at a steady rate of 12 litres per minute. How many kilolitres does it deliver in 2.5 hours?

  1. 18 kL
  2. 1.8 kL Correct answer.
  3. 180 kL
  4. 0.18 kL

Explanation

2.5 hours is 150 minutes, and at 12 litres per minute the tap delivers 150 × 12 = 1 800 litres. Since 1 kilolitre is 1 000 litres, this is 1.8 kL.

Question 6Academic and Quantitative Literacy (AQL)

Read the passage and answer the question. "The council's latest plan for the library, announced with great fanfare, promises 'a world-class facility'. Readers might be forgiven for noting that the same promise accompanied the closure of the reading room in 2009." The writer's attitude towards the plan is best described as:

  1. enthusiastic
  2. sceptical Correct answer.
  3. indifferent
  4. confused

Explanation

By recalling that an identical promise preceded an unpopular closure, the writer signals doubt that the new plan will deliver. The irony is directed at the plan, which shows neither approval nor indifference.

Question 7Academic and Quantitative Literacy (AQL)

A recipe for 4 people requires 300 g of rice. At the same rate, how much rice is needed for 10 people?

  1. 675 g
  2. 750 g Correct answer.
  3. 600 g
  4. 700 g

Explanation

The recipe uses 300 g for 4 people, which is 75 g per person. For 10 people the amount is 10 × 75 g = 750 g.

Question 8Academic and Quantitative Literacy (AQL)

A learner obtains marks of 4, 7, 9, 12 and 18 in five short tasks. What is the mean mark?

  1. 9
  2. 10 Correct answer.
  3. 12.5
  4. 9.5

Explanation

The mean is the total of the values divided by the number of values: 4 + 7 + 9 + 12 + 18 = 50, and 50 ÷ 5 = 10.

Question 9Academic and Quantitative Literacy (AQL)

The price of a product is increased by 20% and the new price is later reduced by 20%. Compared with the original price, the final price is:

  1. 4% higher than the original price
  2. 4% lower than the original price Correct answer.
  3. 2% lower than the original price
  4. the same as the original price

Explanation

Multiplying by 1.20 and then by 0.80 gives 0.96, which is 96% of the original price. The final price is therefore 4% below the starting price.

Question 10Academic and Quantitative Literacy (AQL)

In a survey of 500 households, 45% reported that they mainly use public transport, 30% mainly use private cars and the remainder mainly walk. How many households mainly walk?

  1. 200
  2. 125 Correct answer.
  3. 175
  4. 150

Explanation

Public transport and private cars together account for 45% + 30% = 75% of households, so walking accounts for the remaining 25%. Then 25% of 500 is 125.

Question 11Academic and Quantitative Literacy (AQL)

Read the argument and answer the question. "The city should ban cars from the central business district on Saturdays. Shops in the district have reported falling sales, and pedestrian-only streets elsewhere have attracted more shoppers." Which statement is an assumption on which the argument depends?

  1. Congestion and parking problems account for much of the fall in sales. Correct answer.
  2. Most shopkeepers in the district support the proposed ban.
  3. Other cities that pedestrianised their business districts reported higher sales.
  4. Saturday is by far the busiest shopping day of the week in the district.

Explanation

The recommendation links falling sales to car traffic, so it must assume that a car ban would remove something that is actually causing the decline. Without that causal link, the evidence about falling sales would not support a ban.

Question 12Academic and Quantitative Literacy (AQL)

Consider these two statements: 1. All first-year students must complete a statistics module. 2. Some students who complete the statistics module also take a course in economics. Which conclusion must be true?

  1. Every student who takes economics is also a first-year student in the faculty.
  2. No student who takes economics is a first-year student at the university.
  3. Some first-year students take economics as one of their courses.
  4. Some students who take economics have completed the statistics module. Correct answer.

Explanation

Statement 2 says there are students who both completed the statistics module and take economics, so at least some economics students have completed the module. Any claim about first-year students taking economics goes beyond what the statements say.

Question 13Academic and Quantitative Literacy (AQL)

A learner scores 60% in a test that counts for 40% of the final mark and 80% in an examination that counts for 60% of the final mark. What is the final mark?

  1. 72% Correct answer.
  2. 74%
  3. 70%
  4. 76%

Explanation

Each mark is weighted by its contribution: 60 × 0.40 = 24 and 80 × 0.60 = 48. Adding the two contributions gives a final mark of 72%.

Question 14Academic and Quantitative Literacy (AQL)

An amount of R450 000 is divided among three partners in the ratio 2 : 3 : 4. How much does the partner with the largest share receive?

  1. R225 000
  2. R250 000
  3. R200 000 Correct answer.
  4. R150 000

Explanation

The ratio contains 2 + 3 + 4 = 9 equal parts, so one part is R450 000 ÷ 9 = R50 000. The largest share is 4 parts, which is 4 × R50 000 = R200 000.

Question 15Academic and Quantitative Literacy (AQL)

A country's exports were worth R90 billion in 2020 and R135 billion in 2022. By what percentage did the value of exports increase over this period?

  1. 25%
  2. 33%
  3. 50% Correct answer.
  4. 45%

Explanation

The increase is R135bn − R90bn = R45bn. Expressing this against the starting value gives 45 ÷ 90 = 0.5, which is a 50% increase.

Question 16Academic and Quantitative Literacy (AQL)

A bag contains 5 red, 3 blue and 2 green balls. One ball is drawn at random. What is the probability that the ball drawn is not red?

  1. 1/2 Correct answer.
  2. 3/10
  3. 1/5
  4. 7/10

Explanation

There are 10 balls in total, of which 3 + 2 = 5 are not red. The probability is therefore 5/10, which simplifies to 1/2.

Question 17Academic and Quantitative Literacy (AQL)

In the sentence "The dam's release valves are designed to mitigate flood damage downstream," the word "mitigate" most nearly means:

  1. reduce the severity of Correct answer.
  2. measure the cost of
  3. predict the timing of
  4. take responsibility for

Explanation

"Mitigate" means to make something less severe or harmful, so the valves mitigate damage by reducing it. The sentence describes what the valves do to the flood damage, not how it is assessed or forecast.

Question 18Academic and Quantitative Literacy (AQL)

Read the passage and answer the question. "Urban trees are often praised for their beauty. Yet their value is also measurable in hard cash: a single mature tree can intercept thousands of litres of stormwater a year, lowering the cost of drainage infrastructure. Cities that cut their tree budgets are, in effect, deferring maintenance costs rather than avoiding them." What is the function of the second sentence in the passage?

  1. It moves from an aesthetic justification to an economic one. Correct answer.
  2. It concedes that trees are valuable mainly because of their appearance.
  3. It contradicts the claim made in the first sentence.
  4. It summarises the argument of the whole passage.

Explanation

The first sentence mentions beauty, while the second turns to measurable cash benefits such as stormwater interception. The second sentence therefore changes the basis of the argument from appearance to money.

Question 19Academic and Quantitative Literacy (AQL)

A cyclist covers 45 km in 1 hour 30 minutes at a constant speed. At the same speed, how long will it take to cover 90 km?

  1. 3 h Correct answer.
  2. 2 h 15 min
  3. 2 h 30 min
  4. 3 h 30 min

Explanation

The cyclist's speed is 45 km ÷ 1.5 h = 30 km/h. Covering 90 km at 30 km/h takes 90 ÷ 30 = 3 hours.

Question 20Academic and Quantitative Literacy (AQL)

In a race, Thabo finished ahead of Sipho but behind Lerato. Nomsa finished immediately ahead of Lerato. Who finished first?

  1. Lerato
  2. Nomsa Correct answer.
  3. Sipho
  4. Thabo

Explanation

Nomsa finished ahead of Lerato, and Lerato finished ahead of Thabo, who in turn finished ahead of Sipho. The finishing order is therefore Nomsa, Lerato, Thabo, Sipho.

Question 21Academic and Quantitative Literacy (AQL)

After a 15% increase, a salary is R11 500 per month. What was the salary before the increase?

  1. R9 775
  2. R10 000 Correct answer.
  3. R10 350
  4. R9 500

Explanation

The new salary is 115% of the old salary, so divide by 1.15: R11 500 ÷ 1.15 = R10 000. Checking the result, R10 000 × 1.15 = R11 500.

Question 22Academic and Quantitative Literacy (AQL)

Pipe A can fill a tank on its own in 6 hours and pipe B can fill the same tank on its own in 4 hours. If both pipes run together, how long will they take to fill the empty tank?

  1. 2 h 12 min
  2. 2 h 24 min Correct answer.
  3. 2 h 40 min
  4. 2 h

Explanation

In one hour pipe A fills 1/6 of the tank and pipe B fills 1/4, giving a combined rate of 5/12 of the tank per hour. The tank is filled in 12/5 = 2.4 hours, which is 2 hours 24 minutes.

Question 23Academic and Quantitative Literacy (AQL)

Read the argument and answer the question. "Every student who scored above 80% attended the revision sessions. Therefore, attending the revision sessions will raise your mark above 80%." What is the main flaw in this reasoning?

  1. It treats a shared trait as the cause of the high marks. Correct answer.
  2. It draws a conclusion about a large population from a small sample.
  3. It generalises from the experience of a single student.
  4. It uses the word "mark" in two different senses in the same argument.

Explanation

The evidence shows only that attendance went together with high marks, which is a correlation. Concluding that attendance produces high marks assumes that the shared feature is the cause, which the evidence does not establish.

Question 24Academic and Quantitative Literacy (AQL)

In 2010 a country had a population of 50 million and used 250 TWh of electricity. In 2020 its population was 60 million and it used 288 TWh. What happened to electricity use per person over the decade?

  1. a decrease of 15.2%
  2. a decrease of 4% Correct answer.
  3. an increase of 4%
  4. an increase of 15.2%

Explanation

In 2010 use per person was 250 TWh ÷ 50 million = 5 MWh, and in 2020 it was 288 TWh ÷ 60 million = 4.8 MWh. The change is (4.8 − 5) ÷ 5 = −0.04, a decrease of 4%.

Question 25Academic and Quantitative Literacy (AQL)

A motorist travels 120 km at 60 km/h and then returns along the same road at 40 km/h. What is the average speed for the whole round trip?

  1. 48 km/h Correct answer.
  2. 45 km/h
  3. 46 km/h
  4. 50 km/h

Explanation

Average speed is total distance divided by total time. The round trip covers 240 km and takes 2 hours out plus 3 hours back, a total of 5 hours, so the average speed is 240 ÷ 5 = 48 km/h.

Question 26Academic and Quantitative Literacy (AQL)

In the sentence "The report was terse, offering no detail beyond the bare facts," the word "terse" most nearly means:

  1. hard to believe
  2. badly organised
  3. angry in tone
  4. brief and direct Correct answer.

Explanation

Terse describes speech or writing that is brief and direct, often to the point of seeming abrupt. The context "no detail beyond the bare facts" confirms that the report was short rather than emotional or badly organised.

Question 27Academic and Quantitative Literacy (AQL)

Read the passage and answer the question. "When the town replaced its worn-out street lights with LED bulbs, the electricity bill for lighting fell by nearly half. The town also planted 200 trees along the main road. Residents have since reported cooler afternoons and lower dust levels near the trees." Which statement best expresses the main idea of the passage?

  1. Simple local changes can produce measurable benefits. Correct answer.
  2. Trees are the only way to reduce dust in a town.
  3. Residents opposed the new street lights.
  4. LED bulbs are more useful than trees.

Explanation

The passage describes two local actions, installing LED lights and planting trees, and reports specific benefits from each. The best main idea links both actions to measurable improvements rather than focusing on one detail.

Question 28Academic and Quantitative Literacy (AQL)

What is the next number in the sequence 5, 10, 20, 40, ...?

  1. 45
  2. 60
  3. 100
  4. 80 Correct answer.

Explanation

Each term is double the previous term: 5 × 2 = 10, 10 × 2 = 20, and 20 × 2 = 40. Continuing the pattern gives 40 × 2 = 80.

Question 29Academic and Quantitative Literacy (AQL)

An amount of R84 is shared in the ratio 1 : 2 : 4. How much does the largest share receive?

  1. R14
  2. R36
  3. R24
  4. R48 Correct answer.

Explanation

The ratio 1 : 2 : 4 has 7 equal parts. Each part is R84 ÷ 7 = R12, so the largest share, which is 4 parts, is 4 × R12 = R48.

Question 30Academic and Quantitative Literacy (AQL)

If the library receives funding, it will extend its opening hours. The library did not extend its opening hours. Which conclusion follows?

  1. The library received funding.
  2. The library will close permanently.
  3. The library did not receive funding. Correct answer.
  4. Funding for the library was reduced.

Explanation

The rule is "if funding, then extended hours." Since extended hours did not occur, the condition that would have caused them, namely funding, must be false. This is a valid application of modus tollens.

Question 31Academic and Quantitative Literacy (AQL)

A rectangular garden has a length of 12 m and a width of 7 m. What is its perimeter?

  1. 42 m
  2. 84 m
  3. 19 m
  4. 38 m Correct answer.

Explanation

The perimeter of a rectangle is 2 × (length + width). Here that is 2 × (12 + 7) = 2 × 19 = 38 m.

Question 32Academic and Quantitative Literacy (AQL)

The average of five numbers is 12. Four of the numbers are 8, 10, 14 and 16. What is the fifth number?

  1. 14
  2. 10
  3. 12 Correct answer.
  4. 11

Explanation

The total of the five numbers is 5 × 12 = 60. The four known numbers add to 8 + 10 + 14 + 16 = 48, so the fifth number is 60 − 48 = 12.

Question 33Academic and Quantitative Literacy (AQL)

A fair six-sided die is rolled once. What is the probability that the result is an even number or a number greater than 4?

  1. 1/2 Correct answer.
  2. 2/3
  3. 5/6
  4. 1/3

Explanation

The favourable outcomes are the even numbers {2, 4, 6} and the numbers greater than 4, {5, 6}. Their union is {2, 4, 5, 6}, which is 4 of the 6 equally likely outcomes, so the probability is 4/6 = 2/3.

Question 34Academic and Quantitative Literacy (AQL)

The price of a product is reduced by 25%. By what percentage must the reduced price be increased to return to the original price?

  1. 33⅓% Correct answer.
  2. 20%
  3. 40%
  4. 25%

Explanation

After a 25% reduction, the price is 75% of the original. The increase needed is 25% of the original divided by 75% of the original, which is 25/75 = 1/3, or about 33⅓%.

Question 35Academic and Quantitative Literacy (AQL)

Five machines produce 200 units in 4 hours. At the same rate, how many units will three machines produce in 7 hours?

  1. 180
  2. 240 Correct answer.
  3. 200
  4. 210

Explanation

One machine produces 200 ÷ (5 × 4) = 10 units per hour. Three machines working for 7 hours therefore produce 3 × 7 × 10 = 210 units.

Question 36Academic and Quantitative Literacy (AQL)

The city should replace its diesel buses with electric buses. Electric buses produce no exhaust fumes, so replacing the diesel fleet will improve air quality in the city. Which assumption is required for this argument?

  1. The city already has enough trained bus drivers.
  2. Passengers will prefer travelling on electric buses.
  3. Electric buses will be cheaper to buy than diesel buses.
  4. Charging the buses will not create equivalent harmful emissions within the city. Correct answer.

Explanation

The argument assumes that removing diesel exhaust is not offset by new harmful emissions in the city from generating electricity for the buses. If charging produced equivalent local pollution, the claimed air-quality benefit would not follow.

Question 37Academic and Quantitative Literacy (AQL)

Read the passage and answer the question. "The author describes a new public bicycle scheme, noting its low cost and health benefits, but also warns that poor maintenance could undermine public trust." The author's attitude toward the scheme is best described as:

  1. completely indifferent
  2. entirely hostile
  3. cautiously supportive Correct answer.
  4. uncritically enthusiastic

Explanation

The author acknowledges benefits such as low cost and health gains while warning about maintenance risks. This balanced treatment shows cautious support rather than outright hostility or uncritical enthusiasm.

Question 38Academic and Quantitative Literacy (AQL)

A car uses 6 litres of fuel per 100 km. How much will fuel cost for a 450 km journey if fuel costs R22 per litre?

  1. R396
  2. R594 Correct answer.
  3. R660
  4. R528

Explanation

Fuel used is (450 ÷ 100) × 6 = 4.5 × 6 = 27 litres. At R22 per litre, the cost is 27 × R22 = R594.

Question 39Academic and Quantitative Literacy (AQL)

Twelve workers can build a wall in 8 days. At the same rate, how long will 16 workers take to build the same wall?

  1. 5 days
  2. 7 days
  3. 6 days Correct answer.
  4. 8 days

Explanation

The job requires 12 × 8 = 96 worker-days. With 16 workers, the time needed is 96 ÷ 16 = 6 days.

Question 40Academic and Quantitative Literacy (AQL)

A shop recorded daily sales of R400, R600, R500, R900 and R1100 on five consecutive days. How does the mean compare with the median?

  1. The mean is R100 greater than the median. Correct answer.
  2. The median is R100 greater than the mean.
  3. The mean is R200 greater than the median.
  4. The mean and the median are equal.

Explanation

The total is 400 + 600 + 500 + 900 + 1100 = 3500, so the mean is 3500 ÷ 5 = 700. In order, the values are 400, 500, 600, 900, 1100, so the median is 600; the mean is therefore R100 greater than the median.

Question 41Academic and Quantitative Literacy (AQL)

Read the passage and answer the question. "A study found that employees who worked from home two days a week reported fewer sick days than those who worked in the office full time. However, the same employees were less likely to be promoted over the following three years." Which conclusion is best supported by the passage?

  1. Promotion depends only on attendance at the office.
  2. Working from home causes employees to become ill less often.
  3. Working from home may reduce sick days but could limit promotion. Correct answer.
  4. Working from home always improves employees' health.

Explanation

The passage reports both fewer sick days and lower promotion rates for the same group of employees. A balanced conclusion is that home working may have one benefit and one drawback, without claiming proof of cause.

Question 42Academic and Quantitative Literacy (AQL)

The school should ban smartphones during lessons. Students who use phones in class score lower on tests than those who do not. Which statement most weakens this argument?

  1. Phones can be useful learning tools in some lessons.
  2. Some teachers also use phones during lessons.
  3. Struggling students may be the ones who use phones in class. Correct answer.
  4. Smartphones are costly for many families.

Explanation

The argument treats lower test scores as an effect of phone use, but the reverse is possible: students who already struggle may be more likely to use phones. This weakens the causal claim on which the ban is based.

Question 43Academic and Quantitative Literacy (AQL)

A tank is 2/3 full. After 120 litres are added, it becomes 5/6 full. What is the capacity of the tank?

  1. 600 litres
  2. 720 litres
  3. 840 litres Correct answer.
  4. 480 litres

Explanation

The increase from 2/3 to 5/6 is 5/6 − 4/6 = 1/6 of the tank. If 1/6 of the capacity is 120 litres, then the full capacity is 120 × 6 = 720 litres.

Question 44Academic and Quantitative Literacy (AQL)

A country generated 40 TWh of renewable electricity in 2015 and 70 TWh in 2020. Its total electricity generation rose from 200 TWh to 280 TWh over the same period. What happened to the renewable share of total generation?

  1. It rose by 25 percentage points.
  2. It stayed the same.
  3. It fell slightly.
  4. It rose by 5 percentage points. Correct answer.

Explanation

The renewable share was 40/200 = 20% in 2015 and 70/280 = 25% in 2020. The share therefore rose by 5 percentage points, not by 5% of the original share.

Question 45Academic and Quantitative Literacy (AQL)

No reptiles are warm-blooded. All snakes are reptiles. Which conclusion must be true?

  1. Some reptiles are warm-blooded.
  2. All warm-blooded animals are snakes.
  3. Some snakes are warm-blooded.
  4. No snakes are warm-blooded. Correct answer.

Explanation

All snakes are reptiles, and no reptiles are warm-blooded, so no snake can be warm-blooded. This follows necessarily from the two premises.

Question 46Academic and Quantitative Literacy (AQL)

A boat travels 60 km downstream in 3 hours and returns the same distance upstream in 5 hours. What is the speed of the current?

  1. 3 km/h
  2. 2 km/h
  3. 8 km/h
  4. 4 km/h Correct answer.

Explanation

Downstream speed is 60 ÷ 3 = 20 km/h and upstream speed is 60 ÷ 5 = 12 km/h. The current speed is half the difference: (20 − 12) ÷ 2 = 4 km/h.

Question 47Academic and Quantitative Literacy (AQL)

If a candidate passes the written test, she is invited to an interview. If she is invited to an interview, she must submit references. Lindi passed the written test. Which statement must be true?

  1. Lindi has already submitted her references.
  2. Lindi will be hired for the job.
  3. Lindi may not be invited to an interview.
  4. Lindi is required to submit references. Correct answer.

Explanation

Passing the written test guarantees an interview invitation, and an interview invitation requires references. Therefore Lindi is required to submit references.

Question 48Academic and Quantitative Literacy (AQL)

Read the passage and answer the question. "Dr Maseko argues that the new dam should not be built because it will displace rare frogs. The dam's supporters reply that the frogs can be moved to a nearby wetland. Maseko responds that the wetland is already crowded with a competing frog species." What is the main point of Maseko's response?

  1. The dam should be built after all.
  2. The wetland contains no frogs.
  3. Relocating the frogs is unlikely to succeed. Correct answer.
  4. The competing frog species is also rare.

Explanation

Maseko's reply challenges the proposed solution by suggesting that the receiving wetland cannot easily absorb the frogs because it already supports a competing species. He is therefore questioning the feasibility of relocation.

Question 49Academic and Quantitative Literacy (AQL)

What is the median of the data set 3, 7, 8, 12, 15, 20?

  1. 10 Correct answer.
  2. 12
  3. 11.5
  4. 8

Explanation

With an even number of values, the median is the average of the two middle numbers, 8 and 12. Their average is (8 + 12) / 2 = 10.

Question 50Academic and Quantitative Literacy (AQL)

A jacket is marked at R480. During a sale the price is reduced by 15%. What is the sale price?

  1. R465
  2. R420
  3. R408 Correct answer.
  4. R432

Explanation

15% of R480 is 0.15 × 480 = R72. Subtracting the discount gives R480 − R72 = R408.