NBT NBT Academic and Quantitative Literacy 2 — Questions and Answers
Question 1: A street vendor in Cape Town sells bundles of firewood. He buys each bundle for R24 and sells it for R30. What is his percentage profit on the cost price?
- 20%
- 25% (Correct answer)
- 15%
- 30%
Correct answer: 25%
Profit = R30 - R24 = R6. Percentage profit = (R6 ÷ R24) × 100 = 25%.
Step 1: Calculate the profit per bundle: R30 − R24 = R6. Step 2: Express this as a percentage of the cost price: (R6 ÷ R24) × 100 = 0.25 × 100 = 25%. The answer is 25%. Note that percentage profit is always calculated on the cost price unless otherwise stated. If calculated on the selling price it would be (R6 ÷ R30) × 100 = 20%, but the standard method uses cost price.
Question 2: The table below shows the number of learners who passed Grade 12 in a province over four years: Year | Passed 2019 | 45 000 2020 | 48 600 2021 | 46 800 2022 | 52 200 By what percentage did the number of passes increase from 2019 to 2022?
- 14%
- 16% (Correct answer)
- 15%
- 18%
Correct answer: 16%
Increase = 52 200 − 45 000 = 7 200. Percentage increase = (7 200 ÷ 45 000) × 100 = 16%.
Step 1: Find the increase: 52 200 − 45 000 = 7 200. Step 2: Divide by the original value: 7 200 ÷ 45 000 = 0.16. Step 3: Multiply by 100: 0.16 × 100 = 16%. The number of passes increased by 16% from 2019 to 2022. This type of data interpretation is common in the NBT QL section, requiring learners to read tables accurately and apply percentage change formulas.
Question 3: A pie chart shows how a municipality spends its R5 million budget. The sector for roads represents 72°. How much money is allocated to roads?
- R800 000
- R1 000 000 (Correct answer)
- R900 000
- R1 200 000
Correct answer: R1 000 000
Fraction of budget = 72° ÷ 360° = 0.2 = 1/5. Amount = 1/5 × R5 000 000 = R1 000 000.
A full pie chart represents 360°. The sector for roads is 72°, so the fraction allocated to roads is 72/360 = 1/5 = 0.2 or 20%. Applying this to the total budget: 0.2 × R5 000 000 = R1 000 000. The municipality allocates R1 000 000 to roads. This question tests the ability to link geometric representations (pie charts) to real-world financial data.
Question 4: A family's monthly grocery bill increased from R3 200 to R3 680. By what percentage did it increase?
- 12%
- 15% (Correct answer)
- 18%
- 20%
Correct answer: 15%
Increase = R3 680 − R3 200 = R480. Percentage increase = (R480 ÷ R3 200) × 100 = 15%.
Step 1: Calculate the increase in cost: R3 680 − R3 200 = R480. Step 2: Calculate the percentage increase relative to the original amount: (R480 ÷ R3 200) × 100. Step 3: R480 ÷ R3 200 = 0.15. Step 4: 0.15 × 100 = 15%. The grocery bill increased by 15%. This reflects realistic South African household cost calculations, relevant in the context of rising food inflation.
Question 5: A bar graph shows commuter numbers using different transport modes in Durban: - Private car: 4 500 - Minibus taxi: 7 200 - Bus: 3 600 - Train: 2 700 What fraction of all commuters use the minibus taxi?
- 2/5 (Correct answer)
- 2/3
- 1/3
- 3/8
Correct answer: 2/5
Total commuters = 4 500 + 7 200 + 3 600 + 2 700 = 18 000. Fraction using taxi = 7 200 ÷ 18 000 = 2/5.
Total = 4 500 + 7 200 + 3 600 + 2 700 = 18 000 commuters. Fraction using minibus taxi = 7 200 ÷ 18 000. Simplify: both are divisible by 3 600, giving 2/5. As a percentage: (7 200 ÷ 18 000) × 100 = 40%. Minibus taxis are the dominant transport mode in this dataset, reflecting their real-world significance in South African urban transport.
Question 6: A school tuck shop buys cold drinks at R8.50 each and sells them at a mark-up of 40%. What is the selling price?
- R11.40
- R11.90 (Correct answer)
- R12.00
- R10.50
Correct answer: R11.90
Mark-up = 40% × R8.50 = R3.40. Selling price = R8.50 + R3.40 = R11.90.
Step 1: Calculate 40% of R8.50: 0.40 × R8.50 = R3.40. Step 2: Add the mark-up to the cost price: R8.50 + R3.40 = R11.90. The selling price is R11.90. A mark-up of 40% on the cost price means the profit is 40% of what the shop paid, not 40% of the selling price. This distinction is important and commonly tested in quantitative literacy assessments.
Question 7: The ratio of male to female students at a South African university faculty is 3:5. If there are 960 female students, how many male students are there?
- 576 (Correct answer)
- 640
- 480
- 600
Correct answer: 576
If female = 5 parts = 960, then 1 part = 192. Male = 3 parts = 3 × 192 = 576.
The ratio is 3 (male) : 5 (female). Female students represent 5 parts of the ratio. If 5 parts = 960, then 1 part = 960 ÷ 5 = 192. Male students represent 3 parts: 3 × 192 = 576. There are 576 male students. As a check: total students = 576 + 960 = 1 536, and 576:960 simplifies to 3:5 ✓. Ratio problems are fundamental to quantitative literacy and appear frequently in NBT assessments.
NBT NBT Academic and Quantitative Literacy 2
A street vendor in Cape Town sells bundles of firewood.
He buys each bundle for R24 and sells it for R30.
What is his percentage profit on the cost price?