The real test allows about 43 seconds a question in Quantitative Reasoning. Work through these untimed first, then try again against the clock. If the question types are new to you, read the guide to Quantitative Reasoning first.
Data set with four questions: Corran Cycles
| Bike | First hour | Each extra hour | Full day |
|---|---|---|---|
| Standard | $14 | $8 | $45 |
| Electric | $22 | $12 | $70 |
Helmet hire is $5 per bike for the whole booking. A booking of four or more bikes has 10% taken off its total cost.
Question 1. What does it cost to hire one standard bike for 4 hours, with a helmet?
- A.$38
- B.$43
- C.$46
- D.$48
- E.$51
Show the answer and explanation
Answer: B. $43
$43. The first hour is $14 and the three extra hours are 3 × $8 = $24, giving $38. The helmet adds $5.
Question 2. For an electric bike, what is the smallest whole number of hours for which the full-day price is cheaper than paying by the hour?
- A.3
- B.4
- C.5
- D.6
- E.7
Show the answer and explanation
Answer: D. 6
6. By the hour, five hours cost $22 + 4 × $12 = $70, the same as the full day. Six hours cost $82, so from six hours the full-day price is cheaper.
Question 3. Five people hire five standard bikes for the full day, each with a helmet. What is the total cost?
- A.$202.50
- B.$212.50
- C.$225.00
- D.$227.50
- E.$250.00
Show the answer and explanation
Answer: C. $225.00
$225.00. Each bike costs $45 + $5 = $50, so five cost $250. The booking is for more than four bikes, so 10% comes off the total: $250 × 0.9 = $225.
$227.50 is what you get by discounting the bikes but not the helmets. The discount applies to the total.
Question 4. For a 3-hour hire with no helmet, by what percentage is an electric bike dearer than a standard bike?
- A.53%
- B.57%
- C.60%
- D.65%
- E.77%
Show the answer and explanation
Answer: A. 53%
53%. Electric: $22 + 2 × $12 = $46. Standard: $14 + 2 × $8 = $30. The difference is $16, and 16 ÷ 30 is about 0.53.
Data set with four questions: Wyndale Shire recycling
| Material | 2023 | 2024 |
|---|---|---|
| Paper | 1,240 | 1,116 |
| Glass | 860 | 946 |
| Plastic | 400 | 520 |
| Metal | 300 | 318 |
| Total | 2,800 | 2,900 |
Question 5. By what percentage did the plastic collected increase from 2023 to 2024?
- A.30%
- B.33%
- C.36%
- D.40%
- E.43%
Show the answer and explanation
Answer: A. 30%
30%. The increase is 520 − 400 = 120 tonnes, and 120 ÷ 400 = 0.3.
Question 6. What percentage of all the recycling collected in 2024 was glass?
- A.29.7%
- B.30.7%
- C.32.6%
- D.33.8%
- E.35.1%
Show the answer and explanation
Answer: C. 32.6%
32.6%. 946 ÷ 2,900 = 0.326. Option B, 30.7%, is the 2023 figure (860 ÷ 2,800), there for anyone who reads the wrong column.
Question 7. In 2023, what was the ratio of metal to plastic collected, in its simplest form?
- A.2 : 3
- B.3 : 4
- C.3 : 5
- D.4 : 3
- E.4 : 5
Show the answer and explanation
Answer: B. 3 : 4
3 : 4. 300 : 400 simplifies to 3 : 4. Option D has the ratio the wrong way round.
Question 8. In 2025 the total rises by the same number of tonnes as it did from 2023 to 2024, and metal stays at its 2024 level. What percentage of the 2025 total is metal?
- A.9.4%
- B.9.8%
- C.10.2%
- D.10.6%
- E.11.0%
Show the answer and explanation
Answer: D. 10.6%
10.6%. The total rose by 100 tonnes, so in 2025 it is 3,000. Metal stays at 318, and 318 ÷ 3,000 = 0.106.
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