Multi-Step Data Problems

Many QR questions require more than a single calculation. They might ask you to combine data from different rows, columns, or even different parts of a chart, then perform two or three operations to reach the answer. These multi-step problems are where the time pressure bites hardest. This lesson teaches you how to plan your approach, avoid errors, and execute efficiently.

---

What Makes a Problem "Multi-Step"?

A multi-step problem requires two or more distinct calculations to reach the answer. Examples:

Single-Step	Multi-Step
"What is 15% of £400?"	"What is the total cost including 15% VAT?" (find 15%, then add)
"How many students scored above 60?"	"What percentage of students scored above 60?" (count, then divide by total, then ×100)
"What is the revenue in March?"	"What is the average monthly revenue?" (sum all months, then divide by number of months)

---

The Planning Phase: 5 Seconds Well Spent

Before calculating, spend 5 seconds identifying:

1. What is the final answer? (a value, a percentage, a ratio, etc.)
2. What intermediate values do I need? (a total, a difference, a per-unit cost, etc.)
3. In what order should I calculate?

This prevents you from starting a calculation, realising you need a different value first, and having to start over.

Example Plan

Question: "What percentage of total revenue in Q1 came from Product X?"

Plan:

1. Find Product X's revenue in Q1 (read from table)
2. Find total revenue in Q1 (sum all products' Q1 revenues)
3. Calculate: (Product X Q1 / Total Q1) × 100

---

Common Multi-Step Patterns

Pattern 1: Calculate Then Compare

"Which product had the highest revenue per unit?"

Steps:

1. For each product: Revenue ÷ Units Sold = Revenue per unit
2. Compare the results

Pattern 2: Sum Then Calculate

"What percentage of total sales were in March?"

Steps:

1. Find March sales (read from data)
2. Find total sales (sum all months)
3. (March ÷ Total) × 100

Pattern 3: Calculate Intermediate Values Then Combine

"What is the profit margin? (Revenue − Cost) ÷ Revenue × 100"

Steps:

1. Find Revenue (read from data)
2. Find Cost (read from data)
3. Revenue − Cost = Profit
4. (Profit ÷ Revenue) × 100

Pattern 4: Apply a Condition Then Calculate

"What is the total cost of items priced above £5?"

Steps:

1. Identify which items are priced above £5
2. For each: Quantity × Price
3. Sum all qualifying items

---

Efficient Execution

Use the Whiteboard

For multi-step problems, write down intermediate values on your whiteboard. This prevents you from:

• Forgetting a number you calculated 10 seconds ago
• Having to recalculate something

Use Calculator Memory

If using the calculator, use M+ to accumulate running totals. This is faster than writing intermediate values and re-entering them.

Estimate at Each Step

After each intermediate calculation, quickly check: "Does this look right?" If your intermediate value is obviously wrong, fix it before building on it.

---

UCAT-Style Worked Examples

Worked Example 1: Revenue per Unit

Data:

Product	Units Sold	Revenue (£)
Alpha	240	4,800
Beta	180	5,400
Gamma	320	4,480
Delta	150	5,250

Question: What is the difference in revenue per unit between the highest and lowest?

Step 1: Calculate revenue per unit for each product:

• Alpha: 4,800 ÷ 240 = £20
• Beta: 5,400 ÷ 180 = £30
• Gamma: 4,480 ÷ 320 = £14
• Delta: 5,250 ÷ 150 = £35

Step 2: Identify highest and lowest: