Top 5 Formulas to Memorize for UCAT Decision Making

Sonam Kothari

8th Aug, 2025 3:04 PM

UCAT

Top 5 Formulas to Memorize for UCAT Decision Making

Introduction: Why Decision Making is More Than Just Logic

The UCAT Decision Making subtest is often underestimated. While it only makes up 1/5 of the UCAT sections, it's notorious for mixing logic, probability, statistics, and critical thinking into tightly timed, high-pressure questions. Many students focus heavily on Verbal Reasoning or Quantitative Reasoning, but mastering Decision Making is essential to push your UCAT score above the 700 mark.

And here's the kicker: unlike Quantitative Reasoning, Decision Making doesn’t offer you a calculator—but it does demand mathematical reasoning.

That’s where formulas come in.

This article breaks down the Top 5 must-know formulas for the Decision Making section. These are not just helpful—they're vital for tackling certain question types efficiently. We’ll explore when and how to use them, give UCAT-style examples, and provide strategic tips on speed, accuracy, and time management under pressure.

🧩 The Decision Making Landscape: Where Formulas Fit

Before diving into formulas, let’s define the role of math in UCAT Decision Making:

You’ll face:

• Logical puzzles

• Syllogisms

• Venn diagrams

• Probabilistic reasoning

• Interpreting graphical data

• Recognizing assumptions

You won’t face:

• Complex algebra

• Calculator-intensive math

You will need:

• Mental arithmetic

• Sharp use of basic probability, percentages, and ratios

• Fast pattern recognition

💡 Tip: Decision Making questions often look like they require complex math, but most can be cracked quickly if you apply the right formula at the right time.

🔢 The Top 5 Formulas You Must Know for UCAT Decision Making

1. Probability of Independent Events

Formula:
$P(A \text{ and } B) = P(A) \times P(B)$

✅ When to Use:

When two events occur independently, and you're asked for the probability of both happening.

🎯 UCAT-Style Example:

A student has a 1 in 4 chance of forgetting their notes, and a 1 in 5 chance of arriving late. What is the probability they forget their notes and arrive late?

Apply:

$$P(\text{Forget and Late}) = \frac{1}{4} \times \frac{1}{5} = \frac{1}{20}$$

⏱ Why This Matters:

You’ll see probability questions in graphical interpretation or logical probability chains—this formula turns a “thinking” question into a 5-second calculation.

2. Probability of Either Event (Mutually Exclusive)

Formula:
$P(A \text{ or } B) = P(A) + P(B)$

Only if A and B are mutually exclusive

✅ When to Use:

When two events cannot happen at the same time (like flipping a coin and getting both heads and tails).

🎯 Example:

A die is rolled. What is the probability of getting a 2 or a 4?

Apply:

$$P(2 \text{ or } 4) = \frac{1}{6} + \frac{1}{6} = \frac{1}{3}$$

⚠️ Caution:

If the events are not mutually exclusive, you must subtract the overlap:

General formula:

$$P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$$

3. Percentage Change

Formula:

$$\% \text{ Change} = \frac{\text{New} - \text{Original}}{\text{Original}} \times 100$$

✅ When to Use:

Used in graphical analysis or data-heavy Decision Making questions, especially bar charts and tables.

🎯 Example:

A clinic had 120 patients last month and 150 this month. What’s the % increase?

$$\frac{150 - 120}{120} \times 100 = \frac{30}{120} \times 100 = 25\%$$

💡 Pro Tip:

Use percentages to quickly compare changes without calculating raw differences between values.

4. Expected Value

Formula:

$$\text{Expected Value (EV)} = \sum (\text{Probability} \times \text{Value})$$

✅ When to Use:

When you're given several possible outcomes with attached probabilities—common in risk assessment or decision tree questions.

🎯 Example:

A charity raffle has a 1 in 100 chance of winning £500. Tickets cost £10. What’s the expected value?

$$EV = \left(\frac{1}{100} \times 500\right) + \left(\frac{99}{100} \times -10\right) = 5 - 9.9 = -£4.90$$

🤯 Insight:

EV helps you determine if a decision is worth it—a key skill assessed in UCAT Decision Making.

5. Venn Diagram Totals

Formula:

$$n(A \cup B) = n(A) + n(B) - n(A \cap B)$$

✅ When to Use:

In Venn Diagram or set logic questions—especially those asking “how many people like A or B but not both?”

🎯 Example:

60 students like Biology, 40 like Chemistry, and 20 like both. How many like either subject?

$$60 + 40 - 20 = 80$$

This helps with fast elimination and ensures you don’t double-count students in overlapping sets.

🧠 Bonus: Mental Math Tricks to Speed You Up

UCAT Decision Making is all about thinking under pressure. These formulas save time, but here are 3 bonus hacks:

1. Estimate with Confidence:

If you need an approximate % increase or probability and the answer options are far apart, estimate. Precision is not always necessary.

2. Work Backwards:

For Expected Value or Set Theory, try plugging in answer choices to see what fits fastest.

3. Cross-Out Technique:

Eliminate clearly incorrect options using logic before calculating—narrowing from 5 options to 2 doubles your odds instantly.

📚 Internal Resources to Power Your UCAT Prep

Once you know these formulas, practice is everything. We recommend building speed through:

• Free UCAT practice tests with answers – apply these formulas in full-length mocks.

• Last-minute UCAT revision tips – perfect for formula review before test day.

• UCAT mistakes to avoid – many mistakes stem from misapplied formulas—know what to watch for.

Also, don’t miss our complete UCAT syllabus 2024 breakdown to understand how Decision Making fits in the bigger picture.

❓ FAQ: Quickfire Decision Making Formula Questions

Q: Do I need to memorize formulas for the UCAT Decision Making section?

A: Yes. While the UCAT is not a traditional math test, having these 5 formulas at your fingertips significantly improves speed and accuracy.

Q: Will I get a formula sheet in the UCAT?

A: No. You are expected to rely on mental math and memorized techniques—no calculator, no formula sheet.

Q: What Decision Making questions need math?

A: Primarily those involving:

• Probability

• Expected value

• Graphical interpretation

• Venn diagrams

• Risk-benefit analysis

Q: How long should I spend on each Decision Making question?

A: Around 64 seconds per question, on average. These formulas help you stick to that timeline.

📈 Infographic: The 5 UCAT Decision Making Formulas at a Glance

(Consider adding an infographic here for visual learners. A pie-chart or flowchart mapping each formula to a question type is ideal.)

🚀 Final Thoughts: Formulas Don’t Just Save Time—They Save Points

Memorizing these formulas doesn’t just help you finish faster—it helps you finish smarter. UCAT Decision Making is as much about logic as it is about efficient reasoning, and formulas bridge that gap.

So write them down. Drill them. Use flashcards. Make them second nature.

When test day hits, they’ll feel like muscle memory.

🔗 Ready to Apply What You’ve Learned?

Start practicing with full-length mocks, real-time score tracking, and AI-powered performance insights at PrepMode.ai. Whether you're targeting 650 or 800+, we've built tools designed for real UCAT improvement.

👉 Start your free UCAT skill training session today. No sign-up required.

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