Percentage Change Questions in UCAT QR: The 3-Step Formula

A jumper is reduced by 20% in the sale. At the till, the cashier takes off another 20% with a member’s discount. A student sitting the UCAT Quantitative Reasoning section sees this, types 40% into the calculator, and locks in option C. Option C is wrong. The correct answer is 36%, and it is sitting quietly in option B, where roughly one in three test-takers will skip past it.

Percentage change is the most over-confident topic in UCAT QR. Almost every Australian Year 12 student has done it since Year 7. That familiarity is exactly why the QR section punishes it. The numbers look easy, the formula feels obvious, and you trust your instinct instead of your working. With 25 minutes for 36 questions, instinct is what the examiners are counting on.

This guide walks through the three-step formula that actually works under timer pressure, the multiplier shortcut for compound changes, and the specific trap pattern that shows up across the official UCAT Consortium practice papers.

The percentage change formula students misremember

The standard formula is taught as:

Percentage change = (New − Old) / Old × 100

That is correct. The problem is what students do with it under pressure. Two errors come up repeatedly in r/UCAT QR breakdown threads.

The first is dividing by the new value instead of the original. If a share price goes from $40 to $50, the increase is 25%, not 20%. (10 ÷ 40, not 10 ÷ 50.) The denominator is always the starting number.

The second is forgetting the sign. A decrease from 200 to 150 is a 25% decrease. Some students write 25% and move on, then in a follow-up question are asked “what is the overall change across both years” and forget they were working with a negative. The UCAT loves multi-step questions where a sign error from question one wipes out questions two and three.

The three-step formula to commit to muscle memory:

1. Identify which number is the starting value. Read the question twice if you have to. “From X to Y” means X is the start.
2. Calculate the difference (Y − X). Keep the sign.
3. Divide by the starting value, then multiply by 100.

That is it. The discipline is doing all three steps in order, even when the numbers look trivial. The official UCAT Tour videos on YouTube demonstrate this on the on-screen calculator at the actual exam tempo, and the keystroke pattern is worth rehearsing until your fingers do it without thought.

Increase, decrease, and reverse percentage questions

Three flavours show up in QR, and they require slightly different setups.

Increase questions are the friendliest. “Sales rose from 120 to 150 units. What is the percentage increase?” Difference is 30, divided by 120, times 100, equals 25%.

Decrease questions trip people up when the numbers are not clean. “A council reduced staff from 847 to 692. What is the percentage decrease?” Most students panic at 847. The trick is to commit to the calculator: 847 minus 692 equals 155. 155 divided by 847 equals 0.183. That is 18.3%. Round to whatever the answer options use.

Reverse percentage questions are where the marks are won and lost. “After a 15% discount, a textbook costs $68. What was the original price?” Students instinctively add 15% to $68 and get $78.20. Wrong. $78.20 reduced by 15% is $66.47, not $68.

The correct setup: $68 represents 85% of the original (because 15% was taken off). So original = $68 ÷ 0.85 = $80. Verify: $80 × 0.15 = $12, and $80 − $12 = $68. Tick.

Reverse percentage questions reward the multiplier method, which is the next move in your toolkit.

The ‘multiplier’ method for compound changes

When a value changes more than once, the formula method gets ugly fast. The multiplier method is cleaner, faster, and the only realistic approach inside the 41-second-per-question average in QR.

The idea: any percentage change can be expressed as a single multiplier.

• A 20% increase is ×1.20
• A 20% decrease is ×0.80
• A 7% increase is ×1.07
• A 12.5% decrease is ×0.875

To find the multiplier, you either add the percentage to 1 (for increases) or subtract it from 1 (for decreases). Once values are in multiplier form, you just multiply them together.

Example. A property is valued at $480,000. It rises 8% in year one, falls 3% in year two, and rises 5% in year three. Final value?

Multiplier chain: 1.08 × 0.97 × 1.05 = 1.10. So $480,000 × 1.10 = $528,000. Two calculator strokes if you set it up properly, and the rounding error is negligible.

The same method works in reverse. If you know the final value and need the original, divide instead of multiply. Final $528,000 ÷ 1.10 = $480,000.

For QR practice, the MasterMed question bank reorders compound-change questions so the multiplier setup becomes automatic rather than something you reconstruct from scratch each time. Once it is automatic, you save roughly ten seconds per question, which compounds across a 36-question section.

Why 20% off then 20% back is not the original

This is the single most tested trap pattern in QR percentage change. It shows up dressed as retail sales, share prices, salary cuts, and population changes. The mechanic is always the same.

A jacket is $200. The shop takes 20% off. Then later that month, they raise prices back by 20%. What is the final price?

The wrong answer, which is always sitting in the answer options, is $200. The reasoning trap says “20% off and 20% on cancels out.” It does not.

Working it through with multipliers makes the trap obvious. $200 × 0.80 = $160. Then $160 × 1.20 = $192. The final price is $192, not $200. The overall change is a 4% decrease.

Why? Because the 20% you took off was 20% of $200, but the 20% you added back was 20% of $160. The bases are different. Percentage operations are not symmetric.

The trap is sitting in the answer options in three ways:

1. The “no change” option ($200, or “0% change”) — the gut answer
2. The “double” option (40% off, or $120) — for students who added the percentages instead of chaining multipliers
3. The correct answer ($192 or 4% decrease) — usually buried in option B or D

When you see two consecutive percentage changes that look like they should cancel, slow down and chain the multipliers. The UCAT Consortium official mocks at ucat.ac.uk include at least one of these in every QR set.

Three worked questions with timing

A 36-question QR section in 25 minutes works out to about 41 seconds per question, but percentage change items should be faster than that. Aim for 30 to 35 seconds. Here are three at progressing difficulty.

Question 1 (target: 25 seconds). A car dealership sold 240 cars in March and 312 cars in April. What is the percentage increase in sales?

Working: 312 − 240 = 72. 72 ÷ 240 = 0.30. Answer: 30%.

If you reached for the calculator on 72 ÷ 240, you lost five seconds. 72 ÷ 240 = 72 ÷ 240 = 3/10. That is mental maths if you spot the ratio.

Question 2 (target: 35 seconds). A laptop is listed at $1,400. It is discounted by 15%, and then GST of 10% is added to the discounted price. What is the final price?

Multiplier chain: 1400 × 0.85 × 1.10 = 1400 × 0.935 = $1,309.

The trap option will be $1,400 × 0.95 = $1,330, because students treat “−15% then +10%” as “−5% overall.” It is not.

Question 3 (target: 40 seconds). A town’s population was 18,400 in 2020. It fell by 12% by 2022, then rose by 8% by 2024. To the nearest whole number, what was the 2024 population?

Multiplier chain: 18,400 × 0.88 × 1.08 = 18,400 × 0.9504 = 17,487 (rounded).

The trap: students compute “−12% + 8% = −4%” and pick 18,400 × 0.96 = 17,664. That option will be there. It is wrong by 177 people.

Where the trap usually sits in the answer options

The five-option structure in QR is consistent enough that you can predict where the wrong answers come from. For percentage change questions:

The “obvious” answer is almost never correct on compound percentage change items. If your gut answer matches the first or last option without any working, that is your cue to slow down for ten seconds and verify with multipliers.

Daily drill for the next ten days

Ten days is enough to make the multiplier method automatic if you drill it correctly. The mistake students make is doing 200 mixed QR questions a day with no theme. You need spaced, focused repetition on this single skill.

The drill, 15 minutes per day:

• Days 1 to 3. Twenty single-step percentage change questions, mixed increase and decrease. Time pressure: 25 seconds each. Track which ones you miss.
• Days 4 to 6. Twenty reverse-percentage questions. Force yourself to write the multiplier first (×0.85, ×1.07) before touching the calculator.
• Days 7 to 9. Twenty compound-change questions, two or three steps. This is where the multiplier method earns its place. No additive shortcuts allowed, even when the numbers tempt you.
• Day 10. A full 25-minute QR section under exam conditions. Note every percentage change question. Did you finish them in under 35 seconds each? Did you fall for the additive trap even once?

Free practice for this drill: the UCAT Consortium publishes two full mock papers and roughly 150 official questions at ucat.ac.uk. The r/UCAT subreddit has weekly QR question threads where students post problems and worked solutions, which is useful for spotting trap patterns you have not seen before.

Frequently Asked Questions

Is percentage change the most common QR topic?

It is one of the most consistently tested. Across UCAT Consortium official material, expect three to six percentage-related items per 36-question QR set, sometimes embedded inside ratio or proportion problems rather than as standalone questions.

Can I do percentage change in my head during the exam?

For single-step questions with clean numbers (like 25% of 200), yes. For compound changes and reverse percentages, use the on-screen calculator. The UCAT calculator is slow, so practise the keystrokes ahead of time on the UCAT Consortium’s official interface.

What if I run out of time on QR?

Flag long calculation-heavy questions and guess if you must. There is no negative marking. Better to lock in eight quick percentage change wins than burn three minutes on one complex multi-table problem and rush the rest. The Consortium recommends a 30-to-45-second budget per question.

Does MasterMed cover all four UCAT 2026 sections?

Yes — VR, DM, QR, and SJT. Abstract Reasoning was removed in 2025 so it is not part of the current format. MasterMed runs at $3.83 per week (around $199 per year) with a 5-day free trial that does not ask for a credit card.

How many percentage change questions should I do before the exam?

There is no magic number, but two hundred properly-reviewed questions across the topic types covered above will get most students past the trap patterns. Reviewing why you got one wrong matters more than grinding another fifty.

Open the UCAT Consortium’s free Question Bank tonight, find five percentage change questions, and force yourself to write the multiplier on paper before you touch the calculator. That single habit, drilled for ten days, is what turns this topic from a guessing game into the easiest marks in your QR section.