UCAT-ANZQuantitative Reasoning
QR is a speed test, not a maths test. Marks are won and lost in calculator habits, mental arithmetic, and the discipline to skip the worst 4 questions.
What UCAT-ANZ Quantitative Reasoning actually tests
Quantitative Reasoning is the closest UCAT-ANZ section to a school exam - but mostly only in surface appearance. The maths involved rarely goes beyond junior-secondary level: percentages, ratios, rates, simple algebra, unit conversion, simple statistics, and reading information from charts and tables. There’s no calculus, no trigonometry, no quadratic equations. The challenge is not the maths itself - it’s doing it under time pressure with a clunky on-screen calculator while a chart you barely need to look at takes up half the screen.
Questions most often refer to a shared data context: a chart, a table, a scenario. The naïve approach is to study the chart carefully before tackling the questions - and it’s wrong. The right approach is to skip the chart on first read, jump straight to the first question, and only consult the chart for the specific cell or row you need. You’ll often answer every question linked to a chart having read only a fraction of it.
QR is one of the three cognitive subtests that feed the /2700 scaled total (Verbal Reasoning, Decision Making and Quantitative Reasoning), and it has the widest spread of any subtest - in UCAT-ANZ 2026 its deciles ran from 530 to 880, against 510-730 for Verbal Reasoning. It also carries the highest mean (691 in 2026), so the cohort you are being scaled against is fast. That means QR is the section where speed and calculator dexterity matter more than aptitude - and it’s the section most amenable to practice. Because UCAT-ANZ runs as a single sitting each test cycle, there is no second attempt within the cycle to bank a better QR score, so the few weeks of mental-arithmetic drilling before the test window matter enormously. Most of our students who weren’t scoring well on QR lifted it sharply after 4 weeks of focused drilling.
Mental math shortcuts top scorers use
These get used in 60–70% of QR questions. Drill until automatic.
Percentage building blocks
10% = move decimal one place. 5% = half of 10%. 1% = move decimal two places. To find 23%: 10% + 10% + 1% + 1% + 1%. Faster than the calculator.
Quick fractions
1/8 = 12.5% · 1/6 ≈ 16.7% · 1/3 ≈ 33.3% · 2/3 ≈ 66.7% · 5/6 ≈ 83.3%. Memorise these and a third of QR percentage questions become 5-second answers.
× 11 trick
34 × 11 = 374 (sum the digits, slot between). 47 × 11 = 517 (4 + 7 = 11, carry the 1). Useful for the rare percentage question where 11% appears.
Ratio scaling
If A:B = 3:5 and total = 800, scale: each part = 800 / 8 = 100, so A = 300, B = 500. Faster than algebra.
Estimate, then check
For multiple choice, estimate first. If 3 of the 4 options are clearly wrong by rough order of magnitude, mark the survivor - no calculator needed.
Decimal-to-fraction
0.25 = 1/4 · 0.125 = 1/8 · 0.2 = 1/5 · 0.4 = 2/5. Useful when a probability question gives you a decimal you need to combine.
The on-screen calculator - full strategy
The Pearson VUE on-screen calculator is slower than your phone’s. Mastering its quirks is worth a meaningful chunk of scaled-score points alone.
Open once, keep open
Opening the calculator costs ~2 seconds. Don’t close it between questions in the same set - drag it aside if it covers the chart.
Know what the keyboard can and cannot do
The Consortium says to operate the calculator "by clicking the necessary buttons with your mouse or by using your keyboard for number inputs" (Num Lock on), and that ON/C - or Backspace - is the only clear: there is no shortcut to delete a single digit. Alt + C calls it up. It opens in its own window, so if you click back to the test screen you must click the calculator again before it responds. The keypad is a TI-108 replica: the memory keys are MRC, M− and M+, not MR and MC.
Memory functions for multi-step
When a calculation has 2–3 intermediate values, store each with M+ and recall with MR. Saves the 5+ seconds it takes to re-type each subtotal.
Skip when calculator is overkill
If a question is “15% of 200”, doing it mentally (10% + 5% = 30) is 3× faster than typing. Default to mental for clean numbers.
Top 7 strategies for UCAT-ANZ QR
Skip the data chart on first read
Questions most often share a chart, table or data set. Don't study it up front - read the first question, find the relevant cell, answer, then re-use the same data for any linked questions.
Master percentage shortcuts
10% = move decimal. 5% = half of 10%. 1% = move decimal twice. To find 23%: 10% + 10% + 1% + 1% + 1%. Faster than punching it into the calculator.
Use the calculator memory function
M+, M− and MRC for multi-step calculations rather than re-typing (the TI-108-style calculator has no separate MR or MC key).
Estimate first, calculate only if needed
For multiple-choice, often you can eliminate 3 of 4 options just by rough estimation. If 3 are clearly wrong, mark the survivor and move on.
Flag and skip the worst 3–4 questions
Every QR test has 3–4 brutal questions designed to eat 90+ seconds. Top scorers flag and skip them without remorse - protecting time to bank 5–6 easier questions later.
Drill mental arithmetic daily
Use Brilliant or Khan Academy and do 10 minutes of timed mental arithmetic every day for 4–6 weeks pre-test. The fluency dividend is enormous.
Always sanity-check unit conversions
A common QR trap is mixing units (km vs m, kg vs g, % vs decimal). Before submitting, glance at units in the question and your answer. Wrong units kill more easy QR questions than wrong arithmetic.
Worked examples
A drug dose of 350 mg is increased by 18%. What is the new dose?
A solution is mixed in the ratio 3:5 (concentrate:water). To make 800 ml of solution, how much concentrate is needed?
A train travels 240 km at 80 km/h, then 180 km at 60 km/h. What is the average speed for the whole journey?
A patient drinks 1.5 L of water spread evenly over 6 hours. What is the average rate in mL per minute?
A clinic’s monthly bookings were 40,000 last quarter and 52,000 this quarter. What is the percentage increase?
A bacterial colony doubles every 2 hours. Starting with 50 cells, how many after 8 hours?
Timed mini-quiz
5 questions, 45 seconds each - slightly above live UCAT-ANZ QR pace.
QR speed quiz
Mixed: percentage, ratio, rate, multi-step.
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Decision Making guide
The subtest that takes longest to learn - logic puzzles, syllogisms and probability for UCAT-ANZ.
Open DM guide →Personalised Revision Plan
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Build your plan →UCAT-ANZ score prediction
See what a target /2700 means at Auckland and Otago — Auckland publishes no cut-off and Otago uses percentile thresholds (VR at or above the 20th, SJT at or above the 10th), so we show our NGMP TrueScore estimates.
Predict my score →UCAT-ANZ guide - main page
Back to the UCAT-ANZ hub for subtests, the July–August test window, school cut-offs and the 3-month prep plan.
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Targeted QR drilling with calculator and mental-arithmetic technique. Speed up by 30% in 4 weeks - well before your test date.