UCAT QR Ratios and Proportions: Unitary Scaling, Mixture Splits, and Clinical Drug Dose Calculations

1. How Ratios and Proportions Are Tested in the 2026/2027 UCAT Format

Ratio and proportion questions in UCAT Quantitative Reasoning test your ability to compare relative quantities, scale chemical mixtures, and allocate budgets under a strict 43.3-second per-question limit. Following the permanent removal of Abstract Reasoning, Quantitative Reasoning carries a full one-third weight of your 900 to 2,700 cognitive score.

In my forensic audit of 6,190 UCAT items while engineering the BeambePrep Quantitative Reasoning bank, I found that candidates rarely fail ratio questions because of advanced mathematics. They fail because they misread whether a stem asks for a part-to-part ratio or a part-to-whole proportion, or they invert the numerator and denominator when translating dense prose into calculator keystrokes. With the official UCAT cohort mean for Quantitative Reasoning sitting at 654 out of 900 ($N = 39,935$) and the 90th percentile threshold requiring a total score of 2,270, banking 15 to 20 seconds on every ratio stem is mandatory to fund multi-step tabular sets later in the subtest.

• Zero Formula Sheet Provision: The official Pearson VUE interface provides zero mathematical reference formulas. Every relationship for unitary scaling, dilution conservation, and inverse worker-hour proportion must reside in your immediate active recall memory.
• Three Core Structural Archetypes: Every UCAT ratio problem falls into one of three categories: part-to-part comparisons ($A : B$), part-to-whole proportions ($\frac{A}{A + B + C}$), or dynamic scaling where quantities are added, removed, or diluted.
• Syntactic Signpost Decoding: The preposition "to" immediately precedes the denominator (the right-hand side of a colon ratio), whereas the preposition "of" without "to" designates the total population denominator in a part-to-whole proportion.
• Strict Pacing Architecture: Straightforward two-part ratio simplifications should take 20 to 25 seconds. Multi-step linked ratios ($A : B$ combined with $B : C$) and clinical drug dosage scalings should be resolved in 35 to 45 seconds. Any item threatening to exceed 50 seconds must be estimated, answered, flagged via Alt + F, and revisited on your second pass.

2. Part-to-Part vs. Part-to-Whole Conversions and the Unitary Box Method

Converting between part-to-part ratios and part-to-whole fractions requires summing all individual ratio components to establish the total number of parts ($S = a + b$). A part-to-part ratio of $a : b$ translates into the part-to-whole fraction $\frac{a}{a + b}$ for the first group and $\frac{b}{a + b}$ for the second group.

When candidates rush under test-day pressure, they frequently treat a colon ratio $3 : 7$ as the fraction $\frac{3}{7} \approx 42.86\%$ when the stem actually asks for the percentage of the total cohort, which is $\frac{3}{3 + 7} = \frac{3}{10} = 30.0\%$. To eliminate this error permanently, I teach the Unitary Box Method. Whenever you see a ratio $a : b : c$, imagine each ratio unit as an identical physical container holding an unknown quantity $k$.

• Establishing the Total Parts Denominator: For any ratio $a : b : c$, your very first mental action is summing the parts: $S = a + b + c$. Write this single sum on your erasable laminated scratchpad before looking at the dollar or volume figures.
• Finding the Single Unit Value ($V_{\text{unit}}$): Divide the known actual quantity by the specific number of ratio parts it represents. If the stem gives you the total combined quantity $Q_{\text{total}}$, then $V_{\text{unit}} = \frac{Q_{\text{total}}}{a + b + c}$. If the stem gives you the difference between Group C and Group A, then $V_{\text{unit}} = \frac{\Delta_{C - A}}{c - a}$.
• Projecting to the Target Group: Once you have $V_{\text{unit}}$ on your calculator display, multiply immediately by the target number of parts. Never clear the calculator between dividing for $V_{\text{unit}}$ and multiplying by the target part.
• Benchmarking Against Unity ($1.0$): Before simplifying any two-part ratio $X : Y$, glance at the raw numbers. If $X > Y$, the simplified ratio must have a larger left side (or a decimal value greater than $1.0$). If $X < Y$, the decimal value must lie strictly between $0$ and $1.0$. This 2-second visual check eliminates two or three reciprocal distractors before your fingers touch the physical NumPad.

Perturbed Worked Example 2.1: Multi-Part Budget Allocation via Difference Scaling

• Option A: $£67,765$
• Option B: $£192,000$
• Option C: $£216,000$
• Option D: $£408,000$

1. Isolate the Part Difference: The stem provides the monetary difference between Centre Gamma ($9\text{ parts}$) and Centre Alpha ($3\text{ parts}$), not the total grant. The difference in ratio parts is $9 - 3 = 6\text{ parts}$.
2. Compute the Unitary Box Value ($V_{\text{unit}}$):

$$V_{\text{unit}} = \frac{£144,000}{6\text{ parts}} = £24,000\text{ per part}$$

1. Scale to the Combined Target: The question asks for Centre Alpha and Centre Beta combined, which represents $3 + 5 = 8\text{ parts}$:

$$\text{Combined Allocation}_{\alpha + \beta} = 8\text{ parts} \times £24,000 = £192,000$$

1. Confirm Correct Option: Option B ($£192,000$) is exact.
2. Distractor Autopsy: Option A ($£67,765$) is the trap for candidates who treat $£144,000$ as the total grant and compute $\frac{8}{17} \times £144,000$. Option C ($£216,000$) is Centre Gamma's share alone ($9 \times £24,000$). Option D ($£408,000$) is the entire grant across all three centres ($17 \times £24,000$).

3. Bridging Linked Ratios ($A : B$ and $B : C$) and Algebraic Ratio Shifts

When a UCAT stem presents two separate ratios that share a common middle group, such as $A : B$ and $B : C$, you cannot compare $A$ to $C$ or calculate a part-to-whole proportion until you equalize the shared variable $B$ using its Lowest Common Multiple (LCM).

A second high-difficulty variation involves dynamic ratio shifts, where a baseline ratio $a : b$ changes to $c : d$ after a specific number of items are added or transferred. Attempting to add raw numbers directly to ratio digits (thinking that adding $5$ items to $2 : 3$ produces $2 : 8$) is a fatal mathematical error because ratio digits represent relative proportions, not absolute counts.

• The LCM Bridge Protocol for Disjoint Ratios: Write the three headers $A : B : C$ on your noteboard. Place the first ratio on Row 1 and the second ratio on Row 2. Find the LCM of the two values in column $B$, scale Row 1 by its required multiplier, and scale Row 2 by its required multiplier to produce a single unified ratio $A : B : C$.
• The Unchanged Anchor Method for Dynamic Additions: If a mixture of Acid to Water starts at $3 : 4$, and pure water is added so the new ratio becomes $3 : 7$, notice that the quantity of Acid did not change. Because the Acid ratio number remained $3$ in both ratios, the increase of $+3\text{ parts}$ in the Water column ($4 \implies 7$) corresponds directly to the added volume of water.
• Cross-Multiplier Algebraic Scaling: When both parts change or when the unchanged part has different ratio digits before and after, equalize the unchanged group's ratio number across both states using the LCM, or set up $\frac{a k + \Delta_1}{b k + \Delta_2} = \frac{c}{d}$ and cross-multiply in a single step: $d(a k + \Delta_1) = c(b k + \Delta_2)$.
• Internal Transfer Conservation (Constant Total Sum): If items are transferred internally from Group A to Group B (for example, nurses moving from Ward A to Ward B), the total sum of parts ($A + B$) remains strictly constant. Equalize the total sum of parts before and after the transfer using the LCM of the two sums.

Perturbed Worked Example 3.1: Bridging Three Linked Hospital Cohorts

• Option A: $60$
• Option B: $90$
• Option C: $105$
• Option D: $120$

1. Align the Shared Variable (Registrars):

$$\text{Juniors} : \text{Registrars} = 5 : 3$$

$$\text{Registrars} : \text{Consultants} = 4 : 7$$

1. Equalize via LCM of $3$ and $4$: The LCM of $3$ and $4$ is $12$.

• Multiply the first ratio by $4$: $\text{Juniors} : \text{Registrars} = 20 : 12$.
• Multiply the second ratio by $3$: $\text{Registrars} : \text{Consultants} = 12 : 21$.
• Unified three-part ratio: $\text{Juniors} : \text{Registrars} : \text{Consultants} = 20 : 12 : 21$.

1. Calculate Total Unified Parts and Scale:

$$S = 20 + 12 + 21 = 53\text{ parts}$$

$$V_{\text{unit}} = \frac{265\text{ physicians}}{53\text{ parts}} = 5\text{ physicians per part}$$

$$\text{Senior Consultants} = 21\text{ parts} \times 5 = 105\text{ consultants}$$

1. Confirm Correct Option: Option C ($105$) is correct.
2. Distractor Autopsy: Option A ($60$) is the number of registrars ($12 \times 5 = 60$). If a candidate fails to bridge the ratio and simply sums the unscaled digits ($5 + 3 + 7 = 15$), they land on a false denominator and select Option D or Option B.

4. Solution Dilutions, Mixture Splits, and Mass Conservation ($C_1 V_1 = C_2 V_2$)

Chemical mixtures, pharmaceutical dilutions, and alloy concentration questions are staples of UCAT Quantitative Reasoning. Every dilution problem is governed by a single physical invariant: when you dilute a solution by adding pure solvent (such as water or saline), the absolute mass or volume of the active solute remains completely unchanged.

Expressed mathematically, this conservation of solute gives the universal dilution equation:

$$C_1 \times V_1 = C_2 \times V_2$$

Where $C_1$ and $V_1$ are the initial concentration and volume, and $C_2$ and $V_2$ are the final concentration and total final volume.

• Pure Solvent Addition ($\Delta V = V_2 - V_1$): When a question asks "How much water must be added to dilute $V_1\text{ mL}$ of a $C_1\%$ solution down to $C_2\%$?", solve for the final total volume $V_2 = \frac{C_1 V_1}{C_2}$ first, and then subtract the initial volume $V_1$. Examiner Option A is almost always the unsubtracted final volume $V_2$.
• Mixing Two Solutions of Different Concentrations: When Volume $V_A$ of concentration $C_A$ is mixed with Volume $V_B$ of concentration $C_B$, the final concentration $C_{\text{final}}$ is the weighted average of the two concentrations:

$$C_{\text{final}} = \frac{C_A V_A + C_B V_B}{V_A + V_B}$$

• Alligation (Cross-Subtraction) Shortcut for Mixture Ratios: If a stem asks in what volume ratio ($V_A : V_B$) you must mix a $15\%$ solution with a $40\%$ solution to achieve a target $25\%$ concentration, you do not need simultaneous equations. Compute the absolute distance of each input from the target $25\%$:

$$\frac{V_A}{V_B} = \frac{|C_B - C_{\text{target}}|}{|C_{\text{target}} - C_A|} = \frac{40 - 25}{25 - 15} = \frac{15}{10} = 3 : 2$$

Because $25\%$ is closer to $15\%$ than to $40\%$, you need more of the $15\%$ solution ($3\text{ parts}$) than the $40\%$ solution ($2\text{ parts}$).

Perturbed Worked Example 4.1: Pharmaceutical Stock Dilution

• Option A: $900\text{ mL}$
• Option B: $936\text{ mL}$
• Option C: $1,296\text{ mL}$
• Option D: $1,656\text{ mL}$

1. Apply Mass Conservation ($C_1 V_1 = C_2 V_2$):

$$18\% \times 360\text{ mL} = 5\% \times V_2$$

1. Calculate Total Final Volume ($V_2$):

$$V_2 = \frac{18 \times 360}{5} = \frac{6,480}{5} = 1,296\text{ mL}$$

1. Subtract Initial Stock Volume ($V_1$) to Isolate Added Water ($\Delta V$):

$$\Delta V = V_2 - V_1 = 1,296\text{ mL} - 360\text{ mL} = 936\text{ mL}$$

1. Confirm Correct Option: Option B ($936\text{ mL}$) is correct.
2. Distractor Autopsy: Option C ($1,296\text{ mL}$) is the classic trap for students who solve for $V_2$ and click immediately without subtracting the original $360\text{ mL}$ already in the beaker. Option D ($1,656\text{ mL}$) results from adding $360\text{ mL}$ to $1,296\text{ mL}$ instead of subtracting.

5. Direct vs. Inverse Proportion and Worker-Hour Rate Stems

Proportion questions require distinguishing immediately between direct proportion (where both variables move in the same direction, $\frac{Y_1}{X_1} = \frac{Y_2}{X_2}$) and inverse proportion (where increasing one variable decreases the other such that their product remains constant, $X_1 \times Y_1 = X_2 \times Y_2$).

The classic UCAT trap is presenting an inverse-proportion workforce or pump-rate scenario ("If 6 laboratory machines analyse a batch in 45 minutes, how long will 9 machines take?") and tempting rushed candidates into setting up a direct cross-multiplication ($\frac{9}{6} \times 45 = 67.5\text{ minutes}$). Always perform a 1-second physical reality check: more machines working simultaneously must take less time, never more time.

• Direct Proportion (Constant Quotient): Applies to distance vs. fuel consumed, mass vs. cost, and dosage vs. patient body weight. If $X$ doubles, $Y$ doubles:

$$\frac{Y_1}{X_1} = \frac{Y_2}{X_2} \implies Y_2 = Y_1 \times \left(\frac{X_2}{X_1}\right)$$

• Inverse Proportion (Constant Product): Applies to workers vs. completion time, speed vs. journey duration for a fixed distance, and gear teeth vs. revolutions per minute. If $X$ increases by a factor of $\frac{3}{2}$, $Y$ must decrease by the reciprocal factor $\frac{2}{3}$:

$$W_1 \times T_1 = W_2 \times T_2 \implies T_2 = \frac{W_1 \times T_1}{W_2}$$

• Three-Variable Worker-Output-Time Formula: When a UCAT stem varies workers ($W$), total output ($O$), and time ($T$) simultaneously ("If 6 technicians process 180 PCR swabs in 4 hours, how many hours will 8 technicians take to process 300 swabs?"), use the unified work-rate invariant:

$$\frac{O_1}{W_1 \times T_1} = \frac{O_2}{W_2 \times T_2}$$

Equivalently, calculate the single-worker hourly unit rate first: $R_{\text{unit}} = \frac{180}{6 \times 4} = 7.5\text{ swabs per technician-hour}$. Then for 8 technicians processing 300 swabs: $T_2 = \frac{300}{8 \times 7.5} = \frac{300}{60} = 5\text{ hours}$.

Perturbed Worked Example 5.1: Multi-Variable Pathology Laboratory Throughput

• Option A: $4\text{ hours } 20\text{ minutes}$
• Option B: $6\text{ hours } 18\text{ minutes}$
• Option C: $6\text{ hours } 30\text{ minutes}$
• Option D: $6\text{ hours } 50\text{ minutes}$

1. Compute the Single-Machine Hourly Rate ($R_{\text{unit}}$):

$$R_{\text{unit}} = \frac{540\text{ slides}}{6\text{ machines} \times 3\text{ hours}} = \frac{540}{18} = 30\text{ slides per machine-hour}$$

1. Calculate Combined Hourly Rate for $4$ Active Machines:

$$R_{\text{team}} = 4\text{ machines} \times 30\text{ slides/hr} = 120\text{ slides per hour}$$

1. Divide Target Output ($780\text{ slides}$) by Team Rate:

$$T_2 = \frac{780\text{ slides}}{120\text{ slides/hr}} = 6.5\text{ hours}$$

1. Convert Decimal Hours to Clock Minutes: $0.5\text{ hours} \times 60 = 30\text{ minutes}$, yielding $6\text{ hours } 30\text{ minutes}$ (Option C).
2. Distractor Autopsy: Option A ($4\text{ hours } 20\text{ minutes}$) traps students who apply direct proportion to the machines ($\frac{4}{6} \times 6.5 = 4.33\text{ hours}$). Option D ($6\text{ hours } 50\text{ minutes}$) traps students who misread $6.5\text{ hours}$ as $6\text{ hours } 50\text{ minutes}$.

6. Clinical Drug Dosing, Weight-Based Scaling, and IV Infusion Rates

Recent UCAT cycles have significantly increased the frequency of clinical pharmacology tables testing weight-based paediatric dosing ($\text{mg/kg/day}$), stock ampoule volume calculations, and intravenous (IV) infusion rates. You do not need prior medical knowledge; every required parameter is given in the table or stem footnotes. Your sole enemy is metric unit mismatch between micrograms ($\mu\text{g}$ or $\text{mcg}$), milligrams ($\text{mg}$), grams ($\text{g}$), millilitres ($\text{mL}$), and litres ($\text{L}$).

• The Universal Metric Mass Ladder:

$$1\text{ kg} = 1,000\text{ g} \quad \Big| \quad 1\text{ g} = 1,000\text{ mg} \quad \Big| \quad 1\text{ mg} = 1,000\text{ }\mu\text{g (micrograms)}$$

$$1\text{ L} = 1,000\text{ mL} = 1,000\text{ cm}^3 \quad \Big| \quad 1\text{ m}^3 = 1,000\text{ L}$$

• Percentage Weight-by-Volume ($\text{\% w/v}$) Anchor: In clinical chemistry stems, a $1\%\text{ w/v}$ solution always means $1\text{ gram}$ of solute per $100\text{ mL}$ of solution (which equals $10\text{ mg/mL}$). Therefore, a $0.9\%\text{ w/v}$ saline bag contains $0.9\text{ g}$ ($900\text{ mg}$) of sodium chloride per $100\text{ mL}$, or $9\text{ g}$ per $1,000\text{ mL}$ ($1\text{ L}$).
• The Nursing Formula for Liquid Stock Dosing:

$$\text{Volume to Administer (mL)} = \left(\frac{\text{Dose Prescribed (What You Want)}}{\text{Stock Strength Available (What You Have)}}\right) \times \text{Stock Volume (mL)}$$

Essential rule: What You Want and What You Have must be in the exact same mass unit (both in $\text{mg}$ or both in $\mu\text{g}$) before you divide.

• Divided Daily Regimens ($\text{BD}$, $\text{TDS}$, $\text{QDS}$): Watch the stem wording carefully for whether a table lists the total daily dose ($\text{mg/kg/day}$ divided into 3 equal doses every 8 hours) or the single-administration dose ($\text{mg/kg/dose}$ given 3 times daily). Confusing daily total with per-dose amount creates a $3\times$ error.

Perturbed Worked Example 6.1: Paediatric Weight-Based IV Infusion Rate

• Option A: $2.4\text{ mL}$
• Option B: $7.2\text{ mL}$
• Option C: $18.0\text{ mL}$
• Option D: $21.6\text{ mL}$

1. Compute the Single-Dose Requirement per Kilogram: Since the total daily dose of $45\text{ mg/kg/day}$ is divided into $3\text{ equal doses}$, each single dose requires:

$$\text{Single Dose Rate} = \frac{45\text{ mg/kg/day}}{3\text{ doses}} = 15\text{ mg/kg per dose}$$

1. Scale by Patient Weight ($24\text{ kg}$):

$$\text{Prescribed Single Dose} = 15\text{ mg/kg} \times 24\text{ kg} = 360\text{ mg}$$

1. Harmonize Stock Vial Concentration Units: The vial contains $0.6\text{ g}$ in $12\text{ mL}$. Convert $0.6\text{ g}$ to milligrams immediately:

$$0.6\text{ g} \times 1,000 = 600\text{ mg in } 12\text{ mL} \implies \text{Concentration} = \frac{600\text{ mg}}{12\text{ mL}} = 50\text{ mg/mL}$$

1. Calculate Administered Volume:

$$\text{Volume} = \frac{360\text{ mg}}{50\text{ mg/mL}} = 7.2\text{ mL}$$

1. Confirm Correct Option: Option B ($7.2\text{ mL}$) is exact.
2. Distractor Autopsy: Option D ($21.6\text{ mL}$) is the total 24-hour volume ($7.2\text{ mL} \times 3$), trapping candidates who overlook the bolded words "single dose". Option A ($2.4\text{ mL}$) results from dividing by $3$ twice.

7. Actionable BeambePrep Training Protocol for QR Ratios

Reading mathematical formulas passively will not build the 25-second reflex speed required under Pearson VUE exam conditions. In my design of the BeambePrep UCAT ecosystem, I linked every Quantitative Reasoning concept across three synchronized training layers so you can eliminate calculation hesitation permanently:

1. Master the Printable Visual Frameworks: Review the full derivation tables, fraction benchmarks, and calculator memory (M+, M-, MRC) workflows in my UCAT Percentages, Ratios & Multipliers Study Note. Print the Ink-Saving Print Edition PDF for your desk binder or annotate the Midnight Dark Edition PDF on your tablet.
2. Automate Formula Retrieval via FSRS-6 Active Recall: Drill the 20-Card Ratios, Proportions & Scaling Pulse Subdeck (Study Now) and the Mental Arithmetic & Fraction Benchmarks Subdeck inside our Complete UCAT 2026/2027 Root Flashcard Suite. Our FSRS-6 spaced repetition scheduler tracks your exact retrieval latency and resurfaces any benchmark fraction or dilution rule right before memory decay occurs.
3. Execute Timed NumPad Drills in Swarm Mode: Launch the 386-Question Quantitative Reasoning: Percentages, Ratios & Multipliers QBank Chapter using a physical USB keyboard with NumLock enabled. Once your topical accuracy exceeds 85% at under 38 seconds per question, test your endurance inside the UCAT Exam Hall and take the Free 40-Question UCAT Diagnostic Mock.

Frequently Asked Questions

Q: What is the difference between a part-to-part ratio and a part-to-whole proportion in UCAT QR?

A part-to-part ratio compares two distinct subgroups directly against each other ($a : b$ or $\frac{a}{b}$), ignoring the rest of the dataset. A part-to-whole proportion compares one subgroup against the entire combined population ($\frac{a}{a + b}$). Whenever a UCAT stem asks for a "proportion", "percentage", or "fraction of the total", your denominator must be the sum of all parts ($a + b$), never the other subgroup alone.

Q: How long should I spend on a ratio or proportion question in the 2026/2027 UCAT?

In the 2026/2027 UCAT format, Quantitative Reasoning contains 36 questions in 26 minutes, giving an average budget of 43.3 seconds per question. You should solve single-step part-to-part or part-to-whole ratio stems in 20 to 25 seconds so you can bank time for dense multi-table scenarios. Complex three-part linked ratios or pharmaceutical dilution questions should take 35 to 45 seconds; if any item exceeds 50 seconds, select your best estimate, press Alt + F to flag, and move on.

Q: How do I combine two separate ratios like A:B and B:C quickly?

Identify the shared variable ($B$) that appears in both ratios and find the Lowest Common Multiple (LCM) of its two values. For example, if $A : B = 2 : 3$ and $B : C = 5 : 4$, the values of $B$ are $3$ and $5$, which have an LCM of $15$. Multiply the first ratio by $5$ ($10 : 15$) and the second ratio by $3$ ($15 : 12$) to form the unified ratio $A : B : C = 10 : 15 : 12$.

Q: What is the fastest way to simplify a large ratio when the answer choices are in colon form?

Instead of spending 30 seconds dividing five-digit numbers by prime factors on your scratchpad, press Alt + C to open the on-screen calculator and divide the left side of the ratio by the right side to get a single decimal value. Then compare that decimal against the five answer choices using benchmark fractions (such as $\frac{1}{8} = 0.125$, $\frac{1}{9} = 0.111$, $\frac{1}{11} = 0.0909$). You only need to test one middle option to eliminate three choices at once.

Q: How do I avoid the reciprocal inversion trap in UCAT ratio questions?

Before entering any digits into the calculator, scan the question stem for the words "of" and "to". In the phrase "What is the ratio of $X$ to $Y$?", the entity immediately following "of" ($X$) is always the numerator (left side), and the entity immediately following "to" ($Y$) is always the denominator (right side). Perform a 2-second magnitude check: if $X > Y$, any answer choice where the left number is smaller than the right number is an inverted distractor and can be eliminated immediately.

Q: How do I solve solution dilution questions in UCAT Quantitative Reasoning?

Use the solute mass conservation formula $C_1 \times V_1 = C_2 \times V_2$, where $C_1$ and $V_1$ are the initial concentration and volume, and $C_2$ and $V_2$ are the final concentration and total volume. Rearrange to find the new total volume $V_2 = \frac{C_1 V_1}{C_2}$. If the question asks how much water or solvent was added, remember to subtract the initial volume ($\Delta V = V_2 - V_1$) as your final step.

Q: How do I recognize an inverse proportion question vs. a direct proportion question?

Perform a physical direction test on the two variables. If increasing Variable A causes Variable B to increase (such as buying more litres of fuel increasing total cost), they are in direct proportion ($\frac{Y_1}{X_1} = \frac{Y_2}{X_2}$). If increasing Variable A causes Variable B to decrease (such as assigning more laboratory technicians to reduce the hours needed to process a fixed batch of samples), they are in inverse proportion ($W_1 \times T_1 = W_2 \times T_2$).

Q: Do I need to memorize clinical drug dosages for the UCAT?

No prior clinical knowledge of specific medications is required; all drug concentrations and patient weight rules are supplied in the scenario stimulus. However, the UCAT does not always provide basic metric conversions, so you must memorize that $1\text{ kg} = 1,000\text{ g}$, $1\text{ g} = 1,000\text{ mg}$, $1\text{ mg} = 1,000\text{ }\mu\text{g}$ (micrograms), and $1\text{ L} = 1,000\text{ mL} = 1,000\text{ cm}^3$.

Q: What does a percentage weight-by-volume (% w/v) label mean in UCAT clinical tables?

In pharmaceutical and chemical tables, $\% \text{ w/v}$ represents the number of grams of active solute per $100\text{ mL}$ of solution. A $5\%\text{ w/v}$ glucose infusion contains $5\text{ g}$ ($5,000\text{ mg}$) of glucose in every $100\text{ mL}$ of fluid, which simplifies to $50\text{ mg/mL}$. Converting $\% \text{ w/v}$ directly into $\text{mg/mL}$ by multiplying the percentage number by $10$ saves two conversion steps on the calculator.

Q: What happens if a ratio changes after items are transferred from Group A to Group B?

When items are transferred internally between two groups without any items entering or leaving the system, the total combined sum ($A + B$) remains invariant. Check the sum of the ratio parts before and after the transfer, and scale both ratios to the Lowest Common Multiple of their sums. The difference in Group A's scaled parts then maps directly to the exact number of transferred items.