Master the art of finding two answers that must both satisfy every constraint simultaneously — math-based and verbal.
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The Golden Rule of 2PA
Every Two-Part Analysis question presents one scenario and asks you to select two answers from the same list — one for each of two labeled columns. Both selections must jointly satisfy every stated constraint. Getting one right while ignoring the other earns zero credit.
Math-Based 2PA
Verbal-Based 2PA
The highlighted cells show a valid answer pair. Only one cell per column can be selected.
Each column gets exactly one selection. The pair (C, A) is the only valid combination here.
Question:
A company sells two products, X and Y. Product X generates $3 profit per unit and Product Y generates $5 profit per unit. In a given week, the company sold a combined total of 100 units and earned a total profit of $420. In the table below, select the number of units sold for Product X and the number of units sold for Product Y that are consistent with the given information.
Step-by-Step Solution:
Step 1 — Define variables: Let x = units of Product X, y = units of Product Y.
Step 2 — Write equations:
Step 3 — Solve the system: From equation 1: x = 100 - y. Substitute:
Step 4 — Verify: 40 + 60 = 100 ✓ 3(40) + 5(60) = 120 + 300 = 420 ✓
Question:
Maya has a budget of $200. She wants to buy notebooks (each costs $8) and pens (each costs $3). She must buy at least 10 notebooks. She wants to maximize the number of pens she can buy. In the table, select the number of notebooks and the number of pens that are consistent with Maya buying as many pens as possible while satisfying all constraints.
Step-by-Step Solution:
Step 1 — Constraints: 8n + 3p ≤ 200, n ≥ 10, n and p are whole numbers.
Step 2 — Optimization direction: Maximize p → minimize spending on notebooks → buy exactly the minimum: n = 10.
Step 3 — Calculate:
Step 4 — Verify: 8(10) + 3(40) = 80 + 120 = 200 ≤ 200 ✓, n = 10 ≥ 10 ✓
Question:
City planners argue that extending bus routes into suburban neighborhoods will reduce downtown traffic congestion. They also cite that fuel subsidies for public transit operators will lower ticket prices and thereby increase ridership. In the table, identify which statement serves as the main conclusion of the argument and which serves as an intermediate conclusion (a claim that is both supported by evidence and supports the main conclusion).
Step-by-Step Solution:
Step 1 — Identify the overall conclusion: What is the argument ultimately trying to show? "Extending bus routes will reduce downtown traffic" — this is (C). It is the final destination of the reasoning.
Step 2 — Find the intermediate conclusion: An intermediate conclusion is supported by evidence AND supports the main conclusion. "Lower ticket prices will increase ridership" (B) is supported by the fuel subsidies premise AND feeds into the main conclusion (more riders → less private car use → less congestion).
Step 3 — Eliminate wrong options: (A) is not stated, (D) is an unsupported assumption, (E) is irrelevant.
Step 4 — Verify the logical chain: Subsidies → lower prices → higher ridership (B, intermediate) → less congestion (C, main conclusion). Both are logically compatible. ✓
Trap 1: The Partial Solution
Never select just one answer and move on. Both columns must be filled. The GMAT scores 2PA as all-or-nothing — partial credit does not exist. A correct answer in column 1 with a wrong answer in column 2 earns zero points.
Trap 2: Forgetting a Constraint
Questions often have 2-3 constraints. A common trap is that one answer pair satisfies the primary equation but violates a secondary condition (e.g., "neither value may exceed 60"). Always re-read every constraint after finding a candidate pair.
Trap 3: Logically Incompatible Verbal Pairs
In verbal 2PA, two answer choices may each look attractive individually but contradict each other when paired. Always check that the two selected statements can coexist within a single logical framework or argument structure.
Trap 4: Confusing "Maximize" with "Any valid" solution
Some math 2PA questions ask for the pair that maximizes or minimizes something — not just any pair that satisfies constraints. Look for the word "greatest," "most," "fewest," or "least" and optimize accordingly.
8 GMAT-style questions — 4 math-based, 4 verbal-based. Reveal the answer and full explanation after attempting each.
A farmer grows apples and oranges. Apples sell for $2 each and oranges sell for $3 each. The farmer sold 80 fruits total and earned $195. In the table, select the number of apples sold and the number of oranges sold.
First Component (Apples)
(A) 25
(B) 35
(C) 45
(D) 55
(E) 65
Second Component (Oranges)
(A) 25
(B) 35
(C) 45
(D) 55
(E) 65
Answer: Apples = 45 (C), Oranges = 35 (B)
Setup: a + o = 80 and 2a + 3o = 195.
Solve: From equation 1: a = 80 - o. Substitute: 2(80-o) + 3o = 195 → 160 - 2o + 3o = 195 → o = 35.
Then a = 80 - 35 = 45.
Verify: 45 + 35 = 80 ✓ | 2(45) + 3(35) = 90 + 105 = 195 ✓
A shipping container holds at most 500 kg. Small boxes weigh 4 kg each and large boxes weigh 12 kg each. There must be at least 20 small boxes. What combination maximizes the number of large boxes while meeting all constraints?
First Component (Small boxes)
(A) 20
(B) 25
(C) 30
(D) 40
(E) 50
Second Component (Large boxes)
(A) 32
(B) 33
(C) 34
(D) 35
(E) 36
Answer: Small boxes = 20 (A), Large boxes = 35 (D)
Logic: To maximize large boxes, minimize weight used by small boxes. Set small boxes to minimum: 20.
Calculation: Weight used by small boxes = 4 × 20 = 80 kg. Remaining = 500 - 80 = 420 kg. Large boxes = 420 ÷ 12 = 35 (whole number, since 12 × 35 = 420).
Verify: 4(20) + 12(35) = 80 + 420 = 500 ≤ 500 ✓ | small boxes = 20 ≥ 20 ✓
Machine A produces 6 widgets per hour and Machine B produces 9 widgets per hour. Together, they need to produce exactly 108 widgets. Machine A runs for h hours and Machine B runs for k hours, where h and k are positive integers and h is at least twice as long as k. Select a value of h and a value of k consistent with these conditions.
First Component (h — hours for A)
(A) 3
(B) 6
(C) 9
(D) 12
(E) 15
Second Component (k — hours for B)
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Answer: h = 9 (C), k = 4 (B)
Equation: 6h + 9k = 108 → 2h + 3k = 36, with h ≥ 2k.
Test h = 9: 2(9) + 3k = 36 → 18 + 3k = 36 → k = 6. But h ≥ 2k → 9 ≥ 12? No. ✗
Test h = 9, k = 4: 6(9) + 9(4) = 54 + 36 = 90 ≠ 108. Rethink.
Systematic search: 2h + 3k = 36 and h ≥ 2k. Try k = 4: 2h = 36 - 12 = 24 → h = 12. Check: h ≥ 2k → 12 ≥ 8 ✓. Verify: 6(12) + 9(4) = 72 + 36 = 108 ✓
Corrected Answer: h = 12 (D), k = 4 (B)
A chemist mixes Solution A (30% acid) and Solution B (70% acid) to create 200 mL of a 46% acid solution. In the table, select the volume of Solution A and the volume of Solution B used.
First Component (Solution A, mL)
(A) 60
(B) 80
(C) 100
(D) 120
(E) 140
Second Component (Solution B, mL)
(A) 60
(B) 80
(C) 100
(D) 120
(E) 140
Answer: Solution A = 120 mL (D), Solution B = 80 mL (B)
Equations: a + b = 200 and 0.30a + 0.70b = 0.46 × 200 = 92.
Solve: a = 200 - b. Substitute: 0.30(200-b) + 0.70b = 92 → 60 - 0.30b + 0.70b = 92 → 0.40b = 32 → b = 80.
Then a = 200 - 80 = 120.
Verify: 0.30(120) + 0.70(80) = 36 + 56 = 92 = 46% of 200 ✓
A nutrition researcher concludes that reducing sugar intake will improve public health outcomes nationwide. She bases this on evidence that excessive sugar consumption raises the risk of type 2 diabetes. Increased rates of type 2 diabetes in turn drive up national healthcare costs. Select the statement that serves as the main conclusion and the statement that serves as a supporting premise.
First Component (Main Conclusion)
(A) Healthcare costs are rising nationally.
(B) Sugar consumption causes diabetes.
(C) Reducing sugar will improve public health.
(D) Governments should tax sugary drinks.
(E) Type 2 diabetes is the leading disease.
Second Component (Supporting Premise)
(A) Healthcare costs are rising nationally.
(B) Sugar consumption causes diabetes.
(C) Reducing sugar will improve public health.
(D) Governments should tax sugary drinks.
(E) Type 2 diabetes is the leading disease.
Answer: Main Conclusion = C, Supporting Premise = B
Main conclusion (C): "Reducing sugar will improve public health" is the ultimate claim the researcher is making. Everything else supports this.
Supporting premise (B): "Sugar consumption causes diabetes" is directly cited as evidence in the argument. It is not derived from other premises — it is stated as a foundational fact.
Why not A? Rising healthcare costs is an effect of diabetes, a premise component, not the main point. Why not D or E? Neither appears in the passage — they are outside the scope.
A city council must select one revenue-raising measure and one cost-cutting measure to balance a $5 million budget deficit. The measures must be mutually compatible — no combination may disproportionately harm low-income residents. Select one revenue measure and one cost-cutting measure that together can balance the deficit without violating the equity constraint.
First Component (Revenue Measure)
(A) Raise property taxes on homes above $1M
(B) Increase sales tax on all groceries by 5%
(C) Add a luxury hotel surcharge
(D) Reduce earned income tax credits
(E) Tax public transit riders per trip
Second Component (Cost-Cutting Measure)
(A) Cut subsidized housing maintenance budgets
(B) Reduce park maintenance staff
(C) Eliminate free after-school programs
(D) Reduce executive department travel budgets
(E) Close neighborhood health clinics
Answer: Revenue = C (luxury hotel surcharge), Cost-Cutting = D (reduce executive travel)
Revenue side: Options B, D, and E disproportionately burden low-income residents (grocery taxes, reduced tax credits, transit taxes). Option A targets high-value properties — acceptable. Option C (luxury hotel surcharge) targets wealthy visitors — clearly does not harm low-income residents. Best choice: C.
Cost-cutting side: Options A, C, and E directly remove services used primarily by low-income residents. Option B (parks) affects everyone. Option D (executive travel) falls on upper-level staff — compatible with the equity constraint.
Compatibility check: C + D together raise revenue from wealthy sources and cut spending from administrative overheads, satisfying the equity constraint. ✓
A pharmaceutical company claims that Drug X reduces cholesterol AND has minimal side effects. A critic argues both claims are exaggerated. In the table, select one finding that most strengthens the cholesterol reduction claim and one finding that most strengthens the minimal side effects claim. Both findings should come from the same independent clinical trial.
First Component (Strengthens cholesterol claim)
(A) Trial lasted only 2 weeks
(B) LDL levels dropped 22% in 90% of patients
(C) Patients also changed their diets
(D) Trial included only young adults
(E) HDL levels increased by 3%
Second Component (Strengthens side effects claim)
(A) 2% of patients reported mild headaches
(B) 45% of patients reported nausea
(C) Drug required daily injections
(D) Trial was funded by the company
(E) 30% dropped out due to side effects
Answer: Cholesterol = B, Side Effects = A
Cholesterol (B): "LDL dropped 22% in 90% of patients" is a strong, specific, quantified finding. Options A, C, D weaken the claim (short trial, confounding diet changes, non-representative sample). Option E (HDL up 3%) is weak evidence.
Side effects (A): "2% reported mild headaches" directly supports the minimal side effects claim — low incidence and minor severity. Options B and E show high rates, contradicting the claim. C and D are irrelevant to whether side effects occurred.
Compatibility: Both findings can come from the same trial and mutually reinforce the company's dual claims. ✓
An economist argues: "Countries that adopt free trade agreements will experience GDP growth AND a rise in average wages." The argument relies on two unstated assumptions — one about trade's effect on output and one about trade's effect on workers. In the table, select the assumption underlying the GDP growth claim and the assumption underlying the average wages claim.
First Component (GDP assumption)
(A) Free trade eliminates budget deficits
(B) Export growth from trade will outpace any import-related job losses in value terms
(C) All trading partners have equal tariffs
(D) Currency exchange rates remain stable
(E) GDP is measured the same way in all countries
Second Component (Wages assumption)
(A) Workers in export industries earn higher wages than those displaced from import-competing sectors
(B) All workers have university degrees
(C) Wages are set by government decree
(D) Inflation will remain below 2% annually
(E) Labor unions will negotiate new contracts
Answer: GDP assumption = B, Wages assumption = A
GDP (B): For free trade to grow GDP, the gains from increased exports must exceed losses from industries hurt by cheaper imports. This is the bridging assumption between "free trade" and "GDP growth." Options A, C, D, E are either irrelevant or about external conditions, not core trade economics.
Wages (A): Average wages rise only if the new jobs created (in export industries) pay more than the jobs lost (in sectors unable to compete with imports). Without this assumption, free trade could lower average wages even while growing GDP. Options B-E are either extreme, irrelevant, or address policy/inflation, not wage structure.
Compatibility: Both assumptions operate in the same economic framework — they are independent and jointly support the argument. ✓
# TWO-PART ANALYSIS — QUICK REFERENCE
## Structure
- One question stem, one shared answer list
- Select ONE answer per column (two columns total)
- Both must jointly satisfy ALL stated constraints
- Scored all-or-nothing (no partial credit)
## Math 2PA Formulas
- System: a + b = Total & c*a + d*b = Total_value
- Mixture: p1*V1 + p2*V2 = p_target*(V1+V2)
- Optimize: fix one var at constraint bound, solve other
- Verify: substitute BOTH values into ALL equations
## Verbal 2PA Rules
- Main conclusion: NOT supported by anything in the passage
- Premise: supports conclusion, not derived from it
- Intermediate: supported by evidence AND supports main conclusion
- Assumption: unstated link required for argument to hold
- Compatible pair: both selections must coexist logically
## Top 4 Traps
- Partial solution (filling only one column)
- Missed constraint (satisfied equation 1, not equation 2)
- Incompatible verbal pair (each looks right alone, not together)
- Confusing "valid" with "optimal" (re-read for maximize/minimize)
## Time Strategy
- Budget: ~2.5 min per 2PA question (4 per exam section)
- Read columns first (10 sec), list constraints (15 sec)
- Solve (90 sec), verify pair (15 sec), move on