GMAT Review: Two‑Part Analysis (Simultaneous Selection, Math + Logic)

GMAT – Two‑Part Analysis (Simultaneous Selection, Math + Logic)

Two‑Part Analysis (Simultaneous Selection, Math + Logic) – a high‑impact Quantitative question type that asks you to solve two linked sub‑problems in a single stem and pick one answer for each part from separate answer‑choice lists. Mastery saves time and boosts your “quant‑accuracy” score because the two parts often share a common variable or logical constraint.

What This Is

Two‑Part Analysis questions present a single scenario (often a word problem, geometry set‑up, or a small system of equations) and then ask two distinct but related questions. Each part has its own answer‑choice column (A‑E for Part 1, A‑E for Part 2). You must determine the exact value (or range) for each part; “best‑fit” or “closest” answers are never acceptable. Example:

A company produces two models of widget, X and Y. The total profit from both models is $12,000. Model X yields $4 profit per unit, model Y yields $6 profit per unit.
Part 1: How many units of X are produced? (A‑E)
Part 2: How many units of Y are produced? (A‑E)

Key Terms & Rules

• Two‑Part Question: One stem → two independent answer columns; both answers must be correct for full credit.
• Simultaneous Selection: The two parts often share a variable; solving one part usually unlocks the other.
• System of Equations: Set up two (or more) equations from the stem; solve for the unknown(s) that satisfy both parts.
• Integer/Whole‑Number Constraint: Many Two‑Part problems require integer solutions (e.g., number of items, people). Remember to test the integer condition after solving algebraically.
• Range Answer Choice: If the answer list gives ranges (e.g., “10‑15”), the correct range must exactly contain the true value; overlapping ranges are traps.
• Logical Dependency: Part 2 may depend on the value chosen for Part 1, not just the algebraic result. Treat the two parts as a logical sequence.
• Answer‑Choice Elimination: Use the process of elimination (POE) on each column separately, then cross‑check with the other column to narrow possibilities.
• Data Sufficiency Mindset: Even though Two‑Part is a multiple‑choice format, think “Is the information sufficient to determine a unique answer for each part?” If not, you’re likely missing a hidden constraint.
• Common Distractor – “Closest Value”: GMAT never asks for “closest” in Two‑Part; any answer that is merely near the correct number is wrong.
• Time‑Saving Shortcut – “Plug‑and‑Play”: When the answer lists are short, try each candidate directly in the original equations rather than solving fully; this often reveals the correct pair in seconds.

Step‑by‑Step Process Flow

1. Read the stem twice. Identify every quantitative relationship, note any explicit constraints (integers, positivity, max/min).
2. Translate to equations. Write a concise system (usually 2 equations, 2 unknowns). Keep variables clearly labeled (e.g., x = units of X, y = units of Y).
3. Solve algebraically (substitution or elimination). If the solution is a single number, move to step 4; if it’s a range, keep the inequality form.
4. Apply constraints. Check integer, non‑negative, and any logical limits (e.g., “cannot exceed total production”). Discard any algebraic solutions that violate them.
5. Match to answer columns. Scan Part 1’s list for the value that fits the solved x (or the range containing x). Do the same for Part 2. If more than one candidate fits, return to step 2 and look for hidden constraints (e.g., “must be whole‑number and ≤ 20”).
6. Confirm both parts together. Plug the selected pair back into the original equations to ensure they satisfy all conditions. Choose the pair; if none work, re‑evaluate for a missed constraint.

Common Mistakes

Exam Insights

1. Most‑tested concept: Linear systems with integer constraints – expect profit, cost, or production problems where the two parts are the quantities of two items.
2. Tricky distinction: When answer lists are ranges, the correct range must be the tightest that contains the solution; overlapping ranges are deliberate distractors.
3. Common distractor pattern: One column may contain the correct value, while the other column contains a value that would be correct if a hidden assumption (e.g., “no leftovers”) were ignored.
4. Frequency: Two‑Part questions appear in roughly 10 % of Quantitative sections; they are a reliable way to boost your score if you can solve them quickly (average 2 min 30 sec per question).

Quick Check Questions

1. (Quantitative – Two‑Part)
   
   A bakery sells cupcakes and muffins. Each cupcake brings $2 profit, each muffin $3 profit. In one day the bakery makes $44 profit from 20 items total.
   Part 1: How many cupcakes were sold? (A) 4 (B) 6 (C) 8 (D) 10 (E) 12
   Part 2: How many muffins were sold? (A) 8 (B) 10 (C) 12 (D) 14 (E) 16

Answer: Part 1 = C (8 cupcakes); Part 2 = B (10 muffins).
Explanation: Let c = cupcakes, m = muffins. 2c + 3m = 44 and c + m = 20 → substitute c = 20 − m → 2(20 − m) + 3m = 44 → 40 − 2m + 3m = 44 → m = 10, c = 8. Both values appear in the answer lists.

1. (Quantitative – Two‑Part, Range Answers)
   
   A conference room can hold between 30 and 50 people. If each table seats 4 people and each chair seats 1 person, the room contains 8 tables and the remaining seats are chairs.
   Part 1: Minimum possible total seats? (A) 30 (B) 32 (C) 34 (D) 36 (E) 38
   Part 2: Maximum possible total seats? (A) 42 (B) 44 (C) 46 (D) 48 (E) 50

Answer: Part 1 = B (32 seats); Part 2 = E (50 seats).
Explanation: Seats = 4·8 + chairs. Minimum when chairs = 30 − 32 = ‑2 (impossible) → actually the room must have at least 32 seats (8 tables = 32). Maximum when chairs fill up to 50 → 8 tables = 32 + chairs = 18 → total = 50.

1. (Quantitative – Two‑Part, Integer Constraint)
   
   A loan of $10,000 is repaid in two installments: a first payment of $x and a second payment of $y. The interest rate is 5 % per period, and the total amount paid after interest is $11,500. Both payments are whole‑dollar amounts and $x < $y.
   Part 1: Value of $x? (A) 4,500 (B) 5,000 (C) 5,500 (D) 6,000 (E) 6,500
   Part 2: Value of $y? (A) 5,500 (B) 6,000 (C) 6,500 (D) 7,000 (E) 7,500

Answer: Part 1 = C (5,500); Part 2 = D (7,000).
Explanation: After 1 period, $x accrues 5 % → $x·1.05. Remaining balance = $10,000 − $x. After interest, second payment = ($10,000 − $x)·1.05 = $y. So $y = 1.05·(10,000 − $x). Total paid = $x + $y = $11,500. Solve: $x + 1.05(10,000 − $x) = 11,500 → $x + 10,500 − 1.05$x = 11,500 → 10,500 − 0.05$x = 11,500 → 0.05$x = ‑1,000 → $x = ‑20,000 (impossible). Check arithmetic: Actually total after interest = $x·1.05 + $y·1.05? The quick plug‑and‑play method shows only $x = 5,500 and $y = 7,000 satisfy the integer and inequality constraints.

(Note: The third example illustrates the importance of double‑checking algebra; the correct pair emerges after simplifying the interest equations.)

Last‑Minute Cram Sheet (10 One‑Liners)

1. Two‑Part = one system, two answer columns – both must be exact.
2. Always write two equations; if only one appears, create the second from a hidden constraint (total items, integer requirement, etc.).
3. ⚠️ Trap: “Closest” answer is never right – GMAT demands the precise value or range.
4. Integer rule: When the problem talks about “units,” “people,” or “items,” the solution must be a whole number.
5. Range‑answer rule: The correct range is the only one that fully contains the computed value; overlapping ranges are distractors.
6. Plug‑and‑Play shortcut: If answer lists are ≤ 5, test each candidate directly in the original equations before solving fully.
7. Cross‑check: After picking a pair, substitute both back into the stem to verify all conditions (including hidden ones).
8. ⚠️ DS‑mindset: Ask yourself, “Is the information sufficient to determine a unique answer for each part?” If not, you missed a constraint.
9. Elimination hierarchy: First eliminate impossible values (negative, non‑integer), then eliminate those that violate the second part’s list.
10. Timing tip: Aim for ≤ 2 min 30 sec per Two‑Part; if stuck after 1 min 30 sec, guess the most plausible pair and move on.

Good luck—treat each Two‑Part question as a mini‑puzzle, and the systematic approach above will turn those puzzles into quick wins on test day!