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DATA INSIGHTS · GMAT-DI-TPA-02 · DRAFT

Two-Part Analysis: Numerical Constraints

Solve linked choices under simultaneous equations, rates and feasibility conditions

Learn: Evidence and decisions

One response pair must satisfy the whole model

Two-Part Analysis assesses a linked decision. The values in each column can look plausible separately while violating a shared total, rate, or constraint.

Turn language into relationships

Represent the unknowns first. Use a sum, difference, ratio, cost equation, or rate equation, then solve only what the choices require.

Test the pair against all conditions

Substitute both selections into the original statements. Check units, integer restrictions, and whether each response is permitted.

Learning Objectives

  • Translate totals, ratios, costs and capacity conditions into a compact model.
  • Use one selected value to determine the linked value.
  • Check both choices against every condition, including units and domain restrictions.

Prerequisite Knowledge

  • Ratios and percentages.
  • Linear equations and interpreting units.

Worked Examples

Allocate a total with a known difference

Two vehicles carry 84 cartons in total. The first carries 12 more cartons than the second. Find each load.

  1. Let A and B be the loads. Record the total and difference.
  2. Add the equations to isolate A, then subtract to obtain B.
  3. Check both conditions.

Conclusion: The pair (48, 36) satisfies both conditions; solving only the total would not determine the two loads.

Find the break-even quantity and cost

Vendor A charges a $60 setup fee plus $12 per item. Vendor B charges a $20 setup fee plus $16 per item. At what quantity are their costs equal, and what is that cost?

  1. Write a cost expression for each vendor.
  2. Set the expressions equal and solve for the quantity.
  3. Substitute the quantity into either expression.

Conclusion: The choices are 10 items and $180. At fewer than 10 items Vendor A costs more; after 10 Vendor B costs more.

Convert a rate condition into a linked pair

A technician completes 30% of a job in the first 2 hours and the remaining work at a constant rate over the next 7 hours. Find the first-period rate as a percent of the whole job per hour and the later rate.

  1. The first interval accounts for 30% over 2 hours.
  2. The remaining 70% is completed over 7 hours.
  3. Check total work across the intervals.

Conclusion: The rates are 15% and 10% of the job per hour. The denominator is elapsed time in each interval, not the total duration for both rates.

Think Like a GMAT Test-Taker

Name both unknowns and write the shared condition before scanning the choices.

Solve the condition that most directly links the two columns first.

Substitute the selected pair back into every original statement.

Common Traps

Choosing two values that each appear reasonable but do not satisfy the same equation.

Confusing a fixed fee with a per-unit charge.

Using total elapsed time as the denominator for an interval-specific rate.

Rounding a count even though the constraints require an exact integer.

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