One problem, two linked decisions
Read both column headings before solving. Every selected result must satisfy the entire question simultaneously.
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DATA INSIGHTS · GMAT-DI-TPA-01 · DRAFT
Two-Part Analysis: Linked Decisions
Build two connected answers without losing shared constraints
Learn: Evidence and decisions
Translate the constraints
Use a short equation system or compact table. Eliminate candidates that violate either condition.
Check the ordered pair
Verify both chosen responses together, including units, signs, and direction of comparisons.
Translate before selecting
Name the two requested quantities and their units. Write each independent restriction, then find a pair satisfying all restrictions. A correct value in one column cannot rescue an incompatible value in the other.
Use boundaries and dependencies
For a quantitative threshold, solve the equality first and then interpret the direction and any whole-number restriction. For verbal assignments, eliminate an option together with any role that requires that option.
Use shared choices to complete an underdetermined model
Sometimes the conditions determine a relationship rather than two individual numbers. Keep that relationship and test the ordered pairs in the common answer list. A valid pair must satisfy every condition simultaneously; do not assume the two choices must differ unless the problem requires it.
Learning Objectives
- Translate two linked conditions into equations or a compact model.
- Choose one response in each column from a shared option set.
- Verify the ordered pair against every stated condition.
Prerequisite Knowledge
- Solving linear equations.
- Interpreting rates, totals, and units.
Worked Examples
Find a fixed fee and a later job price
A service charges a fixed fee plus $24 per hour. A 4-hour job costs $132. Find the fixed fee and the cost of a 5-hour job.
- Use the first job to isolate the fixed fee.
- Use that same fee for the second job.
Conclusion: Choose $36 for the fixed fee and $156 for the 5-hour charge; the two selections satisfy both parts of the model.
Solve a linked mixture decision
A 20% solution and a 50% solution are combined to make 12 liters of a 35% solution. Find the amount of each starting solution.
- Let h be liters of the 50% solution. Then 12−h liters are 20%. Equate ingredient amounts.
- Solve for one amount, then use the total volume for the other.
Conclusion: There are 6 liters of each solution. Check the concentration: 3 liters of ingredient from the 50% solution plus 1.2 liters from the 20% solution gives 4.2/12=35%.
Find the boundary, then read the inequality
A rental plan charges $45 plus $9 per day. Another charges $81 plus $6 per day. Find the equal-cost duration and the first whole number of days for which the second plan is cheaper.
- The second plan starts with a larger fixed charge but saves money each day. Set the two total costs equal.
- Equality is the boundary, not the answer to a strictly-cheaper question.
- For a whole-number booking, move to the first integer beyond the boundary.
Conclusion: Select twelve days for equality and thirteen for the first cheaper booking. Check whether the question uses less than or no more than.
Combine rates instead of completion times
Two independent teams would complete the same job alone in 10 hours and 15 hours. They work together at constant rates without interfering. How long does one complete job take?
- Use one completed job as the unit. Convert each time into work per hour.
- Add simultaneous work rates.
- Invert the combined rate and check each team’s contribution.
Conclusion: The result must be shorter than either solo time. Averaging ten and fifteen hours does not model working together.
Eliminate a role assignment using a dependency
Exactly two different speakers fill an opening and a closing slot. L cannot close. M can only close and requires L to open. N can only open and requires P to close. P is unavailable. Determine the assignment.
| L | Cannot close |
| M | Closing only; L must open |
| N | Opening only; P must close |
| P | Unavailable |
- Exclude P. That also excludes N because its required closing partner is unavailable.
- M is the only remaining closing candidate. Its dependency determines the opening speaker.
- Check the pair against every condition: L opens, M closes, they are different, and M has its required partner.
Conclusion: Eliminating an option may eliminate another option that depends on it. Do not treat the two columns independently.
Use the common list when an equation alone has many solutions
Two positive integer order quantities satisfy twice A plus B equals 31, and A is less than B. Each quantity must be selected from 3, 5, 7, 11, and 17. Find the pair.
- Keep the relationship rather than trying to determine each quantity without the choices.
- Test the allowed A values. They require B values 25, 21, 17, 9 and -3 respectively. Only A=7 produces a B value in the list.
- Verify the order and the total.
Conclusion: Choose A=7 and B=17. The common menu supplies an additional constraint.
Guided Practice: Try, then check
Work through each question on paper before opening its hint or explanation. This learning activity is separate from the scored Practice and Simulation pools.
Guided case: quantities with two independent totals
A supplier sells small cartons containing 6 items and large cartons containing 10 items. An order has exactly 12 cartons and 96 items. Find the numbers of small and large cartons.
| Small | 6 |
| Large | 10 |
What two quantities must the selected pair reproduce?
Show hint
One total counts cartons; the other counts items.
Check reasoning
Define one variable for each carton count. The first equation counts cartons and the second counts individual items.
Use an all-small baseline to find the large-carton count.
Show hint
Start with twelve small cartons. How many items does one replacement add?
Check reasoning
The baseline contains seventy-two items. Each replacement adds four, so six replacements supply the missing twenty-four items.
May the same numerical option be selected for both columns?
Show hint
Check the mathematical conditions rather than assuming the answers must differ.
Check reasoning
Yes. Six small and six large cartons satisfy both totals. Equal selected values are allowed unless the problem explicitly excludes them.
Name the units, build two constraints and verify both. A shared option list does not require different answers.
Think Like a GMAT Test-Taker
Solve the more restrictive column first, then use its result to constrain the other.
When responses share a menu, inspect every candidate as an ordered pair, not independently.
Use substitution to verify both conditions.
Before leaving a case, substitute both selections back into every total, restriction and unit.
For a shared option table, test feasible pairs systematically; a repeated value is allowed unless forbidden.
Check both the algebraic relationship and the allowed answer menu before selecting a pair.
Common Traps
Two individually plausible answers may contradict one another.
The same value may be permitted in two columns depending on the question; never assume otherwise.
A numerical condition can constrain one column indirectly through the other.
A break-even value does not satisfy a strictly cheaper condition.
Adding completion times instead of work rates gives the wrong model.
Selecting a feasible first role without checking its required second role.
A relationship can have many numerical solutions but only one ordered pair in the supplied menu.