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Updated on: 31 Aug 2026, 01:30
We ran a live Data Insights workshop on Two-Part Analysis, hosted by hr1212 Harsh Rumalwala. Three questions across the three flavours TPA actually throws at you, one verbal, one algebraic and one logic-based, plus a long discussion on pacing.
This post has all three questions with full solutions behind spoilers, so you can attempt them first.
THE TIMING FRAME
Before the questions, the number that shaped the whole session.
TPA questions are built to be solved in two minutes. Not three, not four. Within that, Harsh recommended 45 to 60 seconds maximum for reading and comprehending the prompt, which leaves the rest for the actual work.
Two pieces of advice followed from that, and both are worth more than any single question.
Reverse-engineer your own delays. If you consistently run past two minutes, do not just resolve to be faster. Break the two minutes into reading, pre-thinking, and evaluating options, then work out which of the three is actually eating your clock. People usually guess wrong about which one it is.
Do not force a wrong option to fit. Harsh made the point that when an answer is wrong, trying to justify it anyway costs you 30 to 60 seconds and produces nothing. The argument should flow naturally. If you are constructing an elaborate story to make a choice work, that is your signal to drop it and move on.
QUESTION 1 - VERBAL TPA (conclusion and weakener)
Several national soccer federations have proposed replacing natural grass in FIFA World Cup stadiums with advanced hybrid playing surfaces. These surfaces require substantially less maintenance while providing nearly identical playing conditions. At present, however, installing hybrid surfaces is considerably more expensive than maintaining natural grass, so few host nations currently find the switch economically worthwhile.
Some sports economists predict, however, that increasing water scarcity and rising labor costs will make maintaining natural-grass fields permanently more expensive than maintaining hybrid surfaces within the next two decades, causing hybrid surfaces to gradually replace natural grass in most World Cup stadiums. Even with the savings from this transition, however, the average cost of preparing a stadium to host World Cup matches is expected to be substantially higher than it is today.
Based on the information above, select the statement that is best supported as a conclusion and the statement that, if true, would most weaken that conclusion. Make only two selections, one in each column.
Conclusion: If the economists' predictions are correct, future host nations will incur greater total stadium-preparation costs than current host nations do.
Weakener: The number of stadiums required to host a World Cup is expected to decline substantially over the next 20 years.
Finding the conclusion first. The economists are making a prediction. Ask what they are ultimately trying to convince you of. They say that even with hybrid savings, the average cost of preparing a stadium will be substantially higher than today. The natural continuation is that if the average goes up, the total goes up. That is the fourth statement, and notice how well it uses the "if the predictions are correct" construction to attach itself to the argument.
Then find the gap. The argument moves from average cost per stadium to total cost. That step only holds if the number of stadiums stays roughly constant.
[center]Total = Average × Number of stadiums[/center]
The argument never says a word about the number of stadiums. That silence is the gap.
Harsh worked the arithmetic live. Say there are 10 stadiums at an average of $5 each, so the total is $50. Now the average rises to $7.5. If the count holds at 10, the total climbs to $75 and the conclusion stands. But if the count falls to 2, the total is $15. The average went up and the total went down.
Why the "existing stadiums" option does not work. Several people picked it, and it is the best trap on the page. Choosing existing stadiums over new construction sounds like a cost saving, but the argument is about preparation cost, not construction cost, and the stimulus has already stipulated that preparation cost per stadium will be higher. That choice changes neither the average nor the count, so it leaves the conclusion intact.
QUESTION 2 - MATH TPA (break-even)
A concert promoter is planning a one-night music event at an outdoor venue. Based on ticket sales from similar events, the promoter estimates that attracting a larger audience will require offering tickets at a lower average price. Specifically, if x tickets are sold, the average price received per ticket, in dollars, is expected to be 80 − x/100. The promoter will incur a fixed cost of $40,000 for permits, equipment, and venue preparation, as well as an additional cost of $30 for each ticket sold to cover security, staffing, and other attendee-related expenses.
Assuming that the promoter's estimates are accurate, select the smaller number of tickets and the larger number of tickets for which total revenue would equal total cost. Make only two selections, one in each column.
Smaller: 1,000. Larger: 4,000.
At break-even, revenue equals cost.
The move that matters is the rearrangement. Subtract 30x from both sides before you do anything else:
Now the options do the work for you. Test 1,000: (50 − 10) = 40, and 1,000 × 40 = 40,000. That is one answer. Test 4,000: (50 − 40) = 10, and 4,000 × 10 = 40,000. That is the other. Both fall out in about ten seconds of mental arithmetic.
An even faster route. Multiply the rearranged equation through by 100 and you get a standard quadratic:
So the two roots must sum to 5,000 and multiply to 4,000,000. Scan the options for a pair summing to 5,000 and you get two candidates, 1,000 with 4,000 and 2,000 with 3,000. Now the product separates them: 1,000 × 4,000 is 4 million, while 2,000 × 3,000 is 6 million. Only the first pair works.
The transferable tip. When you get an equation like x = (y − 1/2)/3 and have to find values for both variables, rearrange so one side holds a single variable, then substitute the option values for the other. You pass through the option list once instead of five times, and the moment you solve for one variable you can check whether its partner is even on the list.
QUESTION 3 - LOGIC TPA (scheduling)
Four associates, Priya, Raj, Sam, and Tina, must each give a presentation at one of four consecutive weekly team meetings, with exactly one associate presenting each week. The schedule must satisfy all of the following conditions:
Select the associate who must present first and the associate who must present last. Make only two selections, one in each column.
First: Raj. Last: Sam. The only valid order is R P T S.
Start with the simplest condition, not the first one. Condition 3 pins someone to Week 2 and has only two branches. Condition 1 is conditional, so it only bites in certain cases. Begin where the constraint is hardest.
Branch A, Priya in Week 2: _ P _ _
If Sam goes first, you get S P R T (Tina must follow Raj). But now Priya is before Raj, so condition 1 demands Sam immediately after Priya, in Week 3. Sam is in Week 1. Fails.
If Tina goes first, condition 2 is impossible, because Tina must come after Raj and nothing is earlier than Week 1.
So Raj goes first: R P _ _, leaving Sam and Tina. If Sam took Week 3 then Tina would land in Week 4, immediately after Sam, which condition 2 forbids. So Sam takes Week 4 and Tina Week 3.
R P T S. Check all four. Condition 1 never triggers, because Priya is after Raj, not before. Condition 2 holds, Tina in Week 3 is after Raj in Week 1 and is not immediately after Sam. Condition 3 holds. Condition 4 holds, since Raj and Sam sit in Weeks 1 and 4.
Branch B, Sam in Week 2: _ S _ _
Condition 4 keeps Raj out of Weeks 1 and 3, so Raj must take Week 4. That leaves nothing after Raj for Tina, and condition 2 fails.
Only one arrangement survives. Please note the habit worth copying here: even after finding a schedule that works, keep going and close out the other branch. On a question that asks who must present first, you have not finished until the alternatives are dead.
EXECUTION NOTES FROM THE DISCUSSION
THE ONE THING TO TAKE AWAY
All three questions rewarded the same instinct, which is to find the structural relationship before doing any work.
On question 1 it was Total = Average × Count, and the whole thing turned on a variable the argument never mentioned. On question 2 it was rearranging before substituting, which turned a quadratic into ten seconds of mental math. On question 3 it was starting from the most constrained condition instead of the first one listed.
None of those is a calculation. They are all decisions about where to start, and they are what fits a TPA question inside two minutes.
Thanks to everyone who worked through these out loud, Nitesh Motwani, Akhil T, Kensiya Kennedy, Nidhi Yadav, yashika bhasin, Nadel Rafel, Thuy Nguyen, Aamod Havaldar, rajiv joarder, Praveen Nedunuri, Aman Khan and Aman Kumar, and to [b]hr1212 Harsh Rumalwala[/b] for hosting.
Post your approach below, especially on question 1. The average-versus-total gap is the kind of thing that shows up again and again once you have seen it named.
This post has all three questions with full solutions behind spoilers, so you can attempt them first.
THE TIMING FRAME
Before the questions, the number that shaped the whole session.
TPA questions are built to be solved in two minutes. Not three, not four. Within that, Harsh recommended 45 to 60 seconds maximum for reading and comprehending the prompt, which leaves the rest for the actual work.
Two pieces of advice followed from that, and both are worth more than any single question.
Reverse-engineer your own delays. If you consistently run past two minutes, do not just resolve to be faster. Break the two minutes into reading, pre-thinking, and evaluating options, then work out which of the three is actually eating your clock. People usually guess wrong about which one it is.
Do not force a wrong option to fit. Harsh made the point that when an answer is wrong, trying to justify it anyway costs you 30 to 60 seconds and produces nothing. The argument should flow naturally. If you are constructing an elaborate story to make a choice work, that is your signal to drop it and move on.
QUESTION 1 - VERBAL TPA (conclusion and weakener)
Several national soccer federations have proposed replacing natural grass in FIFA World Cup stadiums with advanced hybrid playing surfaces. These surfaces require substantially less maintenance while providing nearly identical playing conditions. At present, however, installing hybrid surfaces is considerably more expensive than maintaining natural grass, so few host nations currently find the switch economically worthwhile.
Some sports economists predict, however, that increasing water scarcity and rising labor costs will make maintaining natural-grass fields permanently more expensive than maintaining hybrid surfaces within the next two decades, causing hybrid surfaces to gradually replace natural grass in most World Cup stadiums. Even with the savings from this transition, however, the average cost of preparing a stadium to host World Cup matches is expected to be substantially higher than it is today.
Based on the information above, select the statement that is best supported as a conclusion and the statement that, if true, would most weaken that conclusion. Make only two selections, one in each column.
| Conclusion | Weakener | Statement |
| ○ | ○ | Hybrid playing surfaces are expected to have lower lifetime costs than natural-grass fields because of their lower maintenance requirements. |
| ○ | ○ | Future host nations will increasingly choose existing stadiums over constructing new ones for the World Cup. |
| ○ | ○ | The number of stadiums required to host a World Cup is expected to decline substantially over the next 20 years. |
| ○ | ○ | If the economists' predictions are correct, future host nations will incur greater total stadium-preparation costs than current host nations do. |
| ○ | ○ | Rising water and labor costs will not be the primary reason that hosting future World Cups becomes more expensive in the next few decades. |
Show SpoilerSolution
Conclusion: If the economists' predictions are correct, future host nations will incur greater total stadium-preparation costs than current host nations do.
Weakener: The number of stadiums required to host a World Cup is expected to decline substantially over the next 20 years.
Finding the conclusion first. The economists are making a prediction. Ask what they are ultimately trying to convince you of. They say that even with hybrid savings, the average cost of preparing a stadium will be substantially higher than today. The natural continuation is that if the average goes up, the total goes up. That is the fourth statement, and notice how well it uses the "if the predictions are correct" construction to attach itself to the argument.
Then find the gap. The argument moves from average cost per stadium to total cost. That step only holds if the number of stadiums stays roughly constant.
[center]Total = Average × Number of stadiums[/center]
The argument never says a word about the number of stadiums. That silence is the gap.
Harsh worked the arithmetic live. Say there are 10 stadiums at an average of $5 each, so the total is $50. Now the average rises to $7.5. If the count holds at 10, the total climbs to $75 and the conclusion stands. But if the count falls to 2, the total is $15. The average went up and the total went down.
Why the "existing stadiums" option does not work. Several people picked it, and it is the best trap on the page. Choosing existing stadiums over new construction sounds like a cost saving, but the argument is about preparation cost, not construction cost, and the stimulus has already stipulated that preparation cost per stadium will be higher. That choice changes neither the average nor the count, so it leaves the conclusion intact.
QUESTION 2 - MATH TPA (break-even)
A concert promoter is planning a one-night music event at an outdoor venue. Based on ticket sales from similar events, the promoter estimates that attracting a larger audience will require offering tickets at a lower average price. Specifically, if x tickets are sold, the average price received per ticket, in dollars, is expected to be 80 − x/100. The promoter will incur a fixed cost of $40,000 for permits, equipment, and venue preparation, as well as an additional cost of $30 for each ticket sold to cover security, staffing, and other attendee-related expenses.
Assuming that the promoter's estimates are accurate, select the smaller number of tickets and the larger number of tickets for which total revenue would equal total cost. Make only two selections, one in each column.
| Smaller | Larger | Number of tickets |
| ○ | ○ | 500 |
| ○ | ○ | 1,000 |
| ○ | ○ | 2,000 |
| ○ | ○ | 3,000 |
| ○ | ○ | 4,000 |
Show SpoilerSolution
Smaller: 1,000. Larger: 4,000.
At break-even, revenue equals cost.
Code:
Revenue = x(80 − x/100)
Cost = 40,000 + 30x
x(80 − x/100) = 40,000 + 30x
Cost = 40,000 + 30x
x(80 − x/100) = 40,000 + 30x
The move that matters is the rearrangement. Subtract 30x from both sides before you do anything else:
Code:
x(50 − x/100) = 40,000
Now the options do the work for you. Test 1,000: (50 − 10) = 40, and 1,000 × 40 = 40,000. That is one answer. Test 4,000: (50 − 40) = 10, and 4,000 × 10 = 40,000. That is the other. Both fall out in about ten seconds of mental arithmetic.
An even faster route. Multiply the rearranged equation through by 100 and you get a standard quadratic:
Code:
x2 − 5,000x + 4,000,000 = 0
So the two roots must sum to 5,000 and multiply to 4,000,000. Scan the options for a pair summing to 5,000 and you get two candidates, 1,000 with 4,000 and 2,000 with 3,000. Now the product separates them: 1,000 × 4,000 is 4 million, while 2,000 × 3,000 is 6 million. Only the first pair works.
The transferable tip. When you get an equation like x = (y − 1/2)/3 and have to find values for both variables, rearrange so one side holds a single variable, then substitute the option values for the other. You pass through the option list once instead of five times, and the moment you solve for one variable you can check whether its partner is even on the list.
QUESTION 3 - LOGIC TPA (scheduling)
Four associates, Priya, Raj, Sam, and Tina, must each give a presentation at one of four consecutive weekly team meetings, with exactly one associate presenting each week. The schedule must satisfy all of the following conditions:
- If Priya presents before Raj, then Sam presents in the week immediately after Priya.
- Tina presents later than Raj, but not in the week immediately after Sam.
- Either Priya or Sam presents in Week 2.
- Raj and Sam do not present in consecutive weeks.
Select the associate who must present first and the associate who must present last. Make only two selections, one in each column.
| First | Last | Associate |
| ○ | ○ | Priya |
| ○ | ○ | Raj |
| ○ | ○ | Sam |
| ○ | ○ | Tina |
Show SpoilerSolution
First: Raj. Last: Sam. The only valid order is R P T S.
Start with the simplest condition, not the first one. Condition 3 pins someone to Week 2 and has only two branches. Condition 1 is conditional, so it only bites in certain cases. Begin where the constraint is hardest.
Branch A, Priya in Week 2: _ P _ _
If Sam goes first, you get S P R T (Tina must follow Raj). But now Priya is before Raj, so condition 1 demands Sam immediately after Priya, in Week 3. Sam is in Week 1. Fails.
If Tina goes first, condition 2 is impossible, because Tina must come after Raj and nothing is earlier than Week 1.
So Raj goes first: R P _ _, leaving Sam and Tina. If Sam took Week 3 then Tina would land in Week 4, immediately after Sam, which condition 2 forbids. So Sam takes Week 4 and Tina Week 3.
R P T S. Check all four. Condition 1 never triggers, because Priya is after Raj, not before. Condition 2 holds, Tina in Week 3 is after Raj in Week 1 and is not immediately after Sam. Condition 3 holds. Condition 4 holds, since Raj and Sam sit in Weeks 1 and 4.
Branch B, Sam in Week 2: _ S _ _
Condition 4 keeps Raj out of Weeks 1 and 3, so Raj must take Week 4. That leaves nothing after Raj for Tina, and condition 2 fails.
Only one arrangement survives. Please note the habit worth copying here: even after finding a schedule that works, keep going and close out the other branch. On a question that asks who must present first, you have not finished until the alternatives are dead.
EXECUTION NOTES FROM THE DISCUSSION
- Attempting all 64 questions beats perfect accuracy on fewer. The group settled on completion as the priority.
- Do not skip a question without reading it. Spend up to a minute or 90 seconds working out whether it is genuinely hard. An educated guess is better than a blind skip, and it keeps your rhythm intact.
- No external tools. Practise the way the exam runs, with the on-screen calculator only where the exam gives you one.
THE ONE THING TO TAKE AWAY
All three questions rewarded the same instinct, which is to find the structural relationship before doing any work.
On question 1 it was Total = Average × Count, and the whole thing turned on a variable the argument never mentioned. On question 2 it was rearranging before substituting, which turned a quadratic into ten seconds of mental math. On question 3 it was starting from the most constrained condition instead of the first one listed.
None of those is a calculation. They are all decisions about where to start, and they are what fits a TPA question inside two minutes.
Thanks to everyone who worked through these out loud, Nitesh Motwani, Akhil T, Kensiya Kennedy, Nidhi Yadav, yashika bhasin, Nadel Rafel, Thuy Nguyen, Aamod Havaldar, rajiv joarder, Praveen Nedunuri, Aman Khan and Aman Kumar, and to [b]hr1212 Harsh Rumalwala[/b] for hosting.
Post your approach below, especially on question 1. The average-versus-total gap is the kind of thing that shows up again and again once you have seen it named.
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