The Red Balloon Challenge was an experiment aimed at determining how quickly widely disbursed information could be gathered using social...

GMAT Two Part Analysis : (TPA) Questions

Source: Mock

Two Part Analysis

Quant - Fitting Values

EASY

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Notes

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The Red Balloon Challenge was an experiment aimed at determining how quickly widely disbursed information could be gathered using social media. Competitors tried to locate 10 red weather balloons that had been tethered above random locations around the world in return for a $40,000 prize. The winning team located all of the balloons in just 9 hours, using an incentive-based strategy to encourage information sharing: The first person to send the correct coordinates of a particular balloon to the team received $2,000, but whoever recruited that person received $1,000, and the recruiter's recruiter received $500, and that person's recruiter received $250.

Select for 3 payments per balloon the amount of the prize money that the winning team would have remaining if they had to pay 3 people for each balloon located, and select for 4 payments per balloon the amount of the prize money that the winning team would have remaining if they had to pay 4 people for each balloon located. Make only two selections, one in each column.

3 payments per balloon

4 payments per balloon

$1,000

$2,500

$5,000

$7,500

$10,000

Solution

Let's visualize this problem to make it crystal clear with the payment chain structure.

Phase 1: Owning the Dataset

Understanding the Payment Chain

For each balloon found, the payment chain looks like:
Finder ($2,000) ← Recruiter ($1,000) ← Recruiter's Recruiter ($500) ← Next Recruiter ($250)

Key given information:

Total prize money: $40,000
Number of balloons: 10
Payment amounts: $2,000, $1,000, $500, $250 (in chain order)

Phase 2: Understanding the Question

We need to find:

3 payments per balloon: How much remains if we pay the first 3 people in the chain?
4 payments per balloon: How much remains if we pay all 4 people in the chain?

Phase 3: Finding the Answer

Scenario 1: 3 Payments Per Balloon

If we pay 3 people per balloon, we pay:

Finder: $2,000
Recruiter: $1,000
Recruiter's Recruiter: $500
Total per balloon: $\$2,000 + \$1,000 + \$500 = \$3,500$

For 10 balloons:

Total payments: $\$3,500 \times 10 = \$35,000$
Remaining prize money: $\$40,000 - \$35,000 = \$5,000$

Scenario 2: 4 Payments Per Balloon

If we pay 4 people per balloon, we pay:

Finder: $2,000
Recruiter: $1,000
Recruiter's Recruiter: $500
Next Recruiter: $250
Total per balloon: $\$2,000 + \$1,000 + \$500 + \$250 = \$3,750$

For 10 balloons:

Total payments: $\$3,750 \times 10 = \$37,500$
Remaining prize money: $\$40,000 - \$37,500 = \$2,500$

Phase 4: Solution

Final Answer:

3 payments per balloon: $5,000
4 payments per balloon: $2,500

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