The board of directors for a philanthropic organization is allocating funds for the three fund-raising events they plan to hold...
GMAT Two Part Analysis : (TPA) Questions
The board of directors for a philanthropic organization is allocating funds for the three fund-raising events they plan to hold next year: Events X, Y, and Z. The organizers of the events have requested that the following amounts be allocated to the events:
- Event X: $12,000
- Event Y: $5,000
- Event Z: $3,000
The board has a total budget of $15,000 for the three events, and they will distribute all of the $15,000 among the 3 events. Each event will receive at most the requested amount and at least half the requested amount.
If the board allocates \(\$10,000\) to Event X, select for Event Y and for Event Z amounts the board could allocate to Event Y and Event Z, respectively, so that the amounts would jointly adhere to the constraints described above. Make only two selections, one in each column.
Phase 1: Owning the Dataset
Understanding the Constraints
We have three events with requested amounts and allocation rules:
- Event X: Requested $12,000 → Can receive: $6,000 to $12,000
- Event Y: Requested $5,000 → Can receive: $2,500 to $5,000
- Event Z: Requested $3,000 → Can receive: $1,500 to $3,000
Key constraint: Total allocation must equal $15,000
Visual Representation
| Event | Requested | Min (50%) | Max (100%) | Allocated |
| Event X | $12,000 | $6,000 | $12,000 | $10,000 ✓ |
| Event Y | $5,000 | $2,500 | $5,000 | ? |
| Event Z | $3,000 | $1,500 | $3,000 | ? |
| Total | $20,000 | $15,000 |
Phase 2: Understanding the Question
Given Information
- Event X receives $10,000 (which is between $6,000 and $12,000 ✓)
- We need to find amounts for Events Y and Z
- The amounts must satisfy all constraints
Key Mathematical Relationship
Since \(\mathrm{X + Y + Z = \$15,000}\) and X = $10,000:
\(\mathrm{Y + Z = \$5,000}\)
We need to find Y and Z from the given options such that:
- Y is between $2,500 and $5,000
- Z is between $1,500 and $3,000
- Y + Z = $5,000
Phase 3: Finding the Answer
Systematic Check of Options
Available choices: $1,000, $2,000, $3,000, $4,000, $5,000
Let's check each possible value for Y:
If Y = $3,000:
- \(\mathrm{Z = \$5,000 - \$3,000 = \$2,000}\)
- Is Y = $3,000 between $2,500 and $5,000? Yes ✓
- Is Z = $2,000 between $1,500 and $3,000? Yes ✓
- Both $3,000 and $2,000 are in our options ✓
???? Stop here - we found our answer.
Phase 4: Solution
Final Answer:
- Event Y: $3,000
- Event Z: $2,000
These allocations satisfy all constraints:
- Total: \(\mathrm{\$10,000 + \$3,000 + \$2,000 = \$15,000}\) ✓
- Event Y gets $3,000 (between min $2,500 and max $5,000) ✓
- Event Z gets $2,000 (between min $1,500 and max $3,000) ✓