In a drawing for a certain company's recent holiday party door prizes, 12 employees were awarded a total of $120,...
GMAT Two Part Analysis : (TPA) Questions
In a drawing for a certain company's recent holiday party door prizes, 12 employees were awarded a total of \(\$120\), with each of 4 employees awarded \(\$\mathrm{A}\) and each of 8 employees awarded \(\$\mathrm{B}\).
Select for A and for B values that are jointly consistent with the information provided. Make only two selections, one in each column.
Let's visualize this problem to make it crystal clear...
Understanding the Problem
We have a door prize distribution scenario:
4 employees × $A each = 4A dollars
8 employees × $B each = 8B dollars
Total = $120
This gives us our key equation: \(4\mathrm{A} + 8\mathrm{B} = 120\)
Simplifying the Relationship
Let's simplify by dividing everything by 4:
\(\mathrm{A} + 2\mathrm{B} = 30\)
Rearranging to express A in terms of B:
\(\mathrm{A} = 30 - 2\mathrm{B}\)
Finding Valid Values
Now we'll check each possible B value from our choices to see if it produces a valid A value that's also in our choices.
Testing B = 4:
- \(\mathrm{A} = 30 - 2(4) = 30 - 8 = 22\)
- Is 22 in our choices? No, continue.
Testing B = 5:
- \(\mathrm{A} = 30 - 2(5) = 30 - 10 = 20\)
- Is 20 in our choices? Yes! ✓
? Stop here - we found our answer.
Verification
Let's quickly verify:
- 4 employees × $20 = $80
- 8 employees × $5 = $40
- Total = \(\$80 + \$40 = \$120\) ✓
Final Answer
\(\mathrm{A} = 20\) (the amount each of the 4 employees receives)
\(\mathrm{B} = 5\) (the amount each of the 8 employees receives)