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.
4
5
12
20
30
40
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)