A gift shop buys souvenirs at a wholesale price of $7.00 each and resells them each at a retail price...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
A gift shop buys souvenirs at a wholesale price of \(\$7.00\) each and resells them each at a retail price that is \(290\%\) of the wholesale price. At the end of the season, any remaining souvenirs are marked at a discounted price that is \(80\%\) off the retail price. What is the discounted price of each remaining souvenir, in dollars?
1. TRANSLATE the problem information
- Given information:
- Wholesale price: \(\$7.00\)
- Retail price: 290% of wholesale price
- Discounted price: 80% off the retail price
- Need to find: The discounted price in dollars
2. INFER the solution approach
- This is a two-step percentage problem
- First calculate the retail price, then apply the discount to that retail price
- Key insight: Must work in sequence - can't skip straight to final discount
3. Calculate the retail price
- TRANSLATE: "290% of \(\$7.00\)" means \(\$7.00 \times 2.9\)
- Retail price = \(\$7.00 \times 2.9 = \$20.30\)
4. TRANSLATE the discount correctly
- "80% off" means the customer pays only 20% of the retail price
- \(100\% - 80\% = 20\%\), so multiply by \(0.20\)
5. Calculate the final discounted price
- Discounted price = \(\$20.30 \times 0.20 = \$4.06\)
Answer: \(\$4.06\) (or \(\frac{203}{50}\))
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Misinterpreting "80% off the retail price" as meaning "multiply the retail price by 0.8" instead of "multiply the retail price by 0.2"
Students think: "80% off means I multiply by 80%, so \(\$20.30 \times 0.8 = \$16.24\)"
This fundamental misunderstanding of discount language leads them to calculate the amount of the discount rather than the final price after discount.
Second Most Common Error:
Poor INFER reasoning: Attempting to combine both percentage operations into one step instead of recognizing the sequential relationship.
Students might try: \(\$7.00 \times 2.9 \times 0.8 = \$16.24\) (using the wrong discount interpretation) or get confused about which percentages to apply when.
This leads to confusion and either wrong calculations or abandoning systematic solution and guessing.
The Bottom Line:
Success on this problem depends on correctly interpreting percentage language, especially understanding that "\(X\%\) off" means paying \((100-X)\%\) of the price, not multiplying by \(X\%\).