A customer spent $27 to purchase oranges at $3 per pound. How many pounds of oranges did the customer purchase?
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
A customer spent \(\$27\) to purchase oranges at \(\$3\) per pound. How many pounds of oranges did the customer purchase?
1. TRANSLATE the problem information
- Given information:
- Total money spent: $27
- Price per pound: $3
- Find: How many pounds purchased
2. INFER the mathematical relationship
- When you know the total cost and the cost per unit, you find the number of units by dividing:
- Number of units = Total cost ÷ Cost per unit
- This makes sense because if each pound costs $3, then $27 ÷ $3 tells us how many $3 groups fit into $27
3. SIMPLIFY the calculation
- Number of pounds = $27 ÷ $3 = 9
Answer: 9 pounds
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak INFER skill: Students confuse the operation needed and multiply the numbers instead of dividing.
They might think: "I have $27 and oranges cost $3 per pound, so $27 × $3 = $81." This completely misses the relationship between total cost, unit price, and quantity. The result ($81) doesn't even make sense in context - it would mean spending $81 when they only had $27.
This leads to confusion and an incorrect numerical answer that may not match any reasonable expectation.
The Bottom Line:
Success on this problem depends on understanding the inverse relationship between unit price and quantity - when you know total cost and unit price, division reveals the quantity purchased.