A recipe for cookies requires 2.5 cups of flour to make a batch of 30 cookies. A baker needs to...
GMAT Algebra : (Alg) Questions
A recipe for cookies requires \(\mathrm{2.5}\) cups of flour to make a batch of \(\mathrm{30}\) cookies. A baker needs to make enough cookies for an event with \(\mathrm{p}\) attendees, and she expects each attendee to eat \(\mathrm{3}\) cookies. Which equation represents the total amount of flour \(\mathrm{F}\), in cups, needed to make the cookies for the event?
- \(\mathrm{F = \frac{p}{12}}\)
- \(\mathrm{F = \frac{p}{4}}\)
- \(\mathrm{F = 12p}\)
- \(\mathrm{F = 2.5p}\)
\(\mathrm{F} = \frac{\mathrm{p}}{12}\)
\(\mathrm{F} = \frac{\mathrm{p}}{4}\)
\(\mathrm{F} = 12\mathrm{p}\)
\(\mathrm{F} = 2.5\mathrm{p}\)
1. TRANSLATE the problem information
- Given information:
- Recipe: \(2.5\) cups flour makes \(30\) cookies
- Event: \(\mathrm{p}\) attendees, each eating \(3\) cookies
- Find: Total flour needed (F)
2. INFER the solution approach
- This requires a multi-step process:
- Find total cookies needed
- Find flour per cookie from recipe
- Calculate total flour
- We need to work through the chain: attendees → cookies → flour
3. TRANSLATE attendees to total cookies needed
- Total cookies = \(\mathrm{p}\) attendees × \(3\) cookies per attendee = \(3\mathrm{p}\) cookies
4. INFER flour requirement per cookie
- From the recipe: \(2.5\) cups makes \(30\) cookies
- Flour per cookie = \(2.5 \div 30 = \frac{1}{12}\) cups per cookie
5. SIMPLIFY to find total flour equation
- \(\mathrm{F} = (\text{total cookies}) \times (\text{flour per cookie})\)
- \(\mathrm{F} = 3\mathrm{p} \times \frac{1}{12}\)
- \(\mathrm{F} = \frac{3\mathrm{p}}{12}\)
- \(\mathrm{F} = \frac{\mathrm{p}}{4}\)
Answer: B
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak INFER skill: Students miss the multi-step nature and try to directly relate attendees to flour, bypassing the cookies calculation.
They might think "\(\mathrm{p}\) attendees need some flour" and look for a direct relationship, potentially selecting Choice (D) \(\mathrm{F = 2.5\mathrm{p}}\) because they see the \(2.5\) from the recipe and think it applies directly to each attendee.
Second Most Common Error:
Poor SIMPLIFY execution: Students correctly set up \(\mathrm{F} = 3\mathrm{p} \times \frac{1}{12}\) but fail to reduce the fraction properly.
They might leave it as \(\frac{3\mathrm{p}}{12}\) and not recognize this equals \(\frac{\mathrm{p}}{4}\), causing confusion when matching to answer choices. This leads to guessing among the available options.
The Bottom Line:
This problem tests whether students can work through a logical sequence of unit conversions (attendees → cookies → flour) rather than looking for direct relationships that don't exist.
\(\mathrm{F} = \frac{\mathrm{p}}{12}\)
\(\mathrm{F} = \frac{\mathrm{p}}{4}\)
\(\mathrm{F} = 12\mathrm{p}\)
\(\mathrm{F} = 2.5\mathrm{p}\)