GMAT Practice Question: Stephanie has 2 \frac{1}{4} cups of milk on hand and makes 2 batches of cookies, using...
Question
Stephanie has 2 \frac{1}{4} cups of milk on hand and makes 2 batches of cookies, using \frac{2}{3} cup of milk for each batch of cookies. Which of the following describes the amount of milk remaining after she makes the cookies?
- Less than \frac{1}{2} cup
- Between \frac{1}{2} \operatorname{cup} and \frac{3}{4} \operatorname{cup}
- Between \frac{3}{4} cup and 1 cup
- Between 1 cup and 1 \frac{1}{2} cups
- More than 1 \frac{1}{2} cups
Topics: fractions, word problems, translations, calculations
Solution
Step 1
We first define a variable for the total milk Stephanie has.
M_{\text{initial}} = 2\frac{1}{4}\text{ cups}
Step 2
We convert the mixed number to an improper fraction.
2\frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{9}{4}\text{ cups}
Step 3
We translate \textbf{"using }\frac{2}{3}\textbf{\text{ cup of milk for each batch"}} into the milk used for one batch.
m_{\text{per batch}} = \frac{2}{3}\text{ cups}
Step 4
We calculate the total milk used for 2 batches by multiplying by 2.
m_{\text{used}} = 2 \times \frac{2}{3} = \frac{4}{3}\text{ cups}
Step 5
We subtract the milk used from the initial amount to find the remaining milk.
M_{\text{remaining}} = \frac{9}{4} - \frac{4}{3} = \frac{27}{12} - \frac{16}{12} = \frac{11}{12}\text{ cups}
Step 6
We note that \frac{11}{12} is greater than \frac{3}{4} and less than 1.
\frac{3}{4} < \frac{11}{12} < 1
Step 7
Since the remaining milk is between \frac{3}{4} cup and 1 cup, the correct choice is C.
\text{Answer C}
Answer
C
