GMAT Practice Question: Half of a large pizza is cut into 4 equal-sized pieces, and the other half is cut into 6...
Question
Half of a large pizza is cut into 4 equal-sized pieces, and the other half is cut into 6 equal-sized pieces. If a person were to eat 1 of the larger pieces and 2 of the smaller pieces, what fraction of the pizza would remain uneaten?
- \frac{5}{12}
- \frac{13}{24}
- \frac{7}{12}
- \frac{2}{3}
- \frac{17}{24}
Topics: word problems, fractions, translations
Solution
Step 1
We let X represent the whole pizza.
X = 1
Step 2
We interpret \textbf{\text{"Half of a large pizza is cut into 4 equal-sized pieces"}} as splitting half the pizza into 4 equal parts to find the size of one larger piece.
\frac{1}{2}X \times \frac{1}{4} = \frac{1}{8}X
Step 3
We interpret \textbf{\text{"the other half is cut into 6 equal-sized pieces"}} as splitting the remaining half into 6 equal parts to find the size of one smaller piece.
\frac{1}{2}X \times \frac{1}{6} = \frac{1}{12}X
Step 4
We translate \textbf{\text{"eat 1 of the larger pieces and 2 of the smaller pieces"}} into the sum of the amounts eaten.
1 \times \frac{1}{8}X + 2 \times \frac{1}{12}X = \frac{1}{8}X + \frac{2}{12}X
Step 5
We simplify the fraction of smaller pieces eaten by canceling common factors.
\frac{2}{12}X = \frac{\cancel{2}}{\cancel{2} \times 6}X = \frac{1}{6}X
Step 6
We convert to a common denominator and add the eaten portions.
\frac{1}{8}X = \frac{3}{24}X \frac{1}{6}X = \frac{4}{24}X \frac{3}{24}X + \frac{4}{24}X = \frac{7}{24}X
Step 7
We find the remaining uneaten portion by subtracting the eaten fraction from the whole pizza.
X - \frac{7}{24}X = \frac{24}{24}X - \frac{7}{24}X = \frac{17}{24}X
Answer
The fraction of the pizza that remains uneaten is \frac{17}{24} of the pizza, which corresponds to Answer E.
