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?

GMAT Panda · Accepted Answer

The fraction of the pizza that remains uneaten is 17/24 of the pizza, which corresponds to Answer E. We let X represent the whole pizza. X = 1 We interpret "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. 1/2X 1/4 = 1/8X We interpret "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. 1/2X 1/6 = 1/12X We translate "eat 1 of the larger pieces and 2 of the smaller pieces" into the sum of the amounts eaten. 1 1/8X + 2 1/12X = 1/8X + 2/12X We simplify the fraction of smaller pieces eaten by canceling common factors. 2/12X = 22 6X = 1/6X We convert to a common denominator and add the eaten portions. 1/8X = 3/24X 1/6X = 4/24X 3/24X + 4/24X = 7/24X We find the remaining uneaten portion by subtracting the eaten fraction from the whole pizza. X - 7/24X = 24/24X - 7/24X = 17/24X

Explanation	Calculations	Help
$We let X represent the whole pizza.$	$X = 1$
$We interpret "Half of a large pizza is cut into 4 equal-sized pieces" as splitting half the pizza into 4 equal parts to find the size of one larger piece.$	$\frac{1}{2} X \times \frac{1}{4} = \frac{1}{8} X$
$We interpret "the other half is cut into 6 equal-sized pieces" as splitting the remaining half into 6 equal parts to find the size of one smaller piece.$	$\frac{1}{2} X \times \frac{1}{6} = \frac{1}{12} X$
$We translate "eat 1 of the larger pieces and 2 of the smaller pieces" into the sum of the amounts eaten.$	$1 \times \frac{1}{8} X + 2 \times \frac{1}{12} X = \frac{1}{8} X + \frac{2}{12} X$
$We simplify the fraction of smaller pieces eaten by canceling common factors.$	$\frac{2}{12} X = \frac{2}{2 \times 6} X = \frac{1}{6} X$
$We convert to a common denominator and add the eaten portions.$	$\frac{1}{8} X = \frac{3}{24} X \frac{1}{6} X = \frac{4}{24} X \frac{3}{24} X + \frac{4}{24} X = \frac{7}{24} X$
$We find the remaining uneaten portion by subtracting the eaten fraction from the whole pizza.$	$X - \frac{7}{24} X = \frac{24}{24} X - \frac{7}{24} X = \frac{17}{24} X$

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