On Monday, a community kitchen starts with a bulk container of rice. First, \frac{1}{3} of… — GRE General Test

On Monday, a community kitchen starts with a bulk container of rice. First, $\frac{1}{3}$ of the initial supply of rice is used for lunch. Next, $\frac{1}{4}$ of the remaining rice in the container is used for dinner. After preparing both meals, exactly $60$ kilograms of rice remain in the container. How many kilograms of rice were in the container initially?

A
84 kg
B
90 kg
120 kgAnswer
D
144 kg
E
180 kg

Answer

120 kg

The correct option is 120 kg. After using

\frac{1}{3}

of the initial supply for lunch,

\frac{2}{3}

of the supply remains. Using

\frac{1}{4}

of this remaining amount for dinner leaves

\frac{3}{4}

of the

\frac{2}{3}

remaining. Multiplying these fractions gives

\frac{3}{4} \times \frac{2}{3} = \frac{1}{2}

of the original supply. Since

\frac{1}{2}

of the original supply equals

60

kg, the initial total supply was

60 \times 2 = 120

kg.

Step-by-Step Solution

Determine the fraction of rice remaining after lunch.

Since

\frac{1}{3}

of the initial supply is used for lunch,

1 - \frac{1}{3} = \frac{2}{3}

of the initial supply remains.

The remaining portion after lunch is the base for the next fractional reduction.

Determine the fraction of rice used for dinner and the fraction remaining overall.

Dinner uses

\frac{1}{4}

of the remaining

\frac{2}{3}

, which is

\frac{1}{4} \times \frac{2}{3} = \frac{1}{6}

of the initial total supply. The total fraction used is

\frac{1}{3} + \frac{1}{6} = \frac{1}{2}

. Thus, the fraction remaining after dinner is

1 - \frac{1}{2} = \frac{1}{2}

of the initial total.

Sequential fractional reductions require multiplying the second fraction by the remaining fraction from the first step.

Solve for the initial total mass of rice.

Let

R

be the initial mass in kilograms. Then

\frac{1}{2} R = 60 \implies R = 120

kg.

Setting the calculated remaining fraction equal to the given numerical remaining quantity yields the starting total.

Key Concept

Sequential Fraction of Remaining Quantities

Estimated Time:1m 30s

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