A retail warehouse received a large shipment of electronics. On Monday, the warehouse sold… — GMAT

A retail warehouse received a large shipment of electronics. On Monday, the warehouse sold $\frac{2}{5}$ of the total shipment. On Tuesday, it sold $25\%$ of the items that remained after Monday. On Wednesday, it sold $33\frac{1}{3}\%$ of the items that remained after Tuesday. If $120$ items remained unsold at the end of Wednesday, how many items were in the original shipment?

$400$ Answer
B
$600$
C
$1,200$
D
$7,200$
E
$36$

Answer

The original shipment contained

400

items.

The correct option correctly evaluates the fraction remaining after each successive sale. After selling

\frac{2}{5}

on Monday,

\frac{3}{5}

remained. After selling

25\%

(

\frac{1}{4}

) on Tuesday,

\frac{3}{4}

of the previous remainder (

\frac{9}{20}

) remained. After selling

33\frac{1}{3}\%

(

\frac{1}{3}

) on Wednesday,

\frac{2}{3}

of that remainder remained, giving a net remaining fraction of

\frac{3}{10}

. Equating

\frac{3}{10}

of the total to

120

yields an original shipment size of

400

Step-by-Step Solution

Calculate the fraction of items remaining after Monday's sales.

Since

\frac{2}{5}

were sold,

1 - \frac{2}{5} = \frac{3}{5}

of the original shipment remained.

The remaining fraction is

1

minus the fraction sold.

Calculate the fraction of items remaining after Tuesday's sales.

Tuesday sold

25\% = \frac{1}{4}

of the remaining items, leaving

1 - \frac{1}{4} = \frac{3}{4}

of Monday's remainder. The fraction remaining relative to the original total is

\frac{3}{5} \times \frac{3}{4} = \frac{9}{20}

Successive percentage reductions apply to the updated intermediate remainder.

Calculate the fraction of items remaining after Wednesday's sales.

Wednesday sold

33\frac{1}{3}\% = \frac{1}{3}

of Tuesday's remainder, leaving

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

of that remainder. The final fraction remaining relative to the original total is

\frac{9}{20} \times \frac{2}{3} = \frac{6}{20} = \frac{3}{10}

Multiply by the fraction remaining after Wednesday's reduction.

Set up the equation to solve for the original total number of items

N

\frac{3}{10}N = 120 \implies N = 120 \times \frac{10}{3} = 400

Divide the remaining count by the net remaining fraction.

Key Concept

Successive Percent and Fraction Reductions

Estimated Time:1m 30s

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