Damian needs 14 of the wood in the shed on the first day and 29 of the remaining wood on the second day to make a tree-house in his backyard. Given that 25 of the wood in the shed is unusable due to fungal damage what fraction of useable wood is left once he has completed the tree-house?

Damian needs 14 of the wood in the shed on th… | GMAT Sprint

Free Practice Question

PS · Problem Solving

705-805

Fractions/Ratios/Decimals

Damian needs $\frac{1}{4}$ of the wood in the shed on the first day and $\frac{2}{9}$ of the remaining wood on the second day to make a tree-house in his backyard. Given that $\frac{2}{5}$ of the wood in the shed is unusable due to fungal damage what fraction of useable wood is left once he has completed the tree-house?

Correct answer marked below

\frac{11}{36}

Correct

\frac{1}{3}

\frac{13}{36}

\frac{7}{18}

\frac{17}{37}

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Explanation

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Let the total amount of wood be

w

.

Amount of wood consumed on first day:

\frac{1}{4}w

Wood remaining after first day:

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

Amount of wood consumed on second day:

\frac{2}{9} \times \frac{3}{4}w = \frac{1}{6}w

Total wood consumed:

\frac{1}{4}w + \frac{1}{6}w = \frac{5}{12}w

It is given that

\frac{2}{5}w

is unusable, so usable wood is

\frac{3}{5}w

.

The question asks: what fraction of usable wood remains?…

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What this question tests

Your ability to convert between fractions, ratios, and decimals and to reason proportionally.

Cross-multiplying incorrectly or mixing up the ratio parts — a part:part ratio is not a fraction of the whole.