A one foot long rod was marked off in sevenths and also in fourths. If the rod is then cut into separate pieces along the markings, which one of the following gives all the different lengths (in feet) of the pieces thus formed?

Correct answer marked below

\frac{1}{4} , \frac{1}{7} , \frac{1}{14} , \frac{1}{28}

\frac{1}{4} , \frac{1}{7} , \frac{1}{14} , \frac{3}{28}

\frac{1}{4} , \frac{1}{7} , \frac{1}{28} , \frac{3}{28}

\frac{1}{4} , \frac{1}{14} , \frac{1}{28} , \frac{3}{28}

\frac{1}{7} , \frac{1}{14} , \frac{1}{28} , \frac{3}{28}

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Explanation

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Official Explanation

Official

If you cut it in each marked place, you will never get

\frac{1}{4}

because

\frac{1}{7}

is smaller and thus the

\frac{1}{4}

will have a split for sure, which makes the answer to be (E) within 10 seconds.…

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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.