In the coordinate plane, line L passes above… | GMAT Sprint

Free Practice Question

PS · Problem Solving

705-805

Fractions/Ratios/Decimals

In the coordinate plane, line L passes above the points $(50, 70)$ and $(100, 89)$ but below the point $(80, 84)$ . Which of the following could be the slope of line L?

Correct answer marked below

\frac{1}{2}

\frac{1}{4}

\frac{2}{5}

Correct

\frac{6}{7}

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Explanation

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Official Explanation

Official

The slope of line L (call it

m

) must be greater than the slope of the line through

(50, 70)

and

(100, 89)

(Line A), and less than the slope of the line through

(50, 70)

and

(80, 84)

(Line B).

Slope of Line A:

\frac{89-70}{100-50} = \frac{19}{50}

, which is slightly less than 0.4 (since

\frac{20}{50}=0.4

).

Slope of Line B:

\frac{84-70}{80-50} = \frac{14}{30}

, which is slightly less than 0.5 (since

\frac{15}{30}=0.5

).…

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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.