Question

A line graph on a graph sheet shows the revenue for each year from 1990 through 1998 by points and joins the successive points by straight line segments. The point for revenue of 1990 is labeled A, that for 1991 is B, and that for 1992 is C. What is the ratio of growth in revenue between 1991–92 and 1990–91? \medskip Statement I: The angle between AB and X-axis when measured with a protractor is \( 40^\circ \), and the angle between CB and x-axis is \( 80^\circ \).
Statement II: The scale of y-axis is \( 1 \text{ cm} = 1000 \).

• A. if the question can be answered by using one of the statements alone, but cannot be answered using the other statement alone.
• B. if the question can be answered by either statement alone.
• C. if the question can be answered by using both statements together, but cannot be answered using either statement alone.
• D. if the question cannot be answered even by using both the statements together.

Hint:

Geometric data (angles) must be paired with scale information to compute real-world quantities like revenue.

Answer 1

The Correct Option is C

We are asked to compute the ratio of revenue growth between: \[ \frac{\text{Revenue}_{1992} - \text{Revenue}_{1991}}{\text{Revenue}_{1991} - \text{Revenue}_{1990}} \]

Statement I: Gives the angles that AB and CB make with the x-axis, but angles alone do not give revenue unless we know the scaling. So it is insufficient alone. 

Statement II: The scale alone doesn’t help — we don’t know how much y-values differ between A, B, and C unless the angles or coordinates are known. 

Together: With the angle (from slope) and scale (conversion from cm to revenue), we can compute the vertical change: \[ \tan \theta = \frac{\Delta y}{\Delta x} \Rightarrow \Delta y = \Delta x \cdot \tan \theta \Rightarrow \text{Revenue Change} = \Delta x \cdot \tan \theta \cdot 1000 \] Hence, combining both allows calculation of revenue changes and their ratio.