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 labelled A, that for 1991 as B, and that for 1992 as C. What is the ratio of growth in revenue between 91-92 and 90-91?
A. The angle between AB and X-axis when measured with a protractor is 40 degrees, and the angle between CB and X-axis is 80 degrees.
B. The scale of Y-axis is 1 cm = 1000 Rs.

• A. Choose 3 if the question can be answered by using both statements together, but cannot be answered using either statement alone.
• B. Choose 2 if the question can be answered by using either statement alone.
• C. Choose 1 if the question can be answered by using one of the statements alone, but cannot be answered using the other statement alone.
• D. Choose 4 if the question cannot be answered even by using both statements together.

Hint:

On a line graph the points are equally spaced in x, so the growth in each year is proportional to the slope of the segment.

Answer 1

The Correct Option is C

Step 1: Successive years are equally spaced on the X-axis (say by \(h\) cm) and the same Y-scale applies throughout. A segment inclined at angle \(\theta\) to the X-axis rises \(h\tan\theta\) cm, i.e. growth \(\propto\tan\theta\).

Step 2: Statement A alone: Growth 90-91 \(\propto \tan 40^\circ\), growth 91-92 \(\propto \tan 80^\circ\) (CB is the segment of the 91-92 growth). Ratio \(=\dfrac{\tan 80^\circ}{\tan 40^\circ}\approx \dfrac{5.671}{0.839}\approx 6.76\). The scales cancel, so the answer is found.

Step 3: Statement B alone: It gives only the Y scale, with no information about the growth in either year; the ratio cannot be found.

Final Answer:
The correct option is (3): The question can be answered by using one of the statements alone, but cannot be answered using the other statement alone.