Data Interpretation Questions and Answers

Answer: D

The interest is in the ratio 4:3.

In 2006 the graph gives P's rate as 6% and Q's as 4%. Interest is amount times rate, so with amounts in the ratio 8:9:

\[ \begin{aligned} \frac{I_{P}}{I_{Q}} &= \frac{8 \times 6}{9 \times 4} \\ &= \frac{48}{36} = \frac{4}{3} \end{aligned} \]

P earns more despite the smaller deposit because its rate is one and a half times Q's. The ratios 2:3, 3:4 and 6:7 all put Q ahead, which would need Q's rate to be the higher one, as it was in 2002, 2004 and 2005 but not in 2006.

Answer: B

The largest revenue share comes from Executive.

Add the four quarters for each razor and multiply by its price:

\[ \begin{aligned} \text{Elegance} &= 102510 \times 48 = 4920480 \\ \text{Smooth} &= 80059 \times 63 = 5043717 \\ \text{Soft} &= 72186 \times 78 = 5630508 \\ \text{Executive} &= 39284 \times 173 = 6796132 \end{aligned} \]

Executive sells the fewest pieces but its price is more than twice that of any other razor, so it earns the most. Elegance sells the most pieces, which is the trap, but at the lowest price it earns the least.

Answer: D

The share of renewables rose by 62.5%.

Add the Hydro, Solar and Wind shares for each year:

\[ \begin{aligned} 2007: &\ 30 + 5 + 5 = 40\% \\ 2023: &\ 35 + 20 + 10 = 65\% \\ \text{increase} &= \frac{65 - 40}{40} \times 100 = 62.5\% \end{aligned} \]

Since the total generation is unchanged, the rise in share is also the rise in renewable output.

25% is the increase in percentage points (65 - 40), not the percentage increase. 50% and 77.5% do not follow from the shares in the two charts.

Answer: D

About 86% of the budget is not spent on savings.

First total the budget, then take the savings share away from 100%:

\[ \begin{aligned} \text{Total} &= 4000 + 1200 + 2000 + 1500 + 1800 \\ &= 10500 \\ \text{Savings} &= \frac{1500}{10500} \times 100 \approx 14.3\% \\ \text{Not savings} &\approx 100 - 14.3 = 85.7\% \end{aligned} \]

14% is the share that is saved, the trap answer for anyone who misses the NOT. 10% and 81% match no ratio of the table's figures.

Answer: B

The slice needs 144 degrees.

A full pie chart is 360°, and each slice is the same fraction of 360° as its share of the total:

\[ 0.40 \times 360^{\circ} = 144^{\circ} \]

120° is a third of the circle (about 33%), and 160° is about 44%. 212° is close to the 60% remainder (216°), the slice for deaths not attributed to drunken driving, not the 40% asked for.

Answer: C

The path is best described as Down-Up-Down.

Read the heights from the contours, which are 25 m apart. P lies inside the innermost contour of the left-hand hill, above 550 m, so the path starts near a summit and first goes down, crossing the hill's contours outward into the lower ground between the two hills. It then climbs the right-hand hill, crossing its contours inward past 550 m and through the small 575 m closed contour at the top: up. Q lies outside that 575 m loop but inside the 550 m contour, so the last stretch drops a little from the top: down.

Options beginning 'Up' are wrong because P is already at a peak. 'Down-Up-Down-Up' adds a final climb that the path does not make, since Q is lower than the summit the path crosses.

Answer: B

B and C together received 49,500 valid votes.

Valid votes = 1,15,000 - 5,000 = 1,10,000. B and C together hold 25% + 20% = 45% of the valid votes:

\[ 0.45 \times 110000 = 49500 \]

Taking 45% of all votes cast, including the invalid ones, gives 51,750, the main trap. 45,000 and 54,000 do not come from either total.

Answer: B

Mutual fund A returned 10%.

Let A's rate be r. Each person's total after a year:

\[ \begin{aligned} P_{1} &= 10000(1 + r) + 40000(1.15) = 56000 + 10000r \\ P_{2} &= 20000(1 + r) + 30000(1.15) = 54500 + 20000r \\ P_{1} - P_{2} &= 1500 - 10000r = 500 \Rightarrow r = 0.10 \end{aligned} \]

Check: Person 1 gets 57,000 and Person 2 gets 56,500, a difference of 500. A rate of 15% would give a difference of zero, and 7.5% or 20% give 750 and -500.

Answer: A

The average earning is ₹ 6,100.

First find the mean number of patients per shift from the 100 shifts:

\[ \begin{aligned} \bar{X} &= \frac{5(20) + 6(40) + 7(30) + 8(10)}{100} \\ &= \frac{100 + 240 + 210 + 80}{100} = 6.3 \end{aligned} \]

The earning is a linear function of X, so its average is the same function of the average:

\[ 1000(6.3 - 0.2) = 6100 \]

₹ 6,300 forgets to subtract 0.2, ₹ 6,000 uses the most common value 6 instead of the mean, and ₹ 6,500 does not match any consistent reading of the chart.

Answer: C

The true statement is For any 5000 increment in steps/day the largest risk reduction occurs on going from 0 to 5000.

Reading the plot, the risk falls from 1 to about 0.44 between 0 and 5000 steps, a drop of about 0.56. From 5000 to 10000 it falls by about 0.26, from 10000 to 15000 by about 0.09, and from 15000 to 20000 by about 0.05. The curve is steepest at the start and flattens out.

So the first option is false (a drop of about 0.82 from 0 to 10000 against about 0.14 from 10000 to 20000), the second is false (0.56 against 0.05), and the last picks the smallest drop instead of the largest.