Data Interpretation Questions and Answers

Q: The pie chart presents the percentage contribution of different macronutrients to a typical 2,000 kcal diet of a person.Macronutrient energy contribution (pie chart): Carbohydrates 35%, Proteins 20%, Unsaturated fat 20%, Saturated fat 20%, Trans fat 5%.The typical energy density (kcal/g) of these macronutrients is given in the table.MacronutrientEnergy density (kcal/g)Carbohydrates4Proteins4Unsaturated fat9Saturated fat9Trans fat9The total fat (all three types), in grams, this person consumes is

The person eats 100 g of fat.The three fats together supply 20% + 20% + 5% = 45% of the 2,000 kcal, and every fat gives 9 kcal per gram:\[ \begin{aligned} \text{Fat energy} &= 0.45 \times 2000 = 900\ \text{kcal} \\ \text{Fat mass} &= 900 / 9 = 100\ \text{g} \end{aligned} \]44.4 g is the saturated (or unsaturated) fat alone, \(400/9\). 77.8 g is \(700/9\), which uses the 35% carbohydrate share by mistake. 3,600 multiplies the fat energy by 4 instead of dividing by 9.

Q: A 4 × 4 digital image has pixel intensities (\(U\)) as shown in the figure. The number of pixels with \(U \le 4\) is:0102473355446732

There are 11 pixels with \(U \le 4\).Count row by row the entries that are 4 or less:Row 1 (0, 1, 0, 2): all 4Row 2 (4, 7, 3, 3): 4, 3, 3, that is 3Row 3 (5, 5, 4, 4): the two 4s, that is 2Row 4 (6, 7, 3, 2): 3 and 2, that is 2The total is 4 + 3 + 2 + 2 = 11. Counting only values strictly below 4 drops the three 4s and gives 8, which is the trap in option B. 9 and 3 miss further entries.

Q: The number of patients per shift (\(X\)) consulting Dr. Gita in her past 100 shifts is shown in the figure. If the amount she earns is ₹ 1000(\(X - 0.2\)), what is the average amount (in ₹) she has earned per shift in the past 100 shifts?Note: The figure shown is representative.

She earned ₹ 6,100 per shift on average.The mean number of patients per shift, weighted by the number of shifts, is\[ \begin{aligned} \bar{X} &= \frac{5(20) + 6(40) + 7(30) + 8(10)}{100} \\ &= \frac{100 + 240 + 210 + 80}{100} = 6.3 \end{aligned} \]The earning is linear in X, so the average earning is \(1000(\bar{X} - 0.2) = 1000(6.1) = 6100\) rupees. 6,300 is the mean number of patients times 1000, forgetting to subtract the 0.2 per shift. Because the earning rule is linear, averaging X first and averaging the earnings shift by shift give the same 6,100.

Q: Two finance companies, P and Q, declared fixed annual rates of interest on the amounts invested with them. The rates of interest offered by these companies may differ from year to year. Year-wise annual rates of interest offered by these companies are shown by the line graph provided below.YearPQ200076.5200198200289.5200310820047.5920056.58200664If the amounts invested in the companies, P and Q, in 2006 are in the ratio 8:9, then the amounts received after one year as interests from companies P and Q would be in the ratio:

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.

Q: A shaving set company sells 4 different types of razors, Elegance, Smooth, Soft and Executive. Elegance sells at Rs. 48, Smooth at Rs. 63, Soft at Rs. 78 and Executive at Rs. 173 per piece. The table below shows the numbers of each razor sold in each quarter of a year.Quarter \ ProductEleganceSmoothSoftExecutiveQ12730020009176029999Q22522219392184458942Q328976224291954410234Q421012182291659510109Which product contributes the greatest fraction to the revenue of the company in that year?

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.

Q: The pie charts depict the shares of various power generation technologies in the total electricity generation of a country for the years 2007 and 2023.Year 2007Year 2023Coal35%20%Gas25%15%Wind5%10%Hydro30%35%Solar5%20%The renewable sources of electricity generation consist of Hydro, Solar and Wind. Assuming that the total electricity generated remains the same from 2007 to 2023, what is the percentage increase in the share of the renewable sources of electricity generation over this period?

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.

Q: The data given in the following table summarizes the monthly budget of an average household.CategoryAmount (Rs.)Food4000Clothing1200Rent2000Savings1500Other expenses1800The approximate percentage of the monthly budget NOT spent on savings is

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.

Q: 40% of deaths on city roads may be attributed to drunken driving. The number of degrees needed to represent this as a slice of a pie chart is

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.

Q: A contour line joins locations having the same height above the mean sea level. The following is a contour plot of a geographical region. Contour lines are shown at 25 m intervals in this plot.The path from P to Q is best described by

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.

Important Instructions

131.

Consider the percentage of students of different schools involved in various activities.

School→ Activities↓	SS	BS	CS	DS
Games	25	30	20	23
Music	15	25	25	20
Academic	30	20	25	15
Dance	25	15	22	30

The difference in average number of students in various activities of CS and the average number of students in dance is ________.

Exam Year(s)

DSSSB PGT - 2023,

Answer: A

The difference is 0. For CS, the average over the four activities is (20 + 25 + 25 + 22) / 4 = 92 / 4 = 23. For dance, the average over the four schools is (25 + 15 + 22 + 30) / 4 = 92 / 4 = 23. The difference is 23 - 23 = 0.

2, 3 and 5 would result only from misreading a cell in the table.

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132.

The pie chart presents the percentage contribution of different macronutrients to a typical 2,000 kcal diet of a person.

Macronutrient energy contribution (pie chart): Carbohydrates 35%, Proteins 20%, Unsaturated fat 20%, Saturated fat 20%, Trans fat 5%.

The typical energy density (kcal/g) of these macronutrients is given in the table.

Macronutrient	Energy density (kcal/g)
Carbohydrates	4
Proteins	4
Unsaturated fat	9
Saturated fat	9
Trans fat	9

The total fat (all three types), in grams, this person consumes is

A.44.4
B.77.8
C.100
D.3,600

Exam Year(s)

GATE CS - 2024, GATE AE - 2024, GATE AG - 2024,

Answer: C

The person eats 100 g of fat.

The three fats together supply 20% + 20% + 5% = 45% of the 2,000 kcal, and every fat gives 9 kcal per gram:

\[ \begin{aligned} \text{Fat energy} &= 0.45 \times 2000 = 900\ \text{kcal} \\ \text{Fat mass} &= 900 / 9 = 100\ \text{g} \end{aligned} \]

44.4 g is the saturated (or unsaturated) fat alone, \(400/9\). 77.8 g is \(700/9\), which uses the 35% carbohydrate share by mistake. 3,600 multiplies the fat energy by 4 instead of dividing by 9.

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133.

A 4 × 4 digital image has pixel intensities (\(U\)) as shown in the figure. The number of pixels with \(U \le 4\) is:

0	1	0	2
4	7	3	3
5	5	4	4
6	7	3	2

A.3
B.8
C.11
D.9

Exam Year(s)

GATE Chemistry - 2025, GATE AE - 2025,

Answer: C

There are 11 pixels with \(U \le 4\).

Count row by row the entries that are 4 or less:

Row 1 (0, 1, 0, 2): all 4
Row 2 (4, 7, 3, 3): 4, 3, 3, that is 3
Row 3 (5, 5, 4, 4): the two 4s, that is 2
Row 4 (6, 7, 3, 2): 3 and 2, that is 2

The total is 4 + 3 + 2 + 2 = 11. Counting only values strictly below 4 drops the three 4s and gives 8, which is the trap in option B. 9 and 3 miss further entries.

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134.

The number of patients per shift (\(X\)) consulting Dr. Gita in her past 100 shifts is shown in the figure. If the amount she earns is ₹ 1000(\(X - 0.2\)), what is the average amount (in ₹) she has earned per shift in the past 100 shifts?

Note: The figure shown is representative.

Bar chart of number of shifts against number of patients per shift X: 20 shifts at X=5, 40 shifts at X=6, 30 shifts at X=7, 10 shifts at X=8

A.6,100
B.6,300
C.6,000
D.6,500

Exam Year(s)

GATE AE - 2025,

Answer: A

She earned ₹ 6,100 per shift on average.

The mean number of patients per shift, weighted by the number of shifts, is

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

The earning is linear in X, so the average earning is \(1000(\bar{X} - 0.2) = 1000(6.1) = 6100\) rupees. 6,300 is the mean number of patients times 1000, forgetting to subtract the 0.2 per shift. Because the earning rule is linear, averaging X first and averaging the earnings shift by shift give the same 6,100.

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135.

Two finance companies, P and Q, declared fixed annual rates of interest on the amounts invested with them. The rates of interest offered by these companies may differ from year to year. Year-wise annual rates of interest offered by these companies are shown by the line graph provided below.

Year	P	Q
2000	7	6.5
2001	9	8
2002	8	9.5
2003	10	8
2004	7.5	9
2005	6.5	8
2006	6	4

If the amounts invested in the companies, P and Q, in 2006 are in the ratio 8:9, then the amounts received after one year as interests from companies P and Q would be in the ratio:

A.2:3
B.3:4
C.6:7
D.4:3

Exam Year(s)

GATE AG - 2016,

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.

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136.

A shaving set company sells 4 different types of razors, Elegance, Smooth, Soft and Executive. Elegance sells at Rs. 48, Smooth at Rs. 63, Soft at Rs. 78 and Executive at Rs. 173 per piece. The table below shows the numbers of each razor sold in each quarter of a year.

Quarter \ Product	Elegance	Smooth	Soft	Executive
Q1	27300	20009	17602	9999
Q2	25222	19392	18445	8942
Q3	28976	22429	19544	10234
Q4	21012	18229	16595	10109

Which product contributes the greatest fraction to the revenue of the company in that year?

A.Elegance
B.Executive
C.Smooth
D.Soft

Exam Year(s)

GATE CS - 2016,

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.

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137.

The pie charts depict the shares of various power generation technologies in the total electricity generation of a country for the years 2007 and 2023.

	Year 2007	Year 2023
Coal	35%	20%
Gas	25%	15%
Wind	5%	10%
Hydro	30%	35%
Solar	5%	20%

The renewable sources of electricity generation consist of Hydro, Solar and Wind. Assuming that the total electricity generated remains the same from 2007 to 2023, what is the percentage increase in the share of the renewable sources of electricity generation over this period?

A.25%
B.50%
C.77.5%
D.62.5%

Exam Year(s)

GATE Life Sciences - 2024, GATE CS - 2024, GATE XE - 2024,

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.

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138.

The data given in the following table summarizes the monthly budget of an average household.

Category	Amount (Rs.)
Food	4000
Clothing	1200
Rent	2000
Savings	1500
Other expenses	1800

The approximate percentage of the monthly budget NOT spent on savings is

A.10%
B.14%
C.81%
D.86%

Exam Year(s)

GATE Chemistry - 2012, GATE Mathematics - 2012, GATE Life Sciences - 2012, GATE XE - 2012,

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.

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139.

40% of deaths on city roads may be attributed to drunken driving. The number of degrees needed to represent this as a slice of a pie chart is

A.120
B.144
C.160
D.212

Exam Year(s)

GATE Chemistry - 2017,

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.

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140.

A contour line joins locations having the same height above the mean sea level. The following is a contour plot of a geographical region. Contour lines are shown at 25 m intervals in this plot.

Contour map with two hills; a dashed path runs from P near the top of the left hill, through the low ground between them, across the top of the right hill to Q

The path from P to Q is best described by

A.Up-Down-Up-Down
B.Down-Up-Down-Up
C.Down-Up-Down
D.Up-Down-Up

Exam Year(s)

GATE Chemistry - 2017,

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.

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Data Interpretation Questions and Answers

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