Bar & Line Graphs

Read the Quiz row across all five colleges: 31 + 13 + 21 + 19 + 26 = 110. Average = 110/5 = 22. The Games row averages 23.4, which is why option B is offered.

In column R, Debate = 18 and Quiz = 21, so the total is 39. Column Q would give 24 + 13 = 37 and column S 15 + 19 = 34 — the only real risk is picking the wrong column.

Take the 2020 row only. Boys: 150 + 120 + 100 + 200 = 570. Girls: 130 + 140 + 80 + 150 = 500. Difference = 570 − 500 = 70. Chemistry runs the other way (120 boys against 140 girls), so every column has to be carried with its sign rather than assumed positive.

Take the 2021 row only. Girls: 80 + 100 + 140 + 120 = 440. Boys: 100 + 100 + 150 + 100 = 450. Required percentage = (440/450) × 100 = 97.77…, about 97.7 per cent. Reversing the two gives 102.3 per cent, which is not on offer — a useful sign that you have the ratio the right way up.

Read the 2013 row, taking only the “New” column of each course: Medical 169, Non-Medical 540, Arts 340, Commerce 230, Vocational 192. Non-Medical leads at 540, comfortably ahead of Arts at 340. The “Left” columns are a distraction — the question asks only about fresh enrolment.

Students still studying = everyone enrolled up to that year minus everyone who has left. Arts enrolled: 680 + 256 + 340 = 1,276. Arts left: 140 + 110 = 250. Still studying = 1,276 − 250 = 1026. The three wrong options are the loose parts of that same sum: 1,276 forgets the subtraction, 250 is only those who left, and 340 is just the 2013 intake.

Add each column over the seven years: Sedan 682, Luxury 713, SUV 866, Minivan 612, Truck 786. SUV is the largest. Luxury is the trap because it starts highest in 2001 at 143 — but it falls every year while SUV climbs.

Walk down each column from 2001 to 2006 and check that every step is a fall. Luxury: 143, 125, 115, 95, 75, 60 — down at every step. Minivan: 102, 86, 104 — rises in 2003, so it is out. Truck and Sedan both rise at the first step. Minivan is the tempting answer because it ends far below where it started, but “continuously” requires every single year to be lower than the one before.

The same car-sales table, asked the other way round. Luxury runs 143, 125, 115, 95, 75, 60 — a fall at every step, so Luxury is again the answer. Truck rises at the first step, Sedan rises at the first step, and Minivan rises in 2003.

Column totals again: SUV 866, Truck 786, Luxury 713, Sedan 682 (Minivan, not offered, is 612). SUV is the largest.

From the same car table, read the Luxury column: 2003 = 115 and 2006 = 60. Difference = 115 − 60 = 55 thousand. Option A (60) is the 2006 figure itself and option B (75) is the 2005 figure — both read straight from the wrong cell.

Minivan sales were 104 thousand in 2003 and 100 thousand in 2007 — a fall of 4. Percentage change is taken on the base year: 4/104 × 100 = 3.846%, which the paper prints as 3.84% (truncated rather than rounded). Dividing by the 2007 figure gives exactly 4%, which is where option B comes from.

Read the 2017 column: computers 825, watches 445. Difference = 825 − 445 = 380. Option A (540) comes from pairing 825 with the 2016 watch figure of 358.

TVs: 2018 = 799 and 2019 = 824, so the increase is 25. Percentage increase = (25/799) × 100 = 3.129…, about 3.13%. The base is always the earlier year.

Subtract departures from admissions, year by year, in row B: 2015: 190 − 152 = 38 · 2016: 165 − 109 = 56 · 2017: 129 − 101 = 28 · 2018: 184 − 111 = 73 · 2019: 157 − 129 = 28. The largest gap is 73, in 2018. 2019 looks big only because its admission figure is large — its outflow is large too.

School C: 140 in 2016 and 151 in 2017, an increase of 11. Percentage increase = (11/140) × 100 = 7.86%. Using 151 as the base gives 7.28%, which is what makes 7.52% look plausible.

Failures = appeared − passed. Add each year's column: 2012: 2 + 4 + 1 + 2 = 9 · 2013: 16 · 2014: 15 · 2015: 10 · 2016: 10. The smallest total is 9, in 2012. 2015 and 2016 tie at 10, just one above, which is why both are offered.

Add each school's failures across the five years: A 12, B 14, C 11, D 23. D is highest, chiefly because of 2014, where 83 appeared and only 75 passed — eight failures in one year, more than school C managed in all five.

Vacancies go from 1,000 to 1,240, an increase of 240. Percentage increase = (240/1000) × 100 = 24%. Dividing by 1,240 gives 19.4%, which is where option A's 20% comes from.

The Patwar row for 2020-21 shows 850 vacancies, and 18% of 850 = 153 — a whole number, so no rounding is needed. Using the 2019-20 figure of 700 would give 126, so the right row and the right year both matter.

Add the washing-machine column: 105 + 144 + 156 + 190 + 205 = 800. Average over five years = 160. The sum is exact, so no rounding is involved — the other options come from dropping or misreading one entry.

The refrigerator column shows 256 in 2012 and 279 in 2013, so the increase is 23. Reading the AC column instead (219 to 179) gives a fall of 40, and reading 2013 to 2014 (279 to 226) gives a fall of 53 — the column and the year pair both have to be right.

Chavi's row is 85, 79, 87, 75, 84, which sums to 410. Average = 410/5 = 82%. Option B (85%) is her best single class.

Mohan's entry in the class VII column is 70, i.e. 70%. Marks = 70% of 600 = 420. Option B (480) is 80% of 600, which is the wrong row.

The History column reads 110, 125, 140, 110, 90, 85, which sums to 660. There are six students, so the average is 660/6 = 110. Dividing by five gives 132 and pulls you towards 140.

Arts is marked out of 80, so 70% means 0.70 × 80 = 56 marks. Arts marks: Joseph 35, Kriti 60, Maina 40, Supreet 45, Jai 60, Dev 50. Only Kriti and Jai reach 56, so the answer is 2 students. Treating the marks as percentages directly would wrongly admit Dev and Supreet.

Mobiles: company B = 255 and company D = 175, both in hundreds, so the units cancel. Percentage more = (255 − 175)/175 × 100 = 80/175 × 100 = 45.71%, about 46%. The base must be D, the company being compared against. Using B gives 31.4%.

Add each company's row across all five gadgets (in hundreds): A = 855 · B = 675 · C = 505 · D = 495 · E = 870. E is the largest, just ahead of A. A is the trap: it leads on TVs, but E leads on mobiles, refrigerators, smart watches and washing machines.

Read only the Female row: 45 + 54 + 25 + 89 + 82 = 295 over five subjects. Average = 295/5 = 59. For contrast the Male row averages (53 + 62 + 85 + 55 + 50)/5 = 61, so none of the wrong options is the male figure either.

“Scoring 10 or less” is exactly the 1–10 band, which holds 5 students. The 11–20 band already holds 1. After the grace the 11–20 band holds 1 + 5 = 6. Option A (5) counts only those who moved and forgets the student already there.

“40 or less” covers the first four bands: 5 + 1 + 3 + 4 = 13. Sensible check by subtraction: the whole table holds 15 students and the 41–50 band holds 2, so 15 − 2 = 13.

A score of 30 or less fails, so the failing bands are 1–10, 11–20 and 21–30, holding 5 + 1 + 3 = 9 students. The passing bands are 31–40 and 41–50, holding 4 + 2 = 6. (Total 15: nine fail, six pass.)

Town R has an average male age of 30 and an average female age of 25, with males : females = 2 : 3. Take 2 men and 3 women: total age = 2 × 30 + 3 × 25 = 60 + 75 = 135 over 5 people, so the combined average is 135/5 = 27 years. This is a weighted average, not a midpoint — the plain midpoint 27.5 would ignore that the larger group is the younger one.

Mimicry shows in city M = 0.9 hundreds and drama shows in city O = 12 hundreds. Both are in the same unit, so the hundreds cancel. Required percentage = (0.9/12) × 100 = 90/12 = 7.5. Rounding 0.9 up to 1 gives 8.33, which is where option B comes from.

Only the TUV column is needed: 48.25 lakh in 2018 and 67.25 lakh in 2019. The 2019 growth was (67.25 − 48.25)/48.25 ≈ 39.38 per cent. Applying the same rate to 2019 gives 67.25 × 67.25/48.25 ≈ 93.73 lakh. The neat way to see it: 2020/2019 = 2019/2018, so the three figures form a geometric step. Option C (87.36) is what you get by adding the same absolute rise of 19 lakh.

Read the sales column: newspaper 1 = 3, 2 = 2, 3 = 3, 4 = 3, 5 = 5, 6 = 4 lakh. Test each option: 2 and 4 are 2 and 3 — no. 3 and 6 are 3 and 4 — no. 5 and 6 are 5 and 4 — no. 1, 3 and 4 are all 3 lakh — equal.

Add the first two newspapers in each option and see whether the sum matches the third. The figures are 1 = 3, 2 = 2, 3 = 3, 4 = 3, 5 = 5, 6 = 4 lakh. 1, 2, 5: 3 + 2 = 5, and newspaper 5 sells 5 lakh — a match. 1, 2, 6: 5 against 4 — no. 2, 5, 6: 7 against 4 — no. 2, 4, 6: 5 against 4 — no. The last is the near miss: it produces the right total but points it at the wrong paper.

The Salary column shows 754 lakh in 2016 and 998 lakh in 2019. Required percentage = (754/998) × 100 ≈ 75.55%. Option D (132.36%) is the same comparison the wrong way round — the standard trap when the smaller figure is the one being expressed as a percentage.

The table gives production and a rejection rate, so the rejected count is production × rate. Unit C, 2013: 56 thousand × 0.8% = 448 items. Unit C, 2017: 48 thousand × 0.2% = 96 items. Percentage less = (448 − 96)/448 × 100 = 78.57%, about 78%. Option C (21%) is the fall in production alone, ignoring the rate — the commonest error here. Options B and D exceed 100%, which is impossible for a decrease.

Three of the four counts are printed directly. Male employees in B and D = 35 + 54 = 89. Female employees in A, C and E = 39 + 50 + 54 = 143. Difference = 143 − 89 = 54. The percentages are there to tempt a longer route, and they check out: in company A the men are 48 per cent, so the 39 women are 52 per cent and the staff is 75; in C the 50 women are 40 per cent, giving 125; in E the 54 women are 36 per cent, giving 150. Every derived total is a whole number, which confirms the reading.

Both games are shares of the same total, so the ratio of students is the ratio of the percentages and the 3,000 is never needed. Football : Badminton = 30 : 10 = 3 : 1. (Check: 900 : 300 = 3 : 1.) Option C (1 : 3) is the same ratio the wrong way round.

Gold + platinum = 70% + 5% = 75%. Iron + silver = 15% + 10% = 25%. Ratio = 75 : 25 = 3 : 1. Because both groups are percentages of the same total, the weight of the ring never enters the calculation.

Employed men : employed women = 35 : 20 = 7 : 4 after dividing by 5. In absolute numbers it is the same: 28,000 : 16,000 = 7 : 4.

The five slices are Ration 40%, Other 25%, Study 20%, Electricity 10% and T.V. & Mobile 5%. Largest is Ration at 40%, smallest is T.V. & Mobile at 5%, so the ratio is 40 : 5 = 8 : 1. The income never needs to be known.

Total funds = 76,000 + 1,45,000 + 45,000 + 22,000 + 1,29,000 = ₹4,17,000. Investors : Total = 1,29,000 : 4,17,000 = 129 : 417, and both are divisible by 3, giving 43 : 139. Option B uses the bank-loan slice instead of the investors' slice and leaves it unreduced.

Every head is already a percentage of the same income, so the percentages can be treated as the amounts themselves. Average of travelling and education = (5 + 28)/2 = 16.5. Average of food and house rent = (15 + 12)/2 = 13.5. Excess = 3, taken as a percentage of the second average: 3/13.5 × 100 = 22.22 per cent. Option B (18.18) divides by the first average instead — “more than” always fixes the denominator on the quantity that follows those words.

Half the pie is 50%. The shares are A 21, B 12, C 14, D 17, E 16, F 20, which add to 100. A + C + F = 55 · C + E + F = 50 ✓ · E + D + A = 54 · E + B + D = 45. Only C, E and F make exactly half.

D has 17% and E has 16%, so the gap is just 1% of the total. 1% of ₹68 lakh = ₹68,000. The digits mislead candidates into ₹34,000, which would be half a percentage point.

A + C + E = 21 + 14 + 16 = 51% of the total. 51% of ₹68 lakh = 68 × 51/100 = ₹34.68 lakh. ₹36.75 lakh would need 54.04% — no sum of three shares reaches it.

A + F = 41% and C + D = 31%, so the difference is 10% of the total. 10% of ₹68 lakh = ₹6.8 lakh.

B holds the smallest slice, 12%. 12% of ₹68 lakh = ₹8.16 lakh. Quick check: 1% is ₹0.68 lakh, so 12% = 12 × 0.68 = 8.16.

Hockey takes 15% of the enrolment and the total is 3,000 students. Students in hockey = 15% of 3,000 = 450. Option A (350) would be under 12% and option C (550) over 18% — neither matches the printed slice.

Sand is 15% of the material and cement is 20%, and spending is proportional to consumption. 15% ↔ ₹12,000, so 1% ↔ 12,000/15 = ₹800, and cement at 20% ↔ 20 × 800 = ₹16,000. As a ratio it is one step: cement/sand = 20/15 = 4/3, so 12,000 × 4/3 = ₹16,000.

The chart gives gold 70%, iron 15%, silver 10% and platinum 5%, which totals 100%. Platinum = 5% of 10 g = 0.5 g. Option B (1.0 g) is silver's 10% share, the slice next to platinum on the chart.

Electricity is the 10% slice and the chart gives shares of total income. Electricity bill = 10% of ₹50,000 = ₹5,000. ₹3,000 would need a 6% slice and ₹4,200 an 8.4% slice; neither is on the chart.

Unemployed men are the 15% slice and the population is 80,000. Count = 15% of 80,000 = 12,000. Option A (15,000) is the mistake of reading the label 15 as thousands.

Maharashtra is 25% and Karnataka 15%, so the gap is 10 percentage points. 10% of 3,000 kg = 300 kg. (The long way gives 750 − 450 = 300.)

Rajasthan 20% and Punjab 30% together hold 50% of the crop. 50% of 3,000 kg = 1,500 kg.

Rayon + Silk + Chiffon = 14 + 12 + 17 = 43%. Velvet + Wool + Denim = 8 + 6 + 9 = 23%. Difference = 20% of 45,000 = 9,000. Take the percentage difference first; converting all six slices separately is what produces the 10,500 and 11,200 distractors.

The five sectors are 110 + 86 + 72 + 64 + 28 = 360°, so the whole circle is the full ₹10,000. Makeup accessories take 72°, so the amount = (72/360) × 10,000 = ₹2,000. ₹2,500 is the trap for treating a 72° sector as a quarter of the circle.

Clothing 110° + Footwear 86° + Artificial jewellery 64° = 260°. Percentage = (260/360) × 100 = 72.22%. 75% is the trap for rounding 260° up to 270°, which is exactly three quarters.

The five sectors are 100 + 90 + 80 + 60 + 30 = 360°, so the chart is complete. Orange 100° + Guava 80° = 180°, exactly half the circle, so the area is half of 500 = 250 acres. The three near-miss options exist only to punish eyeballing the sectors instead of adding the printed degrees.

Pomegranate occupies 60°. Transferring 30% of it moves 0.30 × 60 = 18°. Apple was 30°, so the new apple angle = 30 + 18 = 48°. (Pomegranate drops to 42°, and the circle still totals 360°.) The trap is to take 30% of 100 rather than 30% of the 60° sector.

Cotton is 15% and Georgette 19% of the same total, so the shares add and subtract directly. 20% of the Cotton share = 0.20 × 15% = 3% of the total. New Georgette share = 19 + 3 = 22%. The total number of people does not change, so no re-basing is needed. Option D (39%) comes from adding 19% and 20% as if the 20% were of the whole.

Mathematics 14% and History 22% together are 36% of the total marks, and that 36% equals 450. So 1% = 450/36 = 12.5 marks (and the whole paper is 1,250 marks). English is 12%, so English marks = 12 × 12.5 = 150.

Convert each share of the 400 wallets into a count first, then take the female percentage of each: P: 10% of 400 = 40, of which 20% = 8. R: 20% of 400 = 80, of which 30% = 24. S: 25% of 400 = 100, of which 10% = 10. Total = 8 + 24 + 10 = 42. The trap is to add the three female percentages (20 + 30 + 10 = 60) — they apply to different bases and cannot be added.

The 360 girls split Monday 15%, Tuesday 10%, Wednesday 40%, Thursday 35%. Wednesday and Thursday together are 75% of 360 = 270 girls. Boys on the two days = 98 + 105 = 203. Total = 270 + 203 = 473. Adding the two shares first saves computing each day.

Girls from Delhi = 25% of 800 = 200, so Delhi's total = 200 + 124 = 324. Girls from Surat = 24% of 800 = 192, so Surat's total = 192 + 60 = 252. Ratio = 324 : 252; dividing both by 36 gives 9 : 7. Comparing only the girls gives 25 : 24, and forgetting one boy count gives 9 : 5.

Check the chart first: P 20%, Q 10%, R 40%, S 18%, T 12% add to 100%. R makes 40% of 500 = 200 tables at ₹500 each = ₹1,00,000. S makes 18% of 500 = 90 tables at ₹800 each = ₹72,000. Total = ₹1,72,000. Option A (₹1,84,000) swaps the two per-table costs.

Type B is 30% of 2,50,000 = 75,000 sets. 70% are sold, so 30% remain: 30% of 75,000 = 22,500. Note the two different 30%s — one is the share of production, the other the unsold fraction of that share.

Type D is 25% of 2,50,000 = 62,500 sets. 75% are sold, so 25% remain: 25% of 62,500 = 15,625. The word “perfect” in the printed stem adds nothing — no defect rate is given anywhere in the data.

May = 12% of 550 = 66 tickets; July = 50% of 550 = 275 tickets. Males in May = 50% of 66 = 33. Males in July = 60% of 275 = 165. Difference = 165 − 33 = 132. Comparing the female counts instead gives 77.

Total tickets 1,050, so one per cent is 10.5 tickets. Srinagar 22% = 231 tickets, of which 121 female, so males = 110. Kochi 18% = 189 tickets, of which 98 female, so males = 91. Difference = 110 − 91 = 19. Each city total must be reduced by its own female count first.

Q, R and S together hold 35 + 20 + 15 = 70% of the purchases, which is 70% of 240 = 168 sweaters. Three-fourths of those are merino wool: (3/4) × 168 = 126. Leaving out brand S gives 55% of 240 = 132 (option D), and rounding 168 down to 160 gives 120 (option C).

Shares: A 36%, B 24%, X 12%, Y 28%, on a total of 400 chairs. Brand Y made 28% of 400 = 112 chairs costing ₹56,000 in all, so one Y chair costs 56,000/112 = ₹500. One A chair costs ₹100 less = ₹400. Brand A made 36% of 400 = 144 chairs, so the total is 144 × 400 = ₹57,600.

Check the chart first: 15 + 19 + 11 + 16 + 27 + 12 = 100 per cent, so no slice is misread. Medical is 19% of 7,200 = 1,368 faculty. Of those 25% are women, so 75% are men: 1,368 × 0.75 = 1,026. The three wrong options are all within twenty of the right figure, which is exactly where a slipped digit lands — so both steps have to be exact.

First survey: Dal Makhani has 25% of 200 = 50 customers. Second survey: 20% of the extra 100 = 20 customers. New total = 70 out of a new sample of 300, so the share = (70/300) × 100 = 23.3%. The trap is to average the two percentages (giving 22.5%); you must recompute over the enlarged total.

The pie splits 900 orders as October 40%, January 30%, November 20%, December 10%. November = 180, December = 90, January = 270. February is not on the chart — it is given as 96 more than November, so February = 180 + 96 = 276. Average of December, January and February = (90 + 270 + 276)/3 = 636/3 = 212.

The slices are May 20%, June 35%, July 10%, August 20%, September 15% of 1,500. August = 300 and September = 225. June = 525, and October is stated to be 60 more, so October = 585 — it is extra data, not a slice. Average = (300 + 225 + 585)/3 = 1,110/3 = 370.

The five days in the chart share 700 people. Wednesday = 35% of 700 = 245 and Friday = 28% of 700 = 196. The average of Wednesday, Friday and Saturday is 201, so their total is 603. Saturday = 603 − 245 − 196 = 162. Saturday is not on the chart, which is why its figure has to be recovered from the average.

The slices are A 20%, B 12%, C 28%, D 18%, E 22% of 900. D + E = 40% of 900 = 360, so their average is 180. A + B = 32% of 900 = 288, so their average is 144. Difference = 180 − 144 = 36. The difference of the totals would be 72, twice as big — read whether averages or totals are wanted.

Convert each share of 800 laptops: 2001 = 25% = 200, 2002 = 20% = 160, 2003 = 45% = 360, 2004 = 10% = 80. Average for 2001 and 2002 = 180. Average for 2003 and 2004 = 220. Difference = 40. Eighty would be the answer if the question asked for the difference of the totals.

From the graph, cricket has 54 players and kho-kho has 72. Ratio = 54 : 72, and dividing both by 18 gives 3 : 4.

Volleyball has 82 players and basketball 49, so the difference is 33. Option B (28) comes from reading the basketball bar off the gridline as 54 instead of its printed 49 — exactly the error the data labels are there to prevent.

Male employees in Q and S = 360 + 390 = 750. Female employees in R and T = 210 + 240 = 450. Ratio = 750 : 450, and dividing by 150 gives 5 : 3. The ratio must be built from exactly the four bars the question names.

Read the six data labels: P 42, Q 56, R 67, S 39, T 70, U 86, totalling 360. T's share = 70/360 × 100 = 19.44 per cent. Sanity check: one sixth of the total would be 16.67 per cent, and T is a little above the average bar, so just under 20 per cent is exactly what to expect.

Follow Ramya's line across the five subjects: English 80, Hindi 78, Science 85, Mathematics 92, Social Science 76. Mathematics is the single peak of the plot, the only point past 90. Kajol's line (75, 85, 65, 90, 85) also peaks at Mathematics, so the answer is safe on either reading of the two identically drawn lines.

The vertical axis is marked every 2 runs from 0 to 16, and the six bars stand at 4, 15, 8, 7, 10 and 3. The sixth bar stops midway between the 2 and 4 gridlines, so it is 3 runs — the shortest bar on the chart. Option C (4) is the height of the first bar, and it is where the eye lands if the sixth bar is rounded up to the nearest marked gridline.

Imports exceed exports exactly when the plotted ratio is greater than 1. Company B's values are 1993: 0.5, 1994: 0.8, 1995: 0.6, 1996: 1, 1997: 1.2, 1998: 1.4, 1999: 0.8. Only 1997 and 1998 are above 1, so the answer is 2 years. The trap is 1996, where the ratio is exactly 1 — imports then equal exports, which is not “more than”. Counting it gives the wrong answer 3.

The blue bar is the year's total income and the red bar is the percentage of it earned from business A, so A = total × per cent and B is whatever is left. 2010: A = 24, B = 36 · 2011: A = 30, B = 20 · 2012: A = 35, B = 35 · 2013: A = 13.5, B = 31.5 · 2014: A = 52, B = 13. Totals: A = 154.5, B = 135.5. Since both are over the same five years, the excess can be taken on the totals: (154.5 − 135.5)/135.5 × 100 ≈ 14 per cent. The trap is to average the red bars themselves (40, 60, 50, 30, 80 → 52 per cent) and conclude “about 20 per cent more” — a percentage of a changing total cannot be averaged that way.

Only 2016 and 2019 matter, because the question fixes 2016 as the base. Autorickshaws go from about 4.25 to 4.5 thousand, taxis from 2.3 to 2.75, buses from 2 to 5. As percentages of their own 2016 values: autorickshaws 0.25/4.25 ≈ 6%, taxis 0.45/2.3 ≈ 20%, buses 3/2 = 150%. The smallest is autorickshaws. A large base makes a small percentage out of a respectable absolute gain — that is the whole point of the question.

First the average of the six bars: 1170 + 1465 + 975 + 800 + 1140 + 1230 = 6,780, and 6,780/6 = 1,130. Above 1,130: 1170, 1465, 1140, 1230 — four years. Below: 975, 800 — two years. Ratio = 4 : 2 = 2 : 1. The trap is to call 1,140 “about average” and drop it, which would give 3 : 2 — but 1,140 is genuinely greater than 1,130.

Work out the percentage increase colour by colour, using (June − May)/May × 100: Blue 34.01% · Green 79.45% · Orange 13.04% · Red 19.47% · Yellow 2.76%. Only Orange is near 13%. Yellow is the trap for anyone comparing raw gaps instead of percentages — its bars are the closest together, but a small gap on a small base is still only 2.76%.

Add the three companies year by year, using the printed labels: 2014: 232 · 2015: 188 · 2016: 170 · 2017: 182 · 2018: 171 · 2019: 170. Only 2016 and 2019 share a total, 170 crore each. Note how close 2018 comes at 171 — that single crore is what makes the other options wrong, so the totals must be added rather than eyeballed.

Add each company's five yearly figures. Company X: 133 + 145 + 164 + 189 + 190 = 821 thousand. Company Y: 147 + 160 + 140 + 170 + 230 = 847 thousand. Difference = 26 thousand = 26,000 vehicles. The units matter: the graph is in thousands but the options are in plain vehicles.

Work only with the 2015 bars. Students who passed some exam = CAT 840 + CET 470 + CA Foundation 1,100 = 2,410. Students who passed none = 400. Since no student passed more than one exam, the total for 2015 is 2,410 + 400 = 2,810. Required percentage = 2,410/2,810 × 100 = 85.76%. The “assume no student passed more than one exam” sentence is there precisely to license adding the bars without double counting.