Venn diagrams are 32 of the 692 reasoning questions the Punjab Police SI has asked, and they are the most generous marks in the section: the diagram is printed for you. There is nothing to construct and nothing to remember. The whole task is to translate an English phrase into a region of a picture that is already on the page. 26 show a figure — often a circle, a triangle and a rectangle overlapping — and ask which lettered region satisfies a description such as non-urban females who are doctors. 6 put numbers in the regions and ask for a total. Almost every wrong answer here is a reading error, not a thinking error. The cure is to turn the phrase into a checklist of conditions before you look at the figure at all.
The teaching part above and below — the explanations, the figures and the worked examples on screen — is about 10 minutes. The collapsed question banks hold 32 solved past questions in all; working through every one of them takes roughly 55 minutes. Do that across several sittings, not in one go.
Part 1 · Seven regions, and what each one means
Three overlapping shapes cut the page into seven pieces
Break the description into conditions and mark each one in or out before looking at the picture. Non-urban females who are doctors becomes: inside Female, inside Doctor, outside Urban. Three conditions, so exactly one region can satisfy all three. Writing the three words down takes five seconds and removes the whole difficulty.
Every other region-naming question (24)Tap to open
Study the given diagram carefully and answer the question that follows. How many non-urban females are doctors? (SI 19 Aug 2021)
- 16
- 29
- 320
- 411
Show answer
Answer: 2 — 9
'Non-urban females who are doctors' means: inside the triangle (Female) and inside the circle (Doctors), but outside the square (Urban). That is exactly one region of the figure, the one carrying 9. The distractors are the neighbouring regions, and each is wrong for a stated reason. Option 4 (11) is the region where all three shapes overlap — those females who are doctors are urban, so they are excluded. Option 1 (6) lies inside the triangle only: non-urban females who are not doctors. Option 3 (20) is 11 + 9, i.e. all female doctors, urban and non-urban together, which ignores the word 'non-urban'.
From the given options, which part of the figure shows Artists who are Lawyer too? In the figure an upside-down triangle stands for Teachers, a circle for Artists and a rectangle for Lawyers, and the three overlap. The lettered regions are : R, inside the triangle only; K and M, inside the circle only; T, inside both the triangle and the circle but outside the rectangle; P, inside all three; S, inside the circle and the rectangle but outside the triangle; Q, inside the rectangle only. (SI 16 Oct 2022)
- 1T
- 2Q
- 3S
- 4R
Show answer
Answer: 3 — S
Read off what each lettered region means: Region · Inside · Means R · triangle only · Teachers only K, M · circle only · Artists only T · triangle + circle · Artists who are Teachers P · all three · Artists who are both Teachers and Lawyers S · circle + rectangle · Artists who are Lawyers Q · rectangle only · Lawyers only The question asks for Artists who are Lawyers too, so the region must lie inside the circle and inside the rectangle. That is S. Why the others fail: T is inside the circle and the triangle, so it is Artists who are Teachers, not Lawyers; Q is inside the rectangle alone, so those people are Lawyers but not Artists; R is inside the triangle alone, Teachers who are neither. P would also be artists who are lawyers, but P carries the extra condition of being Teachers as well and is not offered as an option — S is the region for artists who are lawyers without any further condition, and it is the only one of the four choices that is inside both the circle and the rectangle.
Identify the diagram that best represents the relationship among the given classes. District, State, Country. (The four options are printed as figures; each is a square frame containing circles.) (SI 16 Oct 2022)
- 1A square containing one large circle, inside which lie two small circles side by side that do not overlap each other
- 2A square containing one large circle, inside which lie two medium circles that partly overlap each other
- 3A square containing three concentric circles — a small circle inside a medium circle inside a large circle
- 4A square containing a large circle with a small circle inside it, and a second small circle lying outside that large circle
Show answer
Answer: 3 — A square containing three concentric circles — a small circle inside a medium circle inside a large circle
Every district lies inside some state, and every state lies inside the country. The classes are therefore fully nested, smallest to largest: District within State within Country. ```puzzle:venn District in State State in Country ``` Only one figure shows total nesting — three circles one inside the other (option 3). Option 1 (two separate small circles inside one big circle) would mean districts and states are two different, non-overlapping kinds of thing that merely share a country; option 2 (two partly overlapping circles inside a big one) would mean only some districts are states; option 4 (a circle-within-a-circle plus a separate circle outside) would put one of the three classes entirely outside the other two. All three contradict the actual administrative hierarchy.
How many people are there whose favourite flavour is chocolate only? (SI 20 Jun 2023)
- 120
- 280
- 330
- 440
Show answer
Answer: 2 — 80
'Chocolate only' is the part of the chocolate circle that lies outside both the strawberry and the vanilla circles. In the diagram that region carries 80. The other chocolate regions — 30 (with strawberry), 40 (with vanilla) and 20 (with both) — are excluded because those people like a second flavour as well; adding them would give the total chocolate count 170, not the 'only' count.
How many people are there who like all three flavours? (SI 20 Jun 2023)
- 120
- 250
- 340
- 430
Show answer
Answer: 1 — 20
The people who like all three flavours sit in the central region where all three circles overlap. That region carries 20. Options 2, 3 and 4 are the two-circle overlaps — 50 for strawberry and vanilla, 40 for vanilla and chocolate and 30 for strawberry and chocolate — each of which excludes the third flavour.
What is the number of IAS women? (SI 21 Jun 2023)
- 173
- 252
- 3109
- 441
Show answer
Answer: 2 — 52
'IAS women' means everyone lying in both the IAS circle and the Women circle, whether or not they are also engineers. That is the IAS-and-Women-only region plus the triple-overlap region: 41 + 11 = 52. Option 4 (41) forgets the 11 who are also engineers, and option 1 (73) is the women-only region.
How many women are engineers but not IAS? (SI 21 Jun 2023)
- 111
- 273
- 323
- 490
Show answer
Answer: 3 — 23
The question asks for the part that lies inside both the Women circle and the Engineer circle but outside the IAS circle. That is exactly the Engineer-and-Women-only region, 23. Option 1 (11) is the triple overlap, which must be excluded because those 11 are IAS as well; option 4 (90) is engineers who are not women at all.
How many Readers read both Novels and Plays? (SI 29 Jun 2023)
- 15
- 210
- 314
- 412
Show answer
Answer: 1 — 5
'Readers who read both Novels and Plays' is the region where all three circles overlap. That central region carries 5. 14 is Readers and Novels without Plays, 12 is Readers and Plays without Novels, and 10 is Novels and Plays without Readers — each of those leaves one of the three conditions out.
How many Plays are also Novels but NOT read by Readers? (SI 29 Jun 2023)
- 118
- 210
- 354
- 429
Show answer
Answer: 2 — 10
The region asked for lies inside both the Plays circle and the Novels circle but outside the Readers circle. That region carries 10. 18 is Plays only, so it misses the Novels condition; 5 would have to be added only if Readers were allowed, and 10 + 5 + 14 = 29 or the whole Plays circle 18 + 12 + 5 + 10 = 45 are the kinds of sums that generate the other options.
How many persons like all three fruits — bananas, apples and grapes? (SI 1 Jul 2023)
- 15
- 23
- 34
- 412
Show answer
Answer: 2 — 3
"All three" is the single central region where the three circles overlap, and it carries 3. Options 1 (5), 3 (4) and 4 (12) are the three two-fruit overlaps — each of those is an "exactly two fruits" region, not the centre.
How many persons like only bananas? (SI 1 Jul 2023)
- 120
- 210
- 318
- 412
Show answer
Answer: 1 — 20
"Only bananas" is the part of the bananas circle that overlaps nothing, and it carries 20. Option 4 (12) is bananas-and-apples only and option 3 (18) is grapes only; the total who like bananas at all would be 20 + 5 + 12 + 3 = 40, which is not what is asked.
In how many bouquets of flowers are there no roses? (SI 2 Jul 2023)
- 125
- 211
- 3140
- 4115
Show answer
Answer: 3 — 140
"No roses" means every region that lies outside the Roses circle: Lilies only + Carnations only + (Lilies and Carnations only). 76 + 39 + 25 = 140. Option 4 (115) drops the 25 shared by Lilies and Carnations, option 1 takes that 25 alone and option 2 is the Roses-and-Carnations region, which does contain roses.
What is the total of only B.Ed and only M.Ed? (SI 3 Jul 2023)
- 182
- 263
- 370
- 479
Show answer
Answer: 2 — 63
'Only B.Ed' is the part of the B.Ed circle that touches neither of the other two circles: 37. 'Only M.Ed' is the matching region of the M.Ed circle: 26. Total = 37 + 26 = 63. Option 3 (70) comes from adding the overlaps 7 + 15 + 9 + 10 + … and option 1 (82) from adding a shared region such as 37 + 26 + … ; the word 'only' rules every shared region out.
How many teachers hold a B.Ed degree but NOT an M.Ed degree? (SI 3 Jul 2023)
- 119
- 29
- 325
- 415
Show answer
Answer: 2 — 9
Three conditions have to hold at once: the person is a Teacher, is in B.Ed, and is outside M.Ed. That is exactly the region shared by the Teachers and B.Ed circles but lying outside the M.Ed circle, which carries 9. 15 (option 4) is the centre region — those teachers hold both degrees, so the 'NOT M.Ed' condition throws them out; 24 or 25 comes from adding 9 + 15, i.e. forgetting the word NOT.
How many shirts are made of cotton as well as silk? (SI 9 Jul 2023)
- 18
- 272
- 333
- 46
Show answer
Answer: 1 — 8
'Shirts made of cotton as well as silk' is the region common to all three circles at once — Shirts ∩ Cotton ∩ Silk. In the diagram that central region carries the number 8. The distractors are each a nearby region: 6 is Cotton ∩ Silk but outside Shirts (silk-and-cotton items that are not shirts), and 33 is 11 + 16 + 6, the three two-circle overlaps added up. Only 8 sits inside all three circles.
How many food items are available that do NOT contain any flour? (SI 14 Jul 2023)
- 116
- 2167
- 352
- 4115
Show answer
Answer: 2 — 167
Add every region that lies outside the Flour circle: desserts only 115, desserts with sugar only 16, and sugar only 36. That gives 115 + 16 + 36 = 167. The same answer comes from working with the whole: the total is 115 + 75 + 36 + 18 + 22 + 16 + 9 = 291, the Flour circle holds 75 + 18 + 22 + 9 = 124, and 291 − 124 = 167. Option 4 (115) counts only plain desserts, and option 3 (52 = 16 + 36) forgets the 115 desserts that have no flour either.
What is the number of Indian women who are NOT graduates? (SI 15 Jul 2023)
- 120
- 21
- 36
- 45
Show answer
Answer: 4 — 5
'Indian women' is the overlap of the Indians circle and the Women circle. That overlap has two parts: the region inside Indians and Women but outside Graduates (5) and the central region inside all three (1) — 6 Indian women in all. The question asks for those who are NOT graduates, so drop the central 1 and keep only the region outside the Graduates circle: 5. Option 3 (6) is the trap — it is the total number of Indian women, graduates included.
How many graduates are also women? (SI 15 Jul 2023)
- 110
- 25
- 34
- 46
Show answer
Answer: 2 — 5
The people who are both graduates and women live in the overlap of the Graduates circle and the Women circle. That overlap is made of two regions: Women and Graduates only (4) and the centre where all three circles meet (1). 4 + 1 = 5. Option 3 (4) is the trap — it leaves out the one woman who is a graduate and also an Indian, but she is still a graduate and still a woman.
How many people drink tea and coffee but do not drink juice? (SI 15 Jul 2023)
- 1120
- 214
- 365
- 48
Show answer
Answer: 2 — 14
The people who drink tea and coffee but not juice occupy the part where only the Coffee and Tea circles overlap — the region marked 14 — and nothing else is added, because the juice circle must be excluded. So the answer is 14. Option 4 (8) is the trap: that is the centre region, the people who drink all three including juice; 14 + 8 = 22 would be everyone who drinks both tea and coffee, but the question rules the juice drinkers out.
Which of the following represents the uneducated merchants who have no agriculture land? (SI 29 Jul 2023)
- 15
- 29
- 311
- 44
Show answer
Answer: 3 — 11
The region asked for must lie inside the rectangle (merchant) and inside the triangle (uneducated) but outside the circle (agriculture land). On the figure the triangle cuts across the bottom of the rectangle. Its part that lies inside the rectangle is split by the circle into two regions: 4, which is also inside the circle, and 11, which is not. So 11 is the uneducated merchants with no agriculture land. 4 (option 4) fails because those people do have agriculture land; 5 lies inside the triangle but below the rectangle, so those people are uneducated non-merchants; and 9 is inside the rectangle only, i.e. merchants who are neither uneducated nor landholders.
How many teachers can teach music but NOT art? (SI 31 Jul 2023)
- 116
- 29
- 322
- 418
Show answer
Answer: 4 — 18
'Teachers who can teach music but not art' is the region common to the Teachers and Musicians circles but outside the Artists circle. That region carries 18. The teachers who are musicians number 18 + 9 = 27; the 9 of them who are also artists are excluded, leaving 18. 9 (option 2) is the triple overlap and 22 (option 3) is the musicians-and-artists region, which has no teachers in it at all.
How many artists are also musicians but NOT teachers? (SI 31 Jul 2023)
- 116
- 218
- 39
- 422
Show answer
Answer: 4 — 22
The region shared by the Artists and Musicians circles but lying outside the Teachers circle carries 22. Artists who are musicians number 22 + 9 = 31; the 9 who are teachers as well are excluded, leaving 22. 18 (option 2) is the teachers-and-musicians region and 16 (option 1) the teachers-and-artists region, neither of which is wanted.
Who among the following are Directors who are Script writers but NOT producers? (SI 31 Jul 2023)
- 1Q
- 2P+M
- 3M
- 4P
Show answer
Answer: 4 — P
The region wanted must lie inside the triangle (Director) and inside the circle (Scriptwriter) but outside the square (Producer). P is the only such region: it sits in the triangle-circle overlap to the left of the square's edge. M (option 3) is inside all three shapes, so those people are producers as well; P+M (option 2) fails for the same reason; Q (option 1) is inside the circle only.
What does N represent? (SI 31 Jul 2023)
- 1Producers who are both Scriptwriters and Directors
- 2Producers who are Scriptwriters but not Directors
- 3Scriptwriters who are not Producers
- 4Producers who are not Scriptwriters
Show answer
Answer: 2 — Producers who are Scriptwriters but not Directors
N lies inside the circle (Scriptwriter) and inside the square (Producer), but it is below the triangle's lower side, so it is outside the triangle (Director). So N stands for producers who are scriptwriters but not directors. Option 1 describes M, which lies in all three shapes; option 3 describes Q; option 4 describes O, which is in the square alone.
Part 2 · When the regions carry numbers — 6 questions
List the regions, then add — never add while reading
Six questions put a number in each region and ask for a total — how many desserts contain no flour, how many engineers are not graduates. The arithmetic is trivial and the slips are not. Work in two passes. First list every region that qualifies, by name or letter, without adding anything. Then add the numbers in that list. Adding while you scan the figure is how a region gets counted twice or missed entirely, and both mistakes are printed as options. A phrase beginning no or not usually covers more regions than one beginning only, so expect the list to be longer and check it against the figure before adding.
Every other numbered-region question (5)Tap to open
A school has 180 students. Among them 150 speak English, 100 speak Hindi, some students speak both English and Hindi. How many of them speak English only ? (SI 2016)
- 130
- 270
- 380
- 4100
Show answer
Answer: 3 — 80
Every student speaks at least one of the two languages, so the union is the whole school: n(E ∪ H) = 180. By the addition rule, n(E ∪ H) = n(E) + n(H) − n(E ∩ H), so 180 = 150 + 100 − n(E ∩ H), giving n(E ∩ H) = 250 − 180 = 70 who speak both. English only = n(E) − n(E ∩ H) = 150 − 70 = 80. Option 2 (70) is the tempting trap — that is the number who speak both, not English alone; option 1 (30) is Hindi only (100 − 70).
The figure shows four equal circles overlapping in a square arrangement — Group I at the top left, Group II at the top right, Group IV at the bottom left and Group III at the bottom right. Two small regions just above the centre of the figure are shaded : the left one lies inside the circles of Group I, Group II and Group IV, and the right one lies inside the circles of Group I, Group II and Group III. The shaded area if combined will have people from how many groups? (SI 20 Aug 2021)
- 1Four
- 2Cannot be determined
- 3Two
- 4Three
Show answer
Answer: 1 — Four
Take the two shaded patches one at a time. The left patch sits where the Group I circle, the Group II circle and the Group IV circle all overlap, so anyone standing in it belongs to Groups I, II and IV. The right patch sits where Group I, Group II and Group III all overlap, so anyone there belongs to Groups I, II and III. The question asks about the two patches combined, so take the union of the two lists: I, II, IV from the left patch and I, II, III from the right. Together they cover Groups I, II, III and IV — all four. Option 4 (Three) is the trap: three is the number of groups covered by either patch on its own, but the two patches lie under different third circles, so combining them adds a fourth group.
How many Engineers are there who are not Doctor? In the figure a circle stands for Artists, a rectangle for Doctors and a triangle for Engineers, and the numbers in the regions are : 18 inside the circle only; 5 inside the circle and the triangle but outside the rectangle; 4 and 3 inside the circle and the rectangle but outside the triangle; 9 inside all three; 15 and 18 inside the rectangle only; 16 inside the rectangle and the triangle but outside the circle; 18 inside the triangle only. (SI 16 Oct 2022)
- 15
- 218
- 323
- 433
Show answer
Answer: 3 — 23
Engineers are everything inside the triangle. List those regions and mark which of them also fall inside the rectangle (Doctors): Region · Value · Inside triangle? · Also inside rectangle? circle + triangle only · 5 · yes · no all three · 9 · yes · yes rectangle + triangle only · 16 · yes · yes triangle only · 18 · yes · no Total engineers = 5 + 9 + 16 + 18 = 48. Engineers who are also doctors = 9 + 16 = 25. Engineers who are not doctors = 48 − 25 = 23, which is just 5 + 18. Why the others fail: 18 is only the triangle-only region and forgets the 5 who are engineers and artists but not doctors; 5 is that piece alone; 33 = 15 + 18 adds the two rectangle-only regions, which are doctors who are not engineers at all — the opposite of what was asked.
How many items of clothing are available for someone who wants only cotton clothing? (SI 9 Jul 2023)
- 153
- 242
- 311
- 467
Show answer
Answer: 1 — 53
The two fabric circles are Cotton and Silk; Shirts is a garment type, not a fabric. Someone who wants clothing made of cotton only must avoid everything that also contains silk, but a shirt made purely of cotton still qualifies. Region · Count · Counts for 'only cotton'? Cotton only · 42 · yes Shirts and Cotton, not Silk · 11 · yes — a pure-cotton shirt Cotton and Silk, not Shirts · 6 · no — contains silk Shirts, Cotton and Silk · 8 · no — contains silk So the total is 42 + 11 = 53. The distractor 67 is the whole Cotton circle, 42 + 11 + 6 + 8, which wrongly keeps the silk-blend items; 42 is the cotton-alone region, which wrongly throws away the pure-cotton shirts.
How many people do not drink coffee? (SI 15 Jul 2023)
- 1137
- 257
- 382
- 425
Show answer
Answer: 1 — 137
'Do not drink coffee' means every region that lies outside the Coffee circle: juice only, tea only, and juice-and-tea only. 55 + 57 + 25 = 137. Do not add the 8 in the centre or the 13 and 14 overlaps — those people all drink coffee as well. 82 is the trap: 57 + 25 = 82 leaves out the 55 who take juice only.
- Reading “at least two” as “exactly two”. The first includes the centre, the second excludes it, and both totals are printed.
- Dropping a negative condition. “Non-urban” is a condition like any other — outside the Urban shape — and forgetting it still leaves a valid-looking region.
- Assuming every shape is a circle. The SI mixes circles, triangles, squares and rectangles, and the legend tells you which stands for what. Read the legend.
- Adding while scanning. List the qualifying regions first and add afterwards; a region counted twice is the commonest wrong total.
- Treating a class as a category it is not. In one SI figure, Shirts is a garment type while Cotton and Silk are fabrics, so “shirts of both fabrics” is the central region, not a pair region.
- Three shapes cut the page into seven regions.
- Write the conditions before looking at the figure.
- “Only A” = one region. “A and B” = two.
- “At least two” = four regions.
- “Exactly two” = three regions.
- “No C” = everything outside C: four regions.
- A negative word is a condition, not decoration.
- Read the legend: not every shape is a circle.
- List regions first, add second.
- The figure is given. Nothing has to be drawn.