{"id":90013,"date":"2025-06-01T10:19:08","date_gmt":"2025-06-01T10:19:08","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=90013"},"modified":"2025-06-01T10:19:08","modified_gmt":"2025-06-01T10:19:08","slug":"in-the-diagram-given-below-there-is-a-circle-a-square-and-a-triangle","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/in-the-diagram-given-below-there-is-a-circle-a-square-and-a-triangle\/","title":{"rendered":"In the diagram given below, there is a circle, a square and a triangle"},"content":{"rendered":"

In the diagram given below, there is a circle, a square and a triangle dividing the region into five disjoint bounded areas. Each of these areas are labelled with number of players belonging to that area. The circle contains cricketers, the square contains football players and the triangle contains hockey players.
\nWhich one of the following is not correct?<\/p>\n

[amp_mcq option1=”Every hockey player plays football” option2=”Every cricket player plays either football or hockey” option3=”There are some hockey players who play both cricket and football” option4=”There are some football players who play neither cricket nor hockey” correct=”option3″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CAPF – 2016<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nThe correct option is C) There are some hockey players who play both cricket and football.
\n<\/section>\n
\nThe question describes a diagram with a circle (cricketers, C), a square (football players, F), and a triangle (hockey players, H), divided into *five disjoint bounded areas*, each with a number of players. This implies that only these five specific areas within the sets contain players, and any intersection not represented by one of these five areas must contain zero players.
\n<\/section>\n
\nLet’s consider a plausible interpretation of the “five disjoint bounded areas” in a 3-set Venn diagram context. A standard 3-set Venn diagram has 7 possible regions inside the sets (C only, F only, H only, C&F only, C&H only, F&H only, C&F&H). If only five of these have players, two must be empty.
\nStatement C is “There are some hockey players who play both cricket and football”. This statement is true if the region representing players who play all three sports (C&F&H) has a number greater than zero. If the five disjoint areas described *do not include* the intersection of all three sets (C&F&H), then the number of players in that region is zero by implication. In this scenario, statement C would be false (“There are NO hockey players who play both cricket and football”).<\/p>\n

Let’s test if this interpretation makes sense by assuming statement C is indeed the “not correct” one. This means C&F&H = 0. The five regions could then be, for example: C only, F only, H only, C&F only, C&H only, F&H only (this is 6, so one more must be 0). Or perhaps C only, F only, H only, C&F only, F&H only (omitting C&H only and C&F&H). Or C only, F only, H only, C&F only, C&H only (omitting F&H only and C&F&H).<\/p>\n

If C&F&H = 0, then statement C is false. Let’s see if the other statements *could* be true under various configurations of 5 non-empty regions (where C&F&H=0):
\nA) “Every hockey player plays football”: Requires H only = 0 and C&H only = 0. Possible if the 5 regions are, for example, F only, C only, C&F only, F&H only, some other.
\nB) “Every cricket player plays either football or hockey”: Requires C only = 0. Possible.
\nD) “There are some football players who play neither cricket nor hockey”: Requires F only > 0. Possible.<\/p>\n

Since statement C (C&F&H > 0) directly contradicts the implication that the region C&F&H is one of the *missing* regions among the five non-empty ones, statement C is the most likely to be the “not correct” one under a plausible interpretation of the five given areas. The wording “five disjoint bounded areas… labelled with number of players belonging to that area” strongly suggests these are the *only* regions within the shapes that contain players. If the C&F&H intersection is not one of these five, its count is 0.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

In the diagram given below, there is a circle, a square and a triangle dividing the region into five disjoint bounded areas. Each of these areas are labelled with number of players belonging to that area. The circle contains cricketers, the square contains football players and the triangle contains hockey players. Which one of the … <\/p>\n

Detailed SolutionIn the diagram given below, there is a circle, a square and a triangle<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1085],"tags":[1098,1102],"class_list":["post-90013","post","type-post","status-publish","format-standard","hentry","category-upsc-capf","tag-1098","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nIn the diagram given below, there is a circle, a square and a triangle<\/title>\n<meta name=\"description\" content=\"The correct option is C) There are some hockey players who play both cricket and football. The question describes a diagram with a circle (cricketers, C), a square (football players, F), and a triangle (hockey players, H), divided into *five disjoint bounded areas*, each with a number of players. 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The question describes a diagram with a circle (cricketers, C), a square (football players, F), and a triangle (hockey players, H), divided into *five disjoint bounded areas*, each with a number of players. 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