{"id":153949,"date":"2023-08-01T14:55:44","date_gmt":"2023-08-01T09:25:44","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=153949"},"modified":"2023-08-01T14:55:45","modified_gmt":"2023-08-01T09:25:45","slug":"the-police-arrested-four-criminals-p-q-r-and-s-the-criminals-knew-each-other-they-made-the-following-statements","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/the-police-arrested-four-criminals-p-q-r-and-s-the-criminals-knew-each-other-they-made-the-following-statements\/","title":{"rendered":"The police arrested four criminals \u2013 P, Q, R and S. The criminals knew each other. They made the following statements"},"content":{"rendered":"\n

Q. The police arrested four criminals \u2013 P, Q, R and S. The criminals knew each other. They made the following statements:<\/p>\n\n\n\n

P says \u201cQ committed the crime.\u201d <\/p>\n\n\n\n

Q says \u201cS committed the crime.\u201d <\/p>\n\n\n\n

R says \u201cI did not do it.\u201d<\/p>\n\n\n\n

S says \u201cWhat Q said about me is false.\u201d<\/p>\n\n\n\n

Assume only one of the arrested four committed the crime and only one of the statements made above is true. Who committed the crime?<\/p>\n\n\n\n

(A) P<\/p>\n\n\n\n

(B) R<\/p>\n\n\n\n

(C) S<\/p>\n\n\n\n

(D) Q<\/p>\n\n\n\n

Ans: R<\/p>\n\n\n\n

Solution:<\/p>\n\n\n\n

Suffix C as criminal, NC as not criminal.<\/p>\n\n\n\n

Case I:<\/p>\n\n\n\n

Criminals<\/td>P<\/td>Q<\/td>R<\/td>S<\/td><\/tr>
Assumption<\/td>T<\/td>F<\/td>F<\/td>F<\/td><\/tr>
Result<\/td>QC<\/td>SNC<\/td>RC<\/td>SC<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Q and R are criminal in the result is impossible because only one person committed the crime.<\/p>\n\n\n\n

Case II:<\/p>\n\n\n\n

Criminals<\/td>P<\/td>Q<\/td>R<\/td>S<\/td><\/tr>
Assumption<\/td>F<\/td>T<\/td>F<\/td>F<\/td><\/tr>
Result<\/td>QNC<\/td>SC<\/td>RC<\/td>SC<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

S and R are criminal in the result is impossible because only one person committed the crime.<\/p>\n\n\n\n

Case III:<\/p>\n\n\n\n

Criminals<\/td>P<\/td>Q<\/td>R<\/td>S<\/td><\/tr>
Assumption<\/td>F<\/td>F<\/td>T<\/td>F<\/td><\/tr>
Result<\/td>QNC<\/td>SNC<\/td>RNC<\/td>SC<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

SNC and SC in the result which is contradiction. [S committed crime and same time not committed crime which is contradiction]<\/p>\n\n\n\n

Case IV:<\/p>\n\n\n\n

Criminals<\/td>P<\/td>Q<\/td>R<\/td>S<\/td><\/tr>
Assumption<\/td>F<\/td>F<\/td>F<\/td>T<\/td><\/tr>
Result<\/td>QNC<\/td>SNC<\/td>RC<\/td>SNC<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

R is criminal in the result.
Hence, this case satisfies only one person committed the crime.<\/p>\n","protected":false},"excerpt":{"rendered":"

Q. The police arrested four criminals \u2013 P, Q, R and S. The criminals knew each other. They made the following statements: P says \u201cQ committed the crime.\u201d Q says \u201cS committed the crime.\u201d R says \u201cI did not do it.\u201d S says \u201cWhat Q said about me is false.\u201d Assume only one of the […]<\/p>\n","protected":false},"author":419,"featured_media":153950,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[5141],"tags":[5140],"class_list":["post-153949","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-gate","tag-gate-questions"],"_links":{"self":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/153949","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/users\/419"}],"replies":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/comments?post=153949"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/153949\/revisions"}],"predecessor-version":[{"id":153951,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/153949\/revisions\/153951"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/153950"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=153949"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=153949"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=153949"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}