{"id":90725,"date":"2025-06-01T10:35:25","date_gmt":"2025-06-01T10:35:25","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=90725"},"modified":"2025-06-01T10:35:25","modified_gmt":"2025-06-01T10:35:25","slug":"a-test-consists-of-25-mcqs-each-correct-answer-gives-4-marks-and-inc","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-test-consists-of-25-mcqs-each-correct-answer-gives-4-marks-and-inc\/","title":{"rendered":"A test consists of 25 MCQs. Each correct answer gives +4 marks and inc"},"content":{"rendered":"

A test consists of 25 MCQs. Each correct answer gives +4 marks and incorrect answer gives -1 mark. If a candidate scores 74 marks, then how many questions were left unattempted?<\/p>\n

[amp_mcq option1=”4″ option2=”3″ option3=”5″ option4=”9″ correct=”option1″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CAPF – 2022<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nLet c be the number of correct answers, i be the number of incorrect answers, and u be the number of unattempted questions.
\nTotal questions: c + i + u = 25
\nTotal score: 4c – i = 74 (unattempted questions contribute 0 marks).
\nWe need to find the value of u. We can test the given options for u.
\nIf u = 4, then c + i = 25 – 4 = 21.
\nWe have the system of equations:
\n1) c + i = 21
\n2) 4c – i = 74
\nAdd the two equations: (c + i) + (4c – i) = 21 + 74 => 5c = 95 => c = 19.
\nSubstitute c = 19 into equation 1: 19 + i = 21 => i = 21 – 19 = 2.
\nCheck the score: 4c – i = 4(19) – 2 = 76 – 2 = 74. This matches the given score.
\nTherefore, the number of unattempted questions is 4.
\n<\/section>\n
\n– Set up equations based on the given information: total number of questions and the scoring system.
\n– Use variables to represent the number of correct, incorrect, and unattempted questions.
\n– The total number of questions is the sum of correct, incorrect, and unattempted questions.
\n– The total score is calculated based on the marks per correct and incorrect answer.
\n<\/section>\n
\nTrying other options for ‘u’ would not yield integer values for ‘c’ and ‘i’ (as shown in the thought process), confirming that u=4 is the unique solution. This type of problem involves solving a system of linear equations, possibly with the added constraint that the variables must be non-negative integers.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

A test consists of 25 MCQs. Each correct answer gives +4 marks and incorrect answer gives -1 mark. If a candidate scores 74 marks, then how many questions were left unattempted? [amp_mcq option1=”4″ option2=”3″ option3=”5″ option4=”9″ correct=”option1″] This question was previously asked in UPSC CAPF – 2022 Download PDFAttempt Online Let c be the number … <\/p>\n

Detailed SolutionA test consists of 25 MCQs. Each correct answer gives +4 marks and inc<\/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":[1108,1102],"class_list":["post-90725","post","type-post","status-publish","format-standard","hentry","category-upsc-capf","tag-1108","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nA test consists of 25 MCQs. Each correct answer gives +4 marks and inc<\/title>\n<meta name=\"description\" content=\"Let c be the number of correct answers, i be the number of incorrect answers, and u be the number of unattempted questions. Total questions: c + i + u = 25 Total score: 4c - i = 74 (unattempted questions contribute 0 marks). We need to find the value of u. We can test the given options for u. If u = 4, then c + i = 25 - 4 = 21. We have the system of equations: 1) c + i = 21 2) 4c - i = 74 Add the two equations: (c + i) + (4c - i) = 21 + 74 => 5c = 95 => c = 19. Substitute c = 19 into equation 1: 19 + i = 21 => i = 21 - 19 = 2. Check the score: 4c - i = 4(19) - 2 = 76 - 2 = 74. This matches the given score. Therefore, the number of unattempted questions is 4. - Set up equations based on the given information: total number of questions and the scoring system. - Use variables to represent the number of correct, incorrect, and unattempted questions. - The total number of questions is the sum of correct, incorrect, and unattempted questions. - The total score is calculated based on the marks per correct and incorrect answer.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/a-test-consists-of-25-mcqs-each-correct-answer-gives-4-marks-and-inc\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A test consists of 25 MCQs. Each correct answer gives +4 marks and inc\" \/>\n<meta property=\"og:description\" content=\"Let c be the number of correct answers, i be the number of incorrect answers, and u be the number of unattempted questions. Total questions: c + i + u = 25 Total score: 4c - i = 74 (unattempted questions contribute 0 marks). We need to find the value of u. We can test the given options for u. If u = 4, then c + i = 25 - 4 = 21. We have the system of equations: 1) c + i = 21 2) 4c - i = 74 Add the two equations: (c + i) + (4c - i) = 21 + 74 => 5c = 95 => c = 19. Substitute c = 19 into equation 1: 19 + i = 21 => i = 21 - 19 = 2. Check the score: 4c - i = 4(19) - 2 = 76 - 2 = 74. This matches the given score. Therefore, the number of unattempted questions is 4. - Set up equations based on the given information: total number of questions and the scoring system. - Use variables to represent the number of correct, incorrect, and unattempted questions. - The total number of questions is the sum of correct, incorrect, and unattempted questions. - The total score is calculated based on the marks per correct and incorrect answer.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/a-test-consists-of-25-mcqs-each-correct-answer-gives-4-marks-and-inc\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T10:35:25+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"A test consists of 25 MCQs. Each correct answer gives +4 marks and inc","description":"Let c be the number of correct answers, i be the number of incorrect answers, and u be the number of unattempted questions. Total questions: c + i + u = 25 Total score: 4c - i = 74 (unattempted questions contribute 0 marks). We need to find the value of u. We can test the given options for u. If u = 4, then c + i = 25 - 4 = 21. We have the system of equations: 1) c + i = 21 2) 4c - i = 74 Add the two equations: (c + i) + (4c - i) = 21 + 74 => 5c = 95 => c = 19. Substitute c = 19 into equation 1: 19 + i = 21 => i = 21 - 19 = 2. Check the score: 4c - i = 4(19) - 2 = 76 - 2 = 74. This matches the given score. Therefore, the number of unattempted questions is 4. - Set up equations based on the given information: total number of questions and the scoring system. - Use variables to represent the number of correct, incorrect, and unattempted questions. - The total number of questions is the sum of correct, incorrect, and unattempted questions. - The total score is calculated based on the marks per correct and incorrect answer.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/exam.pscnotes.com\/mcq\/a-test-consists-of-25-mcqs-each-correct-answer-gives-4-marks-and-inc\/","og_locale":"en_US","og_type":"article","og_title":"A test consists of 25 MCQs. Each correct answer gives +4 marks and inc","og_description":"Let c be the number of correct answers, i be the number of incorrect answers, and u be the number of unattempted questions. Total questions: c + i + u = 25 Total score: 4c - i = 74 (unattempted questions contribute 0 marks). We need to find the value of u. We can test the given options for u. If u = 4, then c + i = 25 - 4 = 21. We have the system of equations: 1) c + i = 21 2) 4c - i = 74 Add the two equations: (c + i) + (4c - i) = 21 + 74 => 5c = 95 => c = 19. Substitute c = 19 into equation 1: 19 + i = 21 => i = 21 - 19 = 2. Check the score: 4c - i = 4(19) - 2 = 76 - 2 = 74. This matches the given score. Therefore, the number of unattempted questions is 4. - Set up equations based on the given information: total number of questions and the scoring system. - Use variables to represent the number of correct, incorrect, and unattempted questions. - The total number of questions is the sum of correct, incorrect, and unattempted questions. - The total score is calculated based on the marks per correct and incorrect answer.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/a-test-consists-of-25-mcqs-each-correct-answer-gives-4-marks-and-inc\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T10:35:25+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/a-test-consists-of-25-mcqs-each-correct-answer-gives-4-marks-and-inc\/","url":"https:\/\/exam.pscnotes.com\/mcq\/a-test-consists-of-25-mcqs-each-correct-answer-gives-4-marks-and-inc\/","name":"A test consists of 25 MCQs. Each correct answer gives +4 marks and inc","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T10:35:25+00:00","dateModified":"2025-06-01T10:35:25+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"Let c be the number of correct answers, i be the number of incorrect answers, and u be the number of unattempted questions. Total questions: c + i + u = 25 Total score: 4c - i = 74 (unattempted questions contribute 0 marks). We need to find the value of u. We can test the given options for u. If u = 4, then c + i = 25 - 4 = 21. We have the system of equations: 1) c + i = 21 2) 4c - i = 74 Add the two equations: (c + i) + (4c - i) = 21 + 74 => 5c = 95 => c = 19. Substitute c = 19 into equation 1: 19 + i = 21 => i = 21 - 19 = 2. Check the score: 4c - i = 4(19) - 2 = 76 - 2 = 74. This matches the given score. Therefore, the number of unattempted questions is 4. - Set up equations based on the given information: total number of questions and the scoring system. - Use variables to represent the number of correct, incorrect, and unattempted questions. - The total number of questions is the sum of correct, incorrect, and unattempted questions. - The total score is calculated based on the marks per correct and incorrect answer.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/a-test-consists-of-25-mcqs-each-correct-answer-gives-4-marks-and-inc\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/a-test-consists-of-25-mcqs-each-correct-answer-gives-4-marks-and-inc\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/a-test-consists-of-25-mcqs-each-correct-answer-gives-4-marks-and-inc\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"UPSC CAPF","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/upsc-capf\/"},{"@type":"ListItem","position":3,"name":"A test consists of 25 MCQs. 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