{"id":162997,"date":"2024-02-23T16:22:07","date_gmt":"2024-02-23T10:52:07","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=162997"},"modified":"2024-02-23T16:22:07","modified_gmt":"2024-02-23T10:52:07","slug":"in-each-of-the-following-questions-two-statements-or-three-statements-are-given-you-are-expected-to-solve-them-and-determine","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/in-each-of-the-following-questions-two-statements-or-three-statements-are-given-you-are-expected-to-solve-them-and-determine\/","title":{"rendered":"In each of the following questions, two statements or three statements are given. You are expected to solve them and determine"},"content":{"rendered":"\n<p> <p class=\"MsoNormal\">Directions: In each of the following questions, two statements or three statements are given. You are expected to solve them and determine which statement or combination of statements is sufficient to answer the question.<\/p> <p class=\"MsoNormal\">1) The LCM of two positive integers P and Q is 165. What will be the 50% of HCF of P and Q?<\/p> <p class=\"MsoNormal\">Statement I: 50% of (P \u2013 Q) is a multiple 3 less than 12<\/p> <p class=\"MsoNormal\">Statement II: 75% of (P + Q) = 36 Statement III: P2 \u2013 55P + 726 = 0<\/p> <p class=\"MsoNormal\">A.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Statement I and II together are sufficient to answer the question<\/p> <p class=\"MsoNormal\">B.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Statement II and III together are sufficient to answer the question<\/p> <p class=\"MsoNormal\">C.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Statement III and I together are sufficient to answer the question<\/p> <p class=\"MsoNormal\"><b>D.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Combination of any two statements are sufficient to answer the question<\/b><\/p> <p class=\"MsoNormal\">E.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 None of these<\/p> <p class=\"MsoNormal\">Sol:<\/p> <p class=\"MsoNormal\">On combining (I + II) <\/p> <p class=\"MsoNormal\">50% of (P \u2013 Q) = 3 or 6 or 9 <\/p> <p class=\"MsoNormal\">(P \u2013 Q) = 6 or 12 or 18\u2026\u2026\u2026\u2026\u2026.. (1)<\/p> <p class=\"MsoNormal\">Also, 75% of (P + Q) = 36 <\/p> <p class=\"MsoNormal\">(P + Q) = 48\u2026\u2026\u2026\u2026\u2026 (2)<\/p> <p class=\"MsoNormal\">On solving both equations we get <\/p> <p class=\"MsoNormal\">P = 27, Q = 21 <\/p> <p class=\"MsoNormal\">P = 30, Q = 18 <\/p> <p class=\"MsoNormal\">P = 33, Q = 15 <\/p> <p class=\"MsoNormal\">LCM of (33, 15) is 165 <\/p> <p class=\"MsoNormal\">33 = 11 x 3 <\/p> <p class=\"MsoNormal\">15 = 5 x 3 <\/p> <p class=\"MsoNormal\">So, HCF of (33, 15) = 3 <\/p> <p class=\"MsoNormal\">Required value = 50% x 3 = 1.5 <\/p> <p class=\"MsoNormal\">This combination of statement is sufficient to <\/p> <p class=\"MsoNormal\">answer the question <\/p> <p class=\"MsoNormal\">On combining (II + III) <\/p> <p class=\"MsoNormal\">75% of (P + Q) = 36 <\/p> <p class=\"MsoNormal\">(P + Q) = 48 <\/p> <p class=\"MsoNormal\">Also, <\/p> <p class=\"MsoNormal\">P2 \u2013 55P + 726 = 0 <\/p> <p class=\"MsoNormal\">(P \u2013 33)(P \u2013 22) = 0 <\/p> <p class=\"MsoNormal\">P = 33, 22 <\/p> <p class=\"MsoNormal\">On putting these values in above equation <\/p> <p class=\"MsoNormal\">Q = 15, 26 <\/p> <p class=\"MsoNormal\">LCM of (33, 15) = 165 <\/p> <p class=\"MsoNormal\">33 = 11 x 3 <\/p> <p class=\"MsoNormal\">15 = 5 x 3 <\/p> <p class=\"MsoNormal\">So, HCF of (33, 15) = 3 <\/p> <p class=\"MsoNormal\">Required value = 50% x 3 = 1.5 <\/p> <p class=\"MsoNormal\">This combination is sufficient to answer the <\/p> <p class=\"MsoNormal\">question. <\/p> <p class=\"MsoNormal\">On combining (III + I) <\/p> <p class=\"MsoNormal\">50% of (P \u2013 Q) = 3 or 6 or 9 <\/p> <p class=\"MsoNormal\">(P \u2013 Q) = 6 or 12 or 18 <\/p> <p class=\"MsoNormal\">Also,<\/p> <p class=\"MsoNormal\">P2 \u2013 55P + 726 = 0 <\/p> <p class=\"MsoNormal\">(P \u2013 33)(P \u2013 22) = 0 <\/p> <p class=\"MsoNormal\">P = 33, 22 <\/p> <p class=\"MsoNormal\">On putting these values in above equation <\/p> <p class=\"MsoNormal\">Q = 27, 16, 21, 10, 15, 4 <\/p> <p class=\"MsoNormal\">Only (33, 15) gives LCM 165 <\/p> <p class=\"MsoNormal\">This combination of statements is sufficient to <\/p> <p class=\"MsoNormal\">answer the question. <\/p> <p class=\"MsoNormal\">So, a combination of any two statementsare <\/p> <p class=\"MsoNormal\">sufficient to answer the <\/p> <p class=\"MsoNormal\">question. <\/p> <p class=\"MsoNormal\">Hence answer is option D<\/p> <p class=\"MsoNormal\">2) In 9thstd there are four sections \u2013 P, Q, R, and S. Find the number of students in section R.<\/p> <p class=\"MsoNormal\">Statement I: The average number of students in P, Q, and R is 260 and the number of students in P is 240 less than S.<\/p> <p class=\"MsoNormal\">Statement II: Number of students in S is twice that of P. Number of students in P and Q together is 600.<\/p> <p class=\"MsoNormal\">Statement III: Number of students in Q is twice of R and 120 less than S.<\/p> <p class=\"MsoNormal\">A.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Statement I and II together are sufficient to answer the question<\/p> <p class=\"MsoNormal\">B.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Statement II and III together are sufficient to answer the question<\/p> <p class=\"MsoNormal\">C.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Statement III and I together are sufficient to answer the question<\/p> <p class=\"MsoNormal\"><b>D.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Combination of any two statements are sufficient to answer the question<\/b><\/p> <p class=\"MsoNormal\">E.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 None of these<\/p> <p class=\"MsoNormal\">Statement I. <\/p> <p class=\"MsoNormal\">(P + Q + R) = 3 x 260 = 780 <\/p> <p class=\"MsoNormal\">S = 240 + P <\/p> <p class=\"MsoNormal\">Statement II. <\/p> <p class=\"MsoNormal\">S = 2P <\/p> <p class=\"MsoNormal\">(P + Q) = 600 <\/p> <p class=\"MsoNormal\">Statement III. <\/p> <p class=\"MsoNormal\">Q = 2R <\/p> <p class=\"MsoNormal\">S = Q + 120 <\/p> <p class=\"MsoNormal\">On combining I and II <\/p> <p class=\"MsoNormal\">(P + Q + R) = 3 x 260 = 780\u2026\u2026\u2026\u2026 (1)<\/p> <p class=\"MsoNormal\">(P + Q) = 600\u2026\u2026\u2026\u2026 (2)<\/p> <p class=\"MsoNormal\">On solving both equations, we get <\/p> <p class=\"MsoNormal\">R = 780 \u2013 600 = 180 <\/p> <p class=\"MsoNormal\">This combination is sufficient to answer the <\/p> <p class=\"MsoNormal\">question <\/p> <p class=\"MsoNormal\">On combining II and III <\/p> <p class=\"MsoNormal\">S = Q + 120 <\/p> <p class=\"MsoNormal\">Also, S = 2P<\/p> <p class=\"MsoNormal\">So, 2P \u2013 Q = 120\u2026\u2026\u2026.. (3)<\/p> <p class=\"MsoNormal\">Also, (P + Q) = 600\u2026\u2026\u2026\u2026. (4)<\/p> <p class=\"MsoNormal\">On solving 3 and 4, <\/p> <p class=\"MsoNormal\">P = 240 and Q = 360 <\/p> <p class=\"MsoNormal\">So, R = Q\/2 = 360\/2 = 180 <\/p> <p class=\"MsoNormal\">This combination is sufficient to answer the <\/p> <p class=\"MsoNormal\">question <\/p> <p class=\"MsoNormal\">On combining I and III <\/p> <p class=\"MsoNormal\">S = 240 + P <\/p> <p class=\"MsoNormal\">Also, S = Q + 120 <\/p> <p class=\"MsoNormal\">So, 240 + P = Q + 120 <\/p> <p class=\"MsoNormal\">P = Q &#8211; 120 <\/p> <p class=\"MsoNormal\">Also, Q = 2R <\/p> <p class=\"MsoNormal\">Also, (P + Q + R) = 780 <\/p> <p class=\"MsoNormal\">So, 2R \u2013 120 + 2R + R = 780 <\/p> <p class=\"MsoNormal\">So, 5R = 900 <\/p> <p class=\"MsoNormal\">R = 180 <\/p> <p class=\"MsoNormal\">This combination of statements is sufficient to <\/p> <p class=\"MsoNormal\">answer the question. <\/p> <p class=\"MsoNormal\">Hence answer is option D<\/p> <p class=\"MsoNormal\">3) A bought an article at Rs. 25600 and sold it to B at Rs. P loss, then B sold it to C at Q% profit, if the marked price of the article is same for all then find the value of Q %.<\/p> <p class=\"MsoNormal\">Statement I: value of P = Rs. 1024 Statement II: Discount % offered to A was 37.5%<\/p> <p class=\"MsoNormal\">Statement III: Discount % offered by B was 31.25%<\/p> <p class=\"MsoNormal\">A.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Statement I and II together are sufficient to answer the question<\/p> <p class=\"MsoNormal\">B.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Statement II and III together are sufficient to answer the question<\/p> <p class=\"MsoNormal\">C.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Statement III and I together are sufficient to answer the question<\/p> <p class=\"MsoNormal\">D.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Combination of any two statements are sufficient to answer the question<\/p> <p class=\"MsoNormal\"><b>E.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 None of these<\/b><\/p> <p class=\"MsoNormal\">Statement I. <\/p> <p class=\"MsoNormal\">Selling price for A or cost price for B = 25600 \u2013<\/p> <p class=\"MsoNormal\">1024 = Rs. 24576 <\/p> <p class=\"MsoNormal\">This statement alone is not sufficient <\/p> <p class=\"MsoNormal\">Statement II. Discount offered to A was 37.5% <\/p> <p class=\"MsoNormal\">So, Marked price of the article = 25600\/62.5 x <\/p> <p class=\"MsoNormal\">100 = 40960 <\/p> <p class=\"MsoNormal\">This statement alone is not sufficient to answer <\/p> <p class=\"MsoNormal\">the question <\/p> <p class=\"MsoNormal\">Statement III. Discount offered by B was 31.25%<\/p> <p class=\"MsoNormal\">This statement alone is not sufficient to answer <\/p> <p class=\"MsoNormal\">the question <\/p> <p class=\"MsoNormal\">On combining I and II <\/p> <p class=\"MsoNormal\">We need to calculate profit % for B, so we need <\/p> <p class=\"MsoNormal\">CP and SP for B. <\/p> <p class=\"MsoNormal\">Cost price for B = 25600 \u2013 1024 = Rs. 24576 <\/p> <p class=\"MsoNormal\">Marked price of the article = 25600\/62.5 x 100 = <\/p> <p class=\"MsoNormal\">Rs.40960 <\/p> <p class=\"MsoNormal\">We don\u2019t know the selling price for B <\/p> <p class=\"MsoNormal\">This combination is not sufficient <\/p> <p class=\"MsoNormal\">On combining II and III <\/p> <p class=\"MsoNormal\">This combination gives MRP and SP for B not <\/p> <p class=\"MsoNormal\">CP. So this combination is not sufficient <\/p> <p class=\"MsoNormal\">On combining III and I <\/p> <p class=\"MsoNormal\">This combination gives only CP for B. this <\/p> <p class=\"MsoNormal\">combination is not sufficient to answer the <\/p> <p class=\"MsoNormal\">question. <\/p> <p class=\"MsoNormal\">On combining I, II and III <\/p> <p class=\"MsoNormal\">CP for B = 24576 <\/p> <p class=\"MsoNormal\">MRP = 40960 <\/p> <p class=\"MsoNormal\">SP for B = 40960 x 11\/16 = 28160 <\/p> <p class=\"MsoNormal\">So, Q % = (28160 \u2013 24576)\/24576 x 100 = <\/p> <p class=\"MsoNormal\">14.5833% <\/p> <p class=\"MsoNormal\">All three statements together necessary to <\/p> <p class=\"MsoNormal\">answer the question <\/p> <p class=\"MsoNormal\">Hence answer is option E<\/p> <p class=\"MsoNormal\"><o:p>\u00a0<\/o:p><\/p> <\/p>\n","protected":false},"excerpt":{"rendered":"<p>Directions: In each of the following questions, two statements or three statements are given. You are expected to solve them and determine which statement or combination of statements is sufficient to answer the question. 1) The LCM of two positive integers P and Q is 165. What will be the 50% of HCF of P [&hellip;]<\/p>\n","protected":false},"author":419,"featured_media":162998,"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":[5138],"tags":[5139],"class_list":["post-162997","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-quantitative-aptitude","tag-quantitative-aptitude"],"_links":{"self":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/162997","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=162997"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/162997\/revisions"}],"predecessor-version":[{"id":162999,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/162997\/revisions\/162999"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/162998"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=162997"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=162997"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=162997"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}