{"id":274409,"date":"2025-07-28T08:29:06","date_gmt":"2025-07-28T08:29:06","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=274409"},"modified":"2025-07-28T08:29:07","modified_gmt":"2025-07-28T08:29:07","slug":"find-the-sum-of-all-two-digit-natural-numbers-which-are-not-divisible-by-3","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/28\/find-the-sum-of-all-two-digit-natural-numbers-which-are-not-divisible-by-3\/","title":{"rendered":"Find the sum of all two-digit natural numbers which are not divisible by 3"},"content":{"rendered":"\n

Find the sum of all two-digit natural numbers which are not divisible by 3.<\/p>\n\n\n\n

The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n

To find the sum of all two-digit natural numbers which are not divisible by 3<\/strong>, follow these steps:<\/p>\n\n\n\n

Step 1: Identify the Range<\/h3>\n\n\n\n

The two-digit natural numbers range from 10 to 99<\/strong>.<\/p>\n\n\n\n

Step 2: Find the Sum of All Two-Digit Numbers<\/h3>\n\n\n\n

To find the sum of all two-digit numbers, use the formula for the sum of an arithmetic series: S=n2\u00d7(a+l)S = \\frac{n}{2} \\times (a + l)<\/p>\n\n\n\n

Where:<\/p>\n\n\n\n

    \n
  • nn is the number of terms<\/li>\n\n\n\n
  • aa is the first term<\/li>\n\n\n\n
  • ll is the last term<\/li>\n<\/ul>\n\n\n\n

    For the numbers from 10 to 99:<\/p>\n\n\n\n

      \n
    • a=10a = 10<\/li>\n\n\n\n
    • l=99l = 99<\/li>\n\n\n\n
    • n=99\u221210+1=90n = 99 – 10 + 1 = 90<\/li>\n<\/ul>\n\n\n\n

      So the sum of all two-digit numbers is: S=902\u00d7(10+99)=45\u00d7109=4905S = \\frac{90}{2} \\times (10 + 99) = 45 \\times 109 = 4905<\/p>\n\n\n\n

      Step 3: Find the Sum of Two-Digit Numbers Divisible by 3<\/h3>\n\n\n\n

      To find the numbers divisible by 3, first identify the smallest and largest two-digit numbers divisible by 3:<\/p>\n\n\n\n

        \n
      • The smallest is 1212 (since 10\u00f73=3.3310 \\div 3 = 3.33 and the next whole number is 12).<\/li>\n\n\n\n
      • The largest is 9999 (since 99\u00f73=3399 \\div 3 = 33).<\/li>\n<\/ul>\n\n\n\n

        These numbers form an arithmetic sequence with:<\/p>\n\n\n\n

          \n
        • First term a=12a = 12<\/li>\n\n\n\n
        • Last term l=99l = 99<\/li>\n\n\n\n
        • Common difference d=3d = 3<\/li>\n<\/ul>\n\n\n\n

          The number of terms in this sequence is: n=99\u2212123+1=30n = \\frac{99 – 12}{3} + 1 = 30<\/p>\n\n\n\n

          So the sum of the numbers divisible by 3 is: S3=302\u00d7(12+99)=15\u00d7111=1665S_3 = \\frac{30}{2} \\times (12 + 99) = 15 \\times 111 = 1665<\/p>\n\n\n\n

          Step 4: Find the Sum of Two-Digit Numbers Not Divisible by 3<\/h3>\n\n\n\n

          Now, subtract the sum of numbers divisible by 3 from the total sum: Snot divisible by 3=4905\u22121665=3240S_{\\text{not divisible by 3}} = 4905 – 1665 = 3240<\/p>\n\n\n\n

          Thus, the sum of all two-digit natural numbers which are not divisible by 3<\/strong> is 3240<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"

          Find the sum of all two-digit natural numbers which are not divisible by 3. The correct answer and explanation is: To find the sum of all two-digit natural numbers which are not divisible by 3, follow these steps: Step 1: Identify the Range The two-digit natural numbers range from 10 to 99. Step 2: Find […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","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-5)","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-5)","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-5)","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":[25],"tags":[],"class_list":["post-274409","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/274409","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=274409"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/274409\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=274409"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=274409"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=274409"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}