{"id":21070,"date":"2019-05-14T11:32:23","date_gmt":"2019-05-14T06:02:23","guid":{"rendered":"https:\/\/e-gmat.com\/blogs\/?p=21070"},"modified":"2023-02-07T11:23:53","modified_gmt":"2023-02-07T05:53:53","slug":"quant-og-solution-377-certain-list-contains","status":"publish","type":"post","link":"https:\/\/e-gmat.com\/blogs\/quant-og-solution-377-certain-list-contains\/","title":{"rendered":"GMAT Quant OG 2020 Question #377 with Solution – A certain list, L, contains… PQID: DS08091.01"},"content":{"rendered":"A <\/span> 2<\/span> min read <\/span><\/span>\n

PQID: <\/strong>DS08091.01 <\/p>\n\n\n\n

GMAT Quant OG 2020 Solution: Question No. 377<\/h2>\n\n\n\n

A certain list, L, contains a total of n numbers, not necessarily distinct, that are arranged in increasing order. If L1<\/sub> is the list consisting of the first n1<\/sub> numbers in L and L2<\/sub> is the list consisting of the last n2<\/sub> numbers in L, is 17 a mode for L?<\/p>\n\n\n\n

  1. 17 is a mode for L1<\/sub> and 17 is a mode for L2<\/sub>.<\/li>
  2. n1<\/sub> + n2<\/sub> = n<\/li><\/ol>\n\n\n\n
    Source<\/td>OG 2020<\/td><\/tr>
    Type<\/td>Data Sufficiency<\/td><\/tr>
    Topic<\/td>Number Properties<\/td><\/tr>
    Sub-Topic<\/td>Statistics<\/td><\/tr>
    Difficulty<\/td>Very Hard<\/td><\/tr>
    PQID<\/td>DS08091.01<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

    Solution to GMAT Quant OG Question no 377<\/h3>\n\n\n\n

    <\/p>\n\n\n\n

    Steps 1 & 2: Understand Question and Draw Inferences<\/u><\/strong><\/h4>\n\n\n\n

    In this question, we are given<\/p>\n\n\n\n

    • A certain list, L, contains a total of n numbers, not necessarily distinct, that are arranged in increasing order.<\/li>
    • L1<\/sub> is the list consisting of the first n1<\/sub> numbers in L.<\/li>
    • L2<\/sub> is the list consisting of the last n2<\/sub> numbers in L.<\/li><\/ul>\n\n\n\n

      We need to determine<\/p>\n\n\n\n

      • Whether 17 is a mode for L or not.<\/li><\/ul>\n\n\n\n

        Step 3: Analyse Statement 1<\/u><\/strong><\/h4>\n\n\n\n

        As per the information given in statement 1, 17 is a mode for L1<\/sub> and 17 is a mode for L2<\/sub>.<\/p>\n\n\n\n

        Therefore, we can infer that<\/p>\n\n\n\n

        • 17 must occur in L1<\/sub>, either same or a greater number of times as any other number in L1<\/sub>.<\/sup><\/li>
        • 17 must occur in L2<\/sub>, either same or a greater number of times as any other number in L2<\/sub>.<\/sup><\/li><\/ul>\n\n\n\n

          As all elements in L are in ascending order, we can also conclude that<\/p>\n\n\n\n

          • Each number between last occurrence of 17 in L1<\/sub> and the first occurrence of 17 in L2<\/sub> must be equal to 17 only.<\/li>
          • Therefore, 17 occurs either same or greater number of times as any other number in L.\n
              \n
            • Thus, 17 is a mode for L.<\/li>\n<\/ul>\n<\/li><\/ul>\n\n\n\n

              Hence, statement 1 is sufficient to answer the question.<\/p>\n\n\n\n

              Step 4: Analyse Statement 2<\/u><\/strong><\/h4>\n\n\n\n

              As per the information given in statement 2, n1<\/sub> + n2<\/sub> = n.<\/p>\n\n\n\n

              • However, from this statement, we cannot conclude anything about the mode of L1<\/sub>, L2<\/sub>, or L.<\/li><\/ul>\n\n\n\n

                Hence, statement 2 is not sufficient to answer the question.<\/p>\n\n\n\n

                Step 5: Combine Both Statements Together (If Needed)<\/u><\/strong><\/h4>\n\n\n\n

                Since we can determine the answer from statement 1 individually, this step is not required.<\/p>\n\n\n\n

                Hence, the correct answer choice is option A.<\/p>\n\n\n\n

                Takeaways from solution to GMAT Quant OG 2020 Question No 377:<\/h3>\n\n\n\n
                1. Mode is the most frequently observed element in a data set.\u202f 
                  1. If 17 is the mode for L1<\/sub>, 17 occurs either the same or a greater number of times as any other number in L1<\/sub>. <\/li>
                  2. Similarly, if 17 is the mode for L2<\/sub>, 17 occurs either the same or a greater number of times as any other number in L2<\/sub>.\u202f <\/li><\/ol><\/li><\/ol>\n\n\n\n

                    \u202f <\/p>\n","protected":false},"excerpt":{"rendered":"

                    PQID: DS08091.01  GMAT Quant OG 2020 Solution: Question No. 377 A certain list, L, contains a total of n numbers, not necessarily distinct, that are arranged in increasing order. If L1 is the list consisting of the first n1 numbers in L and L2 is the list consisting of the last n2 numbers in L, […]<\/p>\n","protected":false},"author":79663,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"","_et_pb_old_content":"","_et_gb_content_width":"","ub_ctt_via":""},"categories":[44,94,60,61,100],"tags":[],"featured_image_src":null,"author_info":{"display_name":"Juhi Gupta","author_link":"https:\/\/e-gmat.com\/blogs\/author\/juhie-gmat-com\/"},"yoast_head":"\nGMAT Quant OG 2020 Question #377 with Solution - A certain list, L, contains... 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