{"id":3425,"date":"2022-12-16T07:35:43","date_gmt":"2022-12-16T07:35:43","guid":{"rendered":"https:\/\/theexampillar.com\/ncert\/?p=3425"},"modified":"2023-01-31T06:49:35","modified_gmt":"2023-01-31T06:49:35","slug":"ncert-solutions-class-8-maths-chapter-16-playing-with-numbers-ex-16-2","status":"publish","type":"post","link":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-maths-chapter-16-playing-with-numbers-ex-16-2\/","title":{"rendered":"NCERT Solutions Class 8 Maths Chapter 16 Playing with Numbers Ex 16.2"},"content":{"rendered":"<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">NCERT Solutions Class 8 Mathematics\u00a0<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Chapter &#8211; 16 (Playing with Numbers)\u00a0<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">The NCERT Solutions in English Language for Class 8 Mathematics <strong>Chapter &#8211; 16 Playing with Numbers <\/strong>Exercise 16.2 has been provided here to help the students in solving the questions from this exercise.\u00a0<\/span><\/p>\n<h4><span style=\"color: #000000;\"><strong>Chapter 16: Playing with Numbers<\/strong><\/span><\/h4>\n<ul>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-maths-chapter-16-playing-with-numbers-ex-16-1\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 8 Maths Ex &#8211; 16.1<\/a><\/li>\n<\/ul>\n<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Exercise &#8211; 16.2\u00a0<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>1. If 21y5 is a multiple of 9, where y is a digit, what is the value of y?<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211; <\/strong><\/span><span style=\"color: #000000;\">Suppose 21y5 is a multiple of 9.<br \/>\n<\/span><span style=\"color: #000000;\">Therefore, according to the divisibility rule of 9, the sum of all the digits should be a multiple of 9.<br \/>\n<\/span><span style=\"color: #000000;\">That is, 2 + 1 + y + 5 = 8 + y<br \/>\n<\/span><span style=\"color: #000000;\">Therefore, 8 + y is a factor of 9.<br \/>\n<\/span><span style=\"color: #000000;\">This is possible when 8 + y is any one of these numbers 0, 9, 18, 27, and so on<br \/>\n<\/span><span style=\"color: #000000;\">However, since y is a single digit number, this sum can be 9 only.<br \/>\n<\/span><span style=\"color: #000000;\">8 + y = 9<br \/>\ny = 9 &#8211; 8<br \/>\ny = 1<br \/>\nTherefore, y should be 1.<br \/>\n<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>2. If 31z5 is a multiple of 9, where z is a digit, what is the value of z? You will find that there are two answers for the last problem. Why is this so?<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211; <\/strong><\/span><span style=\"color: #000000;\">Since, 31z5 is a multiple of 9.<br \/>\n<\/span><span style=\"color: #000000;\">Therefore according to the divisibility rule of 9, the sum of all the digits should be a multiple of 9.<br \/>\n<\/span><span style=\"color: #000000;\">3 + 1 + z + 5 = 9 + z<br \/>\n<\/span><span style=\"color: #000000;\">Therefore, 9 + z is a multiple of 9<br \/>\n<\/span><span style=\"color: #000000;\">This is only possible when 9 + z is any one of these numbers: 0, 9, 18, 27, and so on.<br \/>\n<\/span><span style=\"color: #000000;\">This implies, 9 + 0 = 9 and 9 + 9 = 18<br \/>\n<\/span><span style=\"color: #000000;\">Hence 0 and 9 are two possible answers.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>3. If 24x is a multiple of 3, where x is a digit, what is the value of x? <\/strong><br \/>\n<\/span><span style=\"color: #000000;\">(Since 24x is a multiple of 3, its sum of digits 6+x is a multiple of 3; so 6+x is one of these numbers: 0, 3, 6, 9, 12, 15, 18, \u2026 . But since x is a digit, it can only be that 6+x = 6 or 9 or 12 or 15. Therefore, x = 0 or 3 or 6 or 9. Thus, x can have any of four different values.)<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211; <\/strong><\/span><span style=\"color: #000000;\">Let\u2019s say, 24x is a multiple of 3.<br \/>\n<\/span><span style=\"color: #000000;\">Then, according to the divisibility rule of 3, the sum of all the digits should be a multiple of 3.<br \/>\n<\/span><span style=\"color: #000000;\">2 + 4 + x = 6 + x<br \/>\n<\/span><span style=\"color: #000000;\">So, 6 + x is a multiple of 3, and 6+x is one of these numbers: 0, 3, 6, 9, 12, 15, 18 and so on.<br \/>\n<\/span><span style=\"color: #000000;\">Since, x is a digit, the value of x will be either 0 or 3 or 6 or 9, and the sum of the digits can be 6 or 9 or 12 or 15 respectively.<br \/>\n<\/span><span style=\"color: #000000;\">Thus, x can have any of the four different values: 0 or 3 or 6 or 9.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>4. If 31z5 is a multiple of 3, where z is a digit, what might be the values of z?<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211; <\/strong><\/span><span style=\"color: #000000;\">Since 31z5 is a multiple of 3.<br \/>\n<\/span><span style=\"color: #000000;\">Therefore according to the divisibility rule of 3, the sum of all the digits should be a multiple of 3.<br \/>\n<\/span><span style=\"color: #000000;\">That is, 3 + 1 + z + 5 = 9 + z<br \/>\n<\/span><span style=\"color: #000000;\">Therefore, 9 + z is a multiple of 3.<br \/>\n<\/span><span style=\"color: #000000;\">This is possible when the value of 9 + z is any of the values: 0, 3, 6, 9, 12, 15, and so on.<br \/>\n<\/span><span style=\"color: #000000;\">At z = 0, 9 + z = 9 + 0 = 9<br \/>\n<\/span><span style=\"color: #000000;\">At z = 3, 9 + z = 9 + 3 = 12<br \/>\n<\/span><span style=\"color: #000000;\">At z = 6, 9 + z = 9 + 6 = 15<br \/>\n<\/span><span style=\"color: #000000;\">At z = 9, 9 + z = 9 + 9 = 18<br \/>\n<\/span><span style=\"color: #000000;\">The value of 9+z can be 9 or 12 or 15 or 18.<br \/>\n<\/span><span style=\"color: #000000;\">Hence 0, 3, 6 or 9 are four possible answers for z.<\/span><\/p>\n<p>&nbsp;<\/p>\n<table style=\"width: 100%; border-collapse: collapse;\" border=\"1\">\n<tbody>\n<tr style=\"height: 32px;\">\n<td style=\"width: 100%; background-color: #f2e079; text-align: center; height: 32px;\"><span style=\"color: #ff0000; font-size: 14pt;\"><strong>NCERT Class 8<sup>th\u00a0<\/sup>Solution\u00a0<\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; text-align: left; height: 28px;\"><span style=\"font-size: 14pt;\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\"><a class=\"row-title\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-english\/\" target=\"_blank\" rel=\"noopener\" aria-label=\"\u201cNCERT Solutions Class 6 English\u201d (Edit)\">NCERT Solutions Class 8 English<\/a><\/span><\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; text-align: left; height: 28px;\"><span style=\"font-size: 14pt;\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\"><a class=\"row-title\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-hindi\/\" aria-label=\"\u201cNCERT Solutions Class 6 Maths\u201d (Edit)\">NCERT Solutions Class 8 Hindi<\/a><\/span><\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; text-align: left; height: 28px;\"><span style=\"font-size: 14pt;\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\"><a class=\"row-title\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-maths\/\" target=\"_blank\" rel=\"noopener\" aria-label=\"\u201cNCERT Solutions Class 6 Maths\u201d (Edit)\">NCERT Solutions Class 8 Mathematics<\/a>\u00a0<\/span><\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; text-align: left; height: 28px;\"><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-sanskrit-ruchira\/\" target=\"_blank\" rel=\"noopener\"><span style=\"font-size: 14pt;\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\">NCERT Solutions Class 8 Sanskrit<\/span><\/strong><\/span><\/a><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; text-align: left; height: 28px;\"><span style=\"font-size: 14pt;\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\"><a class=\"row-title\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-science\/\" target=\"_blank\" rel=\"noopener\" aria-label=\"\u201cNCERT Solutions Class 6 Social Science\u201d (Edit)\">NCERT Solutions Class 8 Science<\/a><\/span><\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; text-align: left; height: 28px;\"><span style=\"font-size: 14pt;\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\"><a class=\"row-title\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-social-science\/\" target=\"_blank\" rel=\"noopener\" aria-label=\"\u201cNCERT Solutions Class 6 Social Science\u201d (Edit)\">NCERT Solutions Class 8 Social Science<\/a><\/span><\/strong><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions Class 8 Mathematics\u00a0 Chapter &#8211; 16 (Playing with Numbers)\u00a0 The NCERT Solutions in English Language for Class 8 Mathematics Chapter &#8211; 16 Playing with Numbers Exercise 16.2 has been provided here to help the students in solving the questions from this exercise.\u00a0 Chapter 16: Playing with Numbers NCERT Solution Class 8 Maths Ex [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[442],"tags":[474,475,445,5],"class_list":["post-3425","post","type-post","status-publish","format-standard","hentry","category-class-8-maths","tag-ncert-class-8-maths-chapter-16-playing-with-numbers-in-english","tag-ncert-solutions-class-8-maths-chapter-16-in-english","tag-ncert-solutions-class-8-maths-in-english","tag-ncert-solutions-in-english"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.9 (Yoast SEO v27.3) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>NCERT Solutions Class 8 Maths Chapter 16 Playing with Numbers Ex 16.2 | TheExamPillar NCERT<\/title>\n<meta name=\"description\" content=\"NCERT Solutions Class 8 Mathematics\u00a0Chapter - 16 (Playing with Numbers)\u00a0The NCERT Solutions in English Language for Class 8 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