{"id":55,"date":"2022-08-07T12:18:40","date_gmt":"2022-08-07T12:18:40","guid":{"rendered":"https:\/\/theexampillar.com\/ncert\/?p=55"},"modified":"2024-02-21T05:57:59","modified_gmt":"2024-02-21T05:57:59","slug":"ncert-solutions-class-6-maths-chapter-3-playing-with-numbers-ex-3-3","status":"publish","type":"post","link":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-6-maths-chapter-3-playing-with-numbers-ex-3-3\/","title":{"rendered":"NCERT Solutions Class 6 Maths Chapter 3 Playing with Numbers Ex 3.3"},"content":{"rendered":"<h2 style=\"text-align: center;\"><span style=\"font-family: georgia, palatino, serif;\"><strong><span style=\"color: #000000;\">NCERT Solutions Class 6 Maths<\/span><\/strong><\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif;\"><strong><span style=\"color: #000000;\">Chapter &#8211; 3 (Playing with Numbers)<\/span><\/strong><\/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 6 Mathematics <strong>Chapter &#8211; 3 Playing with Numbers <\/strong>Exercise 3.3 has been provided here to help the students in solving the questions from this exercise.<\/span><\/p>\n<h4 id=\"chapter-3\"><span style=\"font-family: georgia, palatino, serif;\"><strong><span id=\"Chapter_3_Playing_with_Numbers\" style=\"color: #000000;\">Chapter 3: Playing with Numbers<\/span><\/strong><\/span><\/h4>\n<ul>\n<li><span style=\"font-family: georgia, palatino, serif;\"><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-6-maths-chapter-3-playing-with-numbers-ex-3-1\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 6 Maths Exercise &#8211; 3.1<\/a><\/span><\/li>\n<li><span style=\"font-family: georgia, palatino, serif;\"><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-6-maths-chapter-3-playing-with-numbers-ex-3-2\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 6 Maths Exercise &#8211; 3.2<\/a><\/span><\/li>\n<li><span style=\"font-family: georgia, palatino, serif;\"><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-6-maths-chapter-3-playing-with-numbers-ex-3-4\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 6 Maths Exercise &#8211; 3.4<\/a><\/span><\/li>\n<li><span style=\"font-family: georgia, palatino, serif;\"><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-6-maths-chapter-3-playing-with-numbers-ex-3-5\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 6 Maths Exercise &#8211; 3.5<\/a><\/span><\/li>\n<li><span style=\"font-family: georgia, palatino, serif;\"><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-6-maths-chapter-3-playing-with-numbers-ex-3-6\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 6 Maths Exercise &#8211; 3.6<\/a><\/span><\/li>\n<li><span style=\"font-family: georgia, palatino, serif;\"><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-6-maths-chapter-3-playing-with-numbers-ex-3-7\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 6 Maths Exercise &#8211; 3.7<\/a><\/span><\/li>\n<\/ul>\n<h2 style=\"text-align: center;\"><span style=\"font-family: georgia, palatino, serif;\"><strong><span style=\"color: #000000;\">Exercise &#8211; 3.3<\/span><\/strong><\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>1. Using divisibility tests, determine which of the following numbers are divisible by 2; by 3; by 4; by 5; by 6; by 8; by 9; by 10; by 11 (say, yes or no):<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large wp-image-62\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/07\/NCERT-Class-6-Math-Ex-3.3-Q1-1024x393.jpg\" alt=\"NCERT Class 6 Math Solution\" width=\"1024\" height=\"393\" srcset=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/07\/NCERT-Class-6-Math-Ex-3.3-Q1-1024x393.jpg 1024w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/07\/NCERT-Class-6-Math-Ex-3.3-Q1-300x115.jpg 300w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/07\/NCERT-Class-6-Math-Ex-3.3-Q1-768x295.jpg 768w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/07\/NCERT-Class-6-Math-Ex-3.3-Q1-480x184.jpg 480w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/07\/NCERT-Class-6-Math-Ex-3.3-Q1.jpg 1042w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>Solutions:<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large wp-image-61\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/07\/NCERT-Class-6-Math-Ex-3.3-A1-1024x402.jpg\" alt=\"NCERT Class 6 Math Solution\" width=\"1024\" height=\"402\" srcset=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/07\/NCERT-Class-6-Math-Ex-3.3-A1-1024x402.jpg 1024w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/07\/NCERT-Class-6-Math-Ex-3.3-A1-300x118.jpg 300w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/07\/NCERT-Class-6-Math-Ex-3.3-A1-768x302.jpg 768w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/07\/NCERT-Class-6-Math-Ex-3.3-A1-480x188.jpg 480w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/07\/NCERT-Class-6-Math-Ex-3.3-A1.jpg 1052w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><span style=\"color: #000000;\"><strong>2. Using divisibility tests, determine which of the following numbers are divisible by 4; by 8:<br \/>\n<\/strong><\/span><span style=\"color: #000000;\">(a) 572<br \/>\n<\/span><span style=\"color: #000000;\">(b) 726352<br \/>\n<\/span><span style=\"color: #000000;\">(c) 5500<br \/>\n<\/span><span style=\"color: #000000;\">(d) 6000<br \/>\n<\/span><span style=\"color: #000000;\">(e) 12159<br \/>\n<\/span><span style=\"color: #000000;\">(f) 14560<br \/>\n<\/span><span style=\"color: #000000;\">(g) 21084<br \/>\n<\/span><span style=\"color: #000000;\">(h) 31795072<br \/>\n<\/span><span style=\"color: #000000;\">(i) 1700<br \/>\n<\/span><span style=\"color: #000000;\">(j) 2150<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>Solutions:<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><strong><span style=\"color: #000000;\">(a)\u00a0572<br \/>\n<\/span><\/strong><span style=\"color: #000000;\">72 are the last two digits.<br \/>\nSince, 72 is divisible by 4.<br \/>\nHence, 572 is also divisible by 4<br \/>\n<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">572 are the last three digits.<br \/>\nSince, 572 is not divisible by 8.<br \/>\nHence, 572 is not divisible by 8<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><strong><span style=\"color: #000000;\">(b) 726352<br \/>\n<\/span><\/strong><span style=\"color: #000000;\">52 are the last two digits.<br \/>\nSince, 52 is divisible by 4.<br \/>\nHence, 726352 is divisible by 4<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">352 are the last three digits.<br \/>\nSince 352 is divisible by 8.<br \/>\nHence, 726352 is divisible by 8<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><strong><span style=\"color: #000000;\">(c) 5500<br \/>\n<\/span><\/strong><span style=\"color: #000000;\">Since, last two digits are 00.<br \/>\nHence 5500 is divisible by 4<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">500 are the last three digits.<br \/>\nSince, 500 is not divisible by 8.<br \/>\nHence, 5500 is not divisible by 8<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><strong><span style=\"color: #000000;\">(d) 6000<br \/>\n<\/span><\/strong><span style=\"color: #000000;\">Since, last two digits are 00.<br \/>\nHence 6000 is divisible by 4<br \/>\n<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Since, last three digits are 000.<br \/>\nHence, 6000 is divisible by 8<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><strong><span style=\"color: #000000;\">(e) 12159<br \/>\n<\/span><\/strong><span style=\"color: #000000;\">59 are the last two digits.<br \/>\nSince, 59 is not divisible by 4.<br \/>\nHence, 12159 is not divisible by 4<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">159 are the last three digits.<br \/>\nSince, 159 is not divisible by 8.<br \/>\nHence, 12159 is not divisible by 8<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><strong><span style=\"color: #000000;\">(f) 14560<br \/>\n<\/span><\/strong><span style=\"color: #000000;\">60 are the last two digits.<br \/>\nSince 60 is divisible by 4.<br \/>\nHence, 14560 is divisible by 4<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">560 are the last three digits.<br \/>\nSince, 560 is divisible by 8.<br \/>\nHence, 14560 is divisible by 8<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><strong><span style=\"color: #000000;\">(g) 21084<br \/>\n<\/span><\/strong><span style=\"color: #000000;\">84 are the last two digits.<br \/>\nSince, 84 is divisible by 4.<br \/>\nHence, 21084 is divisible by 4<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">084 are the last three digits.<br \/>\nSince, 084 is not divisible by 8.<br \/>\nHence, 21084 is not divisible by 8<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><strong><span style=\"color: #000000;\">(h) 31795072<br \/>\n<\/span><\/strong><span style=\"color: #000000;\">72 are the last two digits.<br \/>\nSince, 72 is divisible by 4.<br \/>\nHence, 31795072 is divisible by 4<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">072 are the last three digits.<br \/>\nSince, 072 is divisible by 8.<br \/>\nHence, 31795072 is divisible by 8<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><strong><span style=\"color: #000000;\">(i) 1700<br \/>\n<\/span><\/strong><span style=\"color: #000000;\">Since, the last two digits are 00.<br \/>\nHence, 1700 is divisible by 4<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">700 are the last three digits.<br \/>\nSince, 700 is not divisible by 8.<br \/>\nHence, 1700 is not divisible by 8<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><strong><span style=\"color: #000000;\">(j) 2150<br \/>\n<\/span><\/strong><span style=\"color: #000000;\">50 are the last two digits.<br \/>\nSince, 50 is not divisible by 4.<br \/>\nHence, 2150 is not divisible by 4<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">150 are the last three digits.<br \/>\nSince, 150 is not divisible by 8.<br \/>\nHence, 2150 is not divisible by 8<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><span style=\"color: #000000;\"><strong>3. Using divisibility tests, determine which of following numbers are divisible by 6:<br \/>\n<\/strong><\/span><span style=\"color: #000000;\">(a) 297144<br \/>\n<\/span><span style=\"color: #000000;\">(b) 1258<br \/>\n<\/span><span style=\"color: #000000;\">(c) 4335<br \/>\n<\/span><span style=\"color: #000000;\">(d) 61233<br \/>\n<\/span><span style=\"color: #000000;\">(e) 901352<br \/>\n<\/span><span style=\"color: #000000;\">(f) 438750<br \/>\n<\/span><span style=\"color: #000000;\">(g) 1790184<br \/>\n<\/span><span style=\"color: #000000;\">(h) 12583<br \/>\n<\/span><span style=\"color: #000000;\">(i) 639210<br \/>\n<\/span><span style=\"color: #000000;\">(j) 17852<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>Solutions:<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><strong><span style=\"color: #000000;\">(a)\u00a0297144<br \/>\n<\/span><\/strong><span style=\"color: #000000;\">Since, last digit of the number is 4.<br \/>\nHence, the number is<strong> divisible by 2<\/strong><br \/>\n<\/span><span style=\"color: #000000;\">By adding all the digits of the number, we get 27 which is divisible by 3.<br \/>\nHence, the number is <strong>divisible by 3<\/strong><br \/>\n<\/span><span style=\"color: #000000;\">\u2234 The number is divisible by both 2 and 3. Hence, the number is <strong>divisible by 6<\/strong><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><strong><span style=\"color: #000000;\">(b) 1258<br \/>\n<\/span><\/strong><span style=\"color: #000000;\">Since, last digit of the number is 8.<br \/>\nHence, the number is <strong>divisible by 2<\/strong><br \/>\n<\/span><span style=\"color: #000000;\">By adding all the digits of the number, we get 16 which is not divisible by 3.<br \/>\nHence, the number is <strong>not divisible by 3<br \/>\n<\/strong><\/span><span style=\"color: #000000;\">\u2234 The number is not divisible by both 2 and 3. Hence, the number is <strong>not divisible by 6<\/strong><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><strong><span style=\"color: #000000;\">(c) 4335<br \/>\n<\/span><\/strong><span style=\"color: #000000;\">Since, last digit of the number is 5 which is not divisible by 2.<br \/>\nHence, the number is <strong>not divisible by 2<br \/>\n<\/strong><\/span><span style=\"color: #000000;\">By adding all the digits of the number, we get 15 which is divisible by 3.<br \/>\nHence, the number is <strong>divisible by 3<br \/>\n<\/strong><\/span><span style=\"color: #000000;\">\u2234 The number is not divisible by both 2 and 3. Hence, the number is <strong>not divisible by 6<\/strong><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><strong><span style=\"color: #000000;\">(d) 61233<br \/>\n<\/span><\/strong><span style=\"color: #000000;\">Since, the last digit of the number is 3 which is not divisible by 2.<br \/>\nHence, the number is <strong>not divisible by 2<br \/>\n<\/strong><\/span><span style=\"color: #000000;\">By adding all the digits of the number, we get 15 which is divisible by 3.<br \/>\nHence, the number is <strong>divisible by 3<br \/>\n<\/strong><\/span><span style=\"color: #000000;\">\u2234 The number is not divisible by both 2 and 3. Hence, the number is <strong>not divisible by 6<\/strong><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><strong><span style=\"color: #000000;\">(e) 901352<br \/>\n<\/span><\/strong><span style=\"color: #000000;\">Since, the last digit of the number is 2.<br \/>\nHence, the number is <strong>divisible by 2<\/strong><br \/>\n<\/span><span style=\"color: #000000;\">By adding all the digits of the number, we get 20 which is not divisible by 3.<br \/>\nHence, the number is <strong>not divisible by 3<br \/>\n<\/strong><\/span><span style=\"color: #000000;\">\u2234 The number is not divisible by both 2 and 3. Hence, the number is <strong>not divisible by 6<\/strong><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><strong><span style=\"color: #000000;\">(f) 438750<br \/>\n<\/span><\/strong><span style=\"color: #000000;\">Since, the last digit of the number is 0.<br \/>\nHence, the number is <strong>divisible by 2<br \/>\n<\/strong><\/span><span style=\"color: #000000;\">By adding all the digits of the number, we get 27 which is divisible by 3.<br \/>\nHence, the number is <strong>divisible by 3<br \/>\n<\/strong><\/span><span style=\"color: #000000;\">\u2234 The number is divisible by both 2 and 3. Hence, the number is <strong>divisible by 6<\/strong><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><strong><span style=\"color: #000000;\">(g) 1790184<br \/>\n<\/span><\/strong><span style=\"color: #000000;\">Since, the last digit of the number is 4.<br \/>\nHence, the number is <strong>divisible by 2<br \/>\n<\/strong><\/span><span style=\"color: #000000;\">By adding all the digits of the number, we get 30 which is divisible by 3.<br \/>\nHence, the number is <strong>divisible by 3<br \/>\n<\/strong><\/span><span style=\"color: #000000;\">\u2234 The number is divisible by both 2 and 3. Hence, the number is <strong>divisible by 6<\/strong><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><strong><span style=\"color: #000000;\">(h) 12583<br \/>\n<\/span><\/strong><span style=\"color: #000000;\">Since, the last digit of the number is 3.<br \/>\nHence, the number is not <strong>divisible by 2<br \/>\n<\/strong><\/span><span style=\"color: #000000;\">By adding all the digits of the number, we get 19 which is not divisible by 3.<br \/>\nHence, the number is <strong>not divisible by 3<br \/>\n<\/strong><\/span><span style=\"color: #000000;\">\u2234 The number is not divisible by both 2 and 3. Hence, the number is <strong>not divisible by 6<\/strong><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><strong><span style=\"color: #000000;\">(i) 639210<br \/>\n<\/span><\/strong><span style=\"color: #000000;\">Since, the last digit of the number is 0.<br \/>\nHence, the number is <strong>divisible by 2<br \/>\n<\/strong><\/span><span style=\"color: #000000;\">By adding all the digits of the number, we get 21 which is divisible by 3.<br \/>\nHence, the number is <strong>divisible by 3<br \/>\n<\/strong><\/span><span style=\"color: #000000;\">\u2234 The number is divisible by both 2 and 3. Hence, the number is <strong>divisible by 6<\/strong><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><strong><span style=\"color: #000000;\">(j) 17852<br \/>\n<\/span><\/strong><span style=\"color: #000000;\">Since, the last digit of the number is 2.<br \/>\nHence, the number is <strong>divisible by 2<br \/>\n<\/strong><\/span><span style=\"color: #000000;\">By adding all the digits of the number, we get 23 which is not divisible by 3.<br \/>\nHence, the number is <strong>not divisible by 3<br \/>\n<\/strong><\/span><span style=\"color: #000000;\">\u2234 The number is not divisible by both 2 and 3. Hence, the number is <strong>not divisible by 6<\/strong><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><span style=\"color: #000000;\"><strong>4. Using divisibility tests, determine which of the following numbers are divisible by 11:<br \/>\n<\/strong><\/span><span style=\"color: #000000;\">(a) 5445<br \/>\n<\/span><span style=\"color: #000000;\">(b) 10824<br \/>\n<\/span><span style=\"color: #000000;\">(c) 7138965<br \/>\n<\/span><span style=\"color: #000000;\">(d) 70169308<br \/>\n<\/span><span style=\"color: #000000;\">(e) 10000001<br \/>\n<\/span><span style=\"color: #000000;\">(f) 901153<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>Solutions:<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><strong><span style=\"color: #000000;\">(a)\u00a05445<br \/>\n<\/span><\/strong><span style=\"color: #000000;\">Sum of the digits at odd places = 5 + 4 <\/span><span style=\"color: #000000;\">= 9<br \/>\n<\/span><span style=\"color: #000000;\">Sum of the digits at even places = 4 + 5 <\/span><span style=\"color: #000000;\">= 9<br \/>\n<\/span><span style=\"color: #000000;\">Difference = 9 \u2013 9 = 0<br \/>\n<\/span><span style=\"color: #000000;\">Since, the difference between sum of digits at odd places and sum of digits at even places is 0.<br \/>\nHence, 5445 is <strong>divisible by 11<\/strong><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><strong><span style=\"color: #000000;\">(b) 10824<br \/>\n<\/span><\/strong><span style=\"color: #000000;\">Sum of digits at odd places = 4 + 8 + 1 <\/span><span style=\"color: #000000;\">= 13<br \/>\n<\/span><span style=\"color: #000000;\">Sum of digits at even places = 2 + 0 <\/span><span style=\"color: #000000;\">= 2<br \/>\n<\/span><span style=\"color: #000000;\">Difference = 13 \u2013 2 = 11<br \/>\n<\/span><span style=\"color: #000000;\">Since, the difference between sum of digits at odd places and sum of digits at even places is 11 which is divisible by 11.<br \/>\nHence, 10824 <strong>is divisible by 11<\/strong><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><strong><span style=\"color: #000000;\">(c) 7138965<br \/>\n<\/span><\/strong><span style=\"color: #000000;\">Sum of digits at odd places = 5 + 9 + 3 + 7 = 24<br \/>\n<\/span><span style=\"color: #000000;\">Sum of digits at even places = 6 + 8 + 1 = 15<br \/>\n<\/span><span style=\"color: #000000;\">Difference = 24 \u2013 15 = 9<br \/>\n<\/span><span style=\"color: #000000;\">Since, the difference between sum of digits at odd places and sum of digits at even places is 9 which is not divisible by 11.<br \/>\nHence, 7138965 is <strong>not divisible by 11<\/strong><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><strong><span style=\"color: #000000;\">(d) 70169308<br \/>\n<\/span><\/strong><span style=\"color: #000000;\">Sum of digits at odd places = 8 + 3 + 6 + 0 <\/span><span style=\"color: #000000;\">= 17<br \/>\n<\/span><span style=\"color: #000000;\">Sum of digits at even places = 0 + 9 + 1 + 7 <\/span><span style=\"color: #000000;\">= 17<br \/>\n<\/span><span style=\"color: #000000;\">Difference = 17 \u2013 17 = 0<br \/>\n<\/span><span style=\"color: #000000;\">Since, the difference between sum of digits at odd places and sum of digits at even places is 0.<br \/>\nHence, 70169308 is <strong>divisible by 11<\/strong><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><strong><span style=\"color: #000000;\">(e) 10000001<br \/>\n<\/span><\/strong><span style=\"color: #000000;\">Sum of digits at odd places = 1<br \/>\n<\/span><span style=\"color: #000000;\">Sum of digits at even places = 1<br \/>\n<\/span><span style=\"color: #000000;\">Difference = 1 \u2013 1 = 0<br \/>\n<\/span><span style=\"color: #000000;\">Since, the difference between sum of digits at odd places and sum of digits at even places is 0.<br \/>\nHence, 10000001 is <strong>divisible by 11<\/strong><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><strong><span style=\"color: #000000;\">(f) 901153<br \/>\n<\/span><\/strong><span style=\"color: #000000;\">Sum of digits at odd places = 3 + 1 + 0 <\/span><span style=\"color: #000000;\">= 4<br \/>\n<\/span><span style=\"color: #000000;\">Sum of digits at even places = 5 + 1 + 9 <\/span><span style=\"color: #000000;\">= 15<br \/>\n<\/span><span style=\"color: #000000;\">Difference = 15 \u2013 4 = 11<br \/>\n<\/span><span style=\"color: #000000;\">Since, the difference between sum of digits at odd places and sum of digits at even places is 11 which is divisible by 11.<br \/>\nHence, 901153 is <strong>divisible by 11<\/strong><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><span style=\"color: #000000;\"><strong>5. Write the smallest digit and the greatest digit in the blank space of each of the following numbers so that the number formed is divisible by 3:<br \/>\n<\/strong><\/span><span style=\"color: #000000;\">(a) __6724<br \/>\n<\/span><span style=\"color: #000000;\">(b) 4765__2<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>Solutions:<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><strong><span style=\"color: #000000;\">(a) __6724<br \/>\n<\/span><\/strong><span style=\"color: #000000;\">Sum of the given digits = 19<br \/>\n<\/span><span style=\"color: #000000;\">Sum of its digit should be divisible by 3 to make the number divisible by 3<br \/>\n<\/span><span style=\"color: #000000;\">Since, 21 is the smallest multiple of 3 which comes after 19<br \/>\n<\/span><span style=\"color: #000000;\">So, smallest number = 21 \u2013 19 <\/span><span style=\"color: #000000;\">= 2<br \/>\n<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><span style=\"color: #000000;\">Now 2 + 3 + 3 = 8<br \/>\n<\/span><span style=\"color: #000000;\">But 2 + 3 + 3 + 3 = 11<br \/>\n<\/span><span style=\"color: #000000;\">Now, if we put 8, sum of digits will be 27 which is divisible by 3.<br \/>\n<\/span><span style=\"color: #000000;\">Therefore the number will be divisible by 3<br \/>\n<\/span><span style=\"color: #000000;\">Hence, the largest number is 8<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><strong><span style=\"color: #000000;\">(b) 4765__2<br \/>\n<\/span><\/strong><span style=\"color: #000000;\">Sum of the given digits = 24<br \/>\n<\/span><span style=\"color: #000000;\">Sum of its digits should be divisible by 3 to make the number divisible by 3<br \/>\n<\/span><span style=\"color: #000000;\">Since, 24 is already divisible by 3.<br \/>\nHence, the smallest number that can be replaced is 0<br \/>\n<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><span style=\"color: #000000;\">Now, 0 + 3 = 3<br \/>\n<\/span><span style=\"color: #000000;\">3 + 3 = 6<br \/>\n<\/span><span style=\"color: #000000;\">3 + 3 + 3 = 9<br \/>\n<\/span><span style=\"color: #000000;\">3 + 3 + 3 + 3 = 12<br \/>\n<\/span><span style=\"color: #000000;\">If we put 9, sum of its digits becomes 33. Since, 33 is divisible by 3.<br \/>\n<\/span><span style=\"color: #000000;\">Therefore the number will be divisible by 3<br \/>\n<\/span><span style=\"color: #000000;\">Hence, the largest number is 9<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><span style=\"color: #000000;\"><strong>6. Write a digit in the blank space of each of the following numbers so that the number formed is divisible by 11:<br \/>\n<\/strong><\/span><span style=\"color: #000000;\">(a) 92__389<br \/>\n<\/span><span style=\"color: #000000;\">(b) 8__9484<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>Solutions:<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><strong><span style=\"color: #000000;\">(a)\u00a092__389<br \/>\n<\/span><\/strong><span style=\"color: #000000;\">Let \u2018a\u2019 be placed here<br \/>\n<\/span><span style=\"color: #000000;\">Sum of its digits at odd places = 9 + 3 + 2 <\/span><span style=\"color: #000000;\">= 14<br \/>\n<\/span><span style=\"color: #000000;\">Sum of its digits at even places = 8 + a + 9 <\/span><span style=\"color: #000000;\">= 17 + a<br \/>\n<\/span><span style=\"color: #000000;\">Difference = 17 + a \u2013 14 <\/span><span style=\"color: #000000;\">= 3 + a<br \/>\n<\/span><span style=\"color: #000000;\">The difference should be 0 or a multiple of 11, then the number is divisible by 11.<br \/>\n<\/span><span style=\"color: #000000;\">If 3 + a = 0<br \/>\n<\/span><span style=\"color: #000000;\">a = -3<br \/>\n<\/span><span style=\"color: #000000;\">But it cannot be a negative<br \/>\n<\/span><span style=\"color: #000000;\">Taking a closest multiple of 11 which is near to 3<br \/>\n<\/span><span style=\"color: #000000;\">It is 11 which is near to 3<br \/>\n<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><span style=\"color: #000000;\">Now, 3 + a = 11<br \/>\n<\/span><span style=\"color: #000000;\">a = 11 \u2013 3<br \/>\n<\/span><span style=\"color: #000000;\">a = 8<br \/>\n<\/span><span style=\"color: #000000;\">Therefore the required digit is 8<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><strong><span style=\"color: #000000;\">(b) 8__9484<br \/>\n<\/span><\/strong><span style=\"color: #000000;\">Let \u2018a\u2019 be placed here<br \/>\n<\/span><span style=\"color: #000000;\">Sum of its digits at odd places = 4 + 4 + a <\/span><span style=\"color: #000000;\">= 8 + a<br \/>\n<\/span><span style=\"color: #000000;\">Sum of its digits at even places = 8 + 9 + 8 <\/span><span style=\"color: #000000;\">= 25<br \/>\n<\/span><span style=\"color: #000000;\">Difference = 25 \u2013 (8 + a) <\/span><span style=\"color: #000000;\">= 17 \u2013 a<br \/>\n<\/span><span style=\"color: #000000;\">The difference should be 0 or a multiple of 11, then the number is divisible by 11<br \/>\n<\/span><span style=\"color: #000000;\">If 17 \u2013 a = 0<br \/>\n<\/span><span style=\"color: #000000;\">a = 17 (which is not possible)<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><span style=\"color: #000000;\">Now, take a multiple of 11.<br \/>\n<\/span><span style=\"color: #000000;\">Let\u2019s take 11<br \/>\n<\/span><span style=\"color: #000000;\">17 \u2013 a = 11<br \/>\n<\/span><span style=\"color: #000000;\">a = 17 \u2013 11<br \/>\n<\/span><span style=\"color: #000000;\">a = 6<br \/>\n<\/span><span style=\"color: #000000;\">Therefore the required digit is 6<\/span><\/span><\/p>\n<p>&nbsp;<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 100%; background-color: #f2e079; text-align: center;\"><span style=\"color: #000000; font-size: 14pt; font-family: georgia, palatino, serif;\"><strong>NCERT Class 6<sup>th\u00a0<\/sup>Solution\u00a0<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 100%; text-align: left;\"><span style=\"color: #ff0000; font-size: 14pt; font-family: georgia, palatino, serif;\"><strong><span style=\"color: #0000ff; font-size: 12pt;\"><a class=\"row-title\" style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-6-english\/\" target=\"_blank\" rel=\"noopener\" aria-label=\"\u201cNCERT Solutions Class 6 English\u201d (Edit)\">NCERT Solutions Class 6 English<\/a><\/span><\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 100%; text-align: left;\"><span style=\"color: #ff0000; font-size: 14pt; font-family: georgia, palatino, serif;\"><strong><span style=\"color: #0000ff; font-size: 12pt;\"><a class=\"row-title\" style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-6-hindi\/\" aria-label=\"\u201cNCERT Solutions Class 6 Maths\u201d (Edit)\">NCERT Solutions Class 6 Hindi<\/a><\/span><\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 100%; text-align: left;\"><span style=\"color: #ff0000; font-size: 14pt; font-family: georgia, palatino, serif;\"><strong><span style=\"color: #0000ff; font-size: 12pt;\"><a class=\"row-title\" style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-6-maths\/\" target=\"_blank\" rel=\"noopener\" aria-label=\"\u201cNCERT Solutions Class 6 Maths\u201d (Edit)\">NCERT Solutions Class 6 Maths<\/a><\/span><\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 100%; text-align: left;\"><span style=\"font-family: georgia, palatino, serif;\"><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-6-sanskrit\/\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff0000; font-size: 14pt;\"><strong><span style=\"color: #0000ff; font-size: 12pt;\">NCERT Solutions Class 6 Sanskrit<\/span><\/strong><\/span><\/a><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 100%; text-align: left;\"><span style=\"color: #ff0000; font-size: 14pt; font-family: georgia, palatino, serif;\"><strong><span style=\"color: #0000ff; font-size: 12pt;\"><a class=\"row-title\" style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-6-science\/\" target=\"_blank\" rel=\"noopener\" aria-label=\"\u201cNCERT Solutions Class 6 Social Science\u201d (Edit)\">NCERT Solutions Class 6 Science<\/a><\/span><\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 100%; text-align: left;\"><span style=\"color: #ff0000; font-size: 14pt; font-family: georgia, palatino, serif;\"><strong><span style=\"color: #0000ff; font-size: 12pt;\"><a class=\"row-title\" style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-6-social-science\/\" target=\"_blank\" rel=\"noopener\" aria-label=\"\u201cNCERT Solutions Class 6 Social Science\u201d (Edit)\">NCERT Solutions Class 6 Social Science<\/a><\/span><\/strong><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions Class 6 Maths Chapter &#8211; 3 (Playing with Numbers) The NCERT Solutions in English Language for Class 6 Mathematics Chapter &#8211; 3 Playing with Numbers Exercise 3.3 has been provided here to help the students in solving the questions from this exercise. Chapter 3: Playing with Numbers NCERT Solution Class 6 Maths Exercise [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[9,8,4,5],"class_list":["post-55","post","type-post","status-publish","format-standard","hentry","category-class-6-maths","tag-chapter-3-playing-with-numbers-in-english","tag-ncert-solutions-class-6-maths-chapter-3-in-english","tag-ncert-solutions-class-6-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 6 Maths Chapter 3 Playing with Numbers Ex 3.3 | TheExamPillar NCERT<\/title>\n<meta name=\"description\" content=\"The NCERT Solutions in English Language for Class 6 Mathematics Chapter - 3 Playing with Numbers Exercise 3.3 has been provided here to help the students in solving the questions from this exercise.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-6-maths-chapter-3-playing-with-numbers-ex-3-3\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions Class 6 Maths Chapter 3 Playing with Numbers Ex 3.3\" \/>\n<meta property=\"og:description\" content=\"The NCERT Solutions in English Language for Class 6 Mathematics Chapter - 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