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Playing with Numbers

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Question
CBSEENMA8002717
Wired Faculty App

Write the following numbers in generalized form.

(i) 25 (ii) 73 (iii) 129 (iv) 302

 

Solution

(i)       25 = 20 + 5
               = 10 x 2 + 5 x 1 = 10 x 2 + 5
(ii)       73 = 70 + 3
                = 10 x 7 + 3 x 1 = 10 x 7 + 3
(iii)      129 = 100 + 20 + 9
                = 100 x 1 + 20 x 2 + 1 x 9 = 100 x 1 + 10 x 2 + 9
(iv)       302 = 100 x 3 + 10 x 0 + 1 x 2 = 300 + 0 + 2

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Question
CBSEENMA8002719
Wired Faculty App

Write the following in the usual form.

(i) 10 x 5 + 6             (ii)  100 x 7 + 10 x 1 + 8        (iii) 100 x a + 10 x c + b

Solution

(i) 10 x 5 + 6 = 50 + 6 = 56
(ii) 100 x 7 + 10 x 1 + 8 = 700 + 10 + 8 = 718
(iii) 100 x a + 10 x c + b = 100 a + 10c + b = <pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>

Question
CBSEENMA8002726
Wired Faculty App

Check what the result would have been if sundaram had chosen the numbers shown below. 1. 27 2. 39 3. 64 4. 17

Solution

1.                      Chosen number = 27
         Number with reversed digits = 72
            Sum of the two numbers  = 27 + 72 = 99
Now,                                   99  = 11[9]
                                              = 11[2 + 7]
                                              = 11(Sum of the digits of the chosen number)

2.                         Chosen number = 39
            Number with reversed digits = 93
                Sum of the two numbers = 39 + 93 = 132
Now,                              132 + 11 = 12
i,e,                                 132 = 11[12]
                                           = 11 [ 3 + 9]
                                           = 11 [ Sum of the digits of the chosen number]            

3.                                     Chosen number = 64
                       Number with reversed digits  = 46
                                                    Sum   = 64 + 46 = 110
Now,                                                110 = 11[10]
                                                            = 11[6 + 4]
                                                 = 11[ Sum of the digits of the chosen number  
4.                                      Chosen number    =  17
                        Number with reversed digits     = 71
                                                        Sum   =  17 + 71 = 88
Now,                                                    88    = 11[8]
                                                                 = 11[1+7]
                                                   = 11[Sum of the digits of the chosen number]
                          

Question
CBSEENMA8002731
Wired Faculty App

Check what result would have been if Sundaram had chosen the numbers shown. 1.17 2.21 3.96 4.37.

Solution

1.                           Chosen number  = 17
             Number with reversed digits  =  71
                                    Difference  = 71 - 17 = 54
                                                   = 9 x [6]
        
2.                                    Chosen number = 21
                       Number with reversed digits = 12
                                             Difference  = 21 - 12 = 9
                                                            = 9 x [1]
           = 9 x [Difference between the digits of the chosen number (2 - 1 = 1)]

3.                      Chosen number = 96
         Number with reversed digits = 69
                               Difference  = 96 - 69 = 27
                                              = 9 x [3]
= 9 x [Difference between the digits of the chosen number (9 - 6)]

4.                                  Chosen number = 37
                    Number with reversed digits  = 73
                                            Difference = 73 - 37 = 36
                                                          = 9 x [4]
      = 9 x [Difference between the digits of the chosen number (7 - 3 = 4)]

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