Question
Find a number between 100 and 200 that leaves a
remainder of 3 when divided by 8, 12, or 15. Once identified, determine the remainder when this number is divided by 17.Solution
Let the number be n+3.
This means that n is completely divisible by 8, 12, 15 or n is a multiple of LCM of 8, 12 and 15.
=> n is a multiple of 120
Since the number lies between 100 and 200, the number must be 123.
123 = 17x7 + 4
Hence remainder = 4
4 ? 113 449 1343 2681
...14 15 34 116 460 2325
...There are three series given below which are following with the same pattern.
Series I: 21, 44, 135, 544, 2725
Series II: 14, B, C, D, E
40    42    87    266    ?     5366
3 2 10 ? 17 16
...91   93   97   100   ?   113
11, 12, 16, 25, ?, 66
1 5 36 343 ? 59049
...2Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 5Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 10Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â ...
59, 170, 301, 452, ?, 814
Relevant for Exams:
