Number System Part-3

Number System Part-3     

Finding out the number at the unit place :

Rule 1: When the given number is odd then try to get the last digit as 1

Ex. Find the number at the unit place in (723)^43

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Ex. Find the number at the unit place in (257)^61

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Rule 2 : When the given number is Even then try to get the last digit as 6

Ex. Find the number at the unit place in (142)^65

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Ex. Find the number at the unit place in (88)^59

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Ex. How many prime numbers exist in exist in


Solution :

 

 

So, total number of prime numbers will be , Sum of powers of prime= 5 + 9 + 4 + 6 = 24

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Ex. A watch ticks 90 times in 95 seconds and another watch ticks 315 times in 323 seconds. If both the watches are started together, how many times will they tick together in first hour ?

The first watch ticks every 95 / 90 seconds, second watch ticks every 323 / 315 seconds.

They will tick together after ( LCM of 95 / 90 and 323 / 315 ) seconds.

= LCM of (95, 323) / HCF of (90, 315) = (19 * 5 * 17 ) / 45

The number of times they will tick in the first 3600 seconds = 3600 / (1615 / 45 ) = 100.30 = 100 + 1 , as it has already ticked first time.