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14 Mar 2020, 08:29
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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Shan2203
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14 Mar 2020, 09:51
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672 = 4K+2 ..
Since cyclicity of 4 is 4 , the unit digit will be 4^2 which is 6
Since cyclicity of 4 is 4 , the unit digit will be 4^2 which is 6
08 Jul 2020, 23:40
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The Cyclicity of the numbers are as follows
(a) 0, 1, 5 and 6 have a cyclicity of 1. This means that every power of a number ending in any of these 4 numbers, will be the number itself. For eg 25^863 = 5, 541 ^ 11523 = 1, 1000^ 2532 = 0
(b) The perfect squares, i.e 4 and 6 have a cyclicity of 2.
So numbers having 4 in the units place and having odd powers will end in 4 those having even powers will end in 6.
eg 24^51. The power is odd, so the last digit is 4.
eg 64^72. The power is even, so the last digit is 6.
Numbers having 9 in the units place and having odd powers will end in 9 those having even powers will end in 1.
eg 29^51. The power is odd, so the last digit is 9.
eg 69^72. The power is even, so the last digit is 1.
(c) The remaining numbers 2,3,7 and 8 have a cyclicity of 4.
This means that every 4 powers, the numbers will repeat itself.
eg for 2: 2^1 = 2, 2^2 = 4, 2^3 = 8, 2^4 = 16, 2^5 (which is 4 powers after 2^1) = 32
Similarly for 3: 3^1 = 3, 3^2 = 9, 3^3 = 27, 3^4 = 81, 3^5 (which is 4 powers after 3^1) = 243
_____________________________________
In the question 4^674. The rule is that if the units place is 4 the power is even, the last number is 6
Therefore Option C
Arun Kumar
(a) 0, 1, 5 and 6 have a cyclicity of 1. This means that every power of a number ending in any of these 4 numbers, will be the number itself. For eg 25^863 = 5, 541 ^ 11523 = 1, 1000^ 2532 = 0
(b) The perfect squares, i.e 4 and 6 have a cyclicity of 2.
So numbers having 4 in the units place and having odd powers will end in 4 those having even powers will end in 6.
eg 24^51. The power is odd, so the last digit is 4.
eg 64^72. The power is even, so the last digit is 6.
Numbers having 9 in the units place and having odd powers will end in 9 those having even powers will end in 1.
eg 29^51. The power is odd, so the last digit is 9.
eg 69^72. The power is even, so the last digit is 1.
(c) The remaining numbers 2,3,7 and 8 have a cyclicity of 4.
This means that every 4 powers, the numbers will repeat itself.
eg for 2: 2^1 = 2, 2^2 = 4, 2^3 = 8, 2^4 = 16, 2^5 (which is 4 powers after 2^1) = 32
Similarly for 3: 3^1 = 3, 3^2 = 9, 3^3 = 27, 3^4 = 81, 3^5 (which is 4 powers after 3^1) = 243
_____________________________________
In the question 4^674. The rule is that if the units place is 4 the power is even, the last number is 6
Therefore Option C
Arun Kumar
