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Number System: Cyclicity Test-1

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Question 1

What will be the unit digit of 13^{41 }?

A

3

B

0

C

1

D

9

Question 1 Explanation:

As we know the last digit depends upon the unit digit of the multiplier numbers so the unit digit of 13^{41 } is same as the last digit of 3^{41} and we know that the cyclicity of 3 is 4 On dividing the number 41 with 4 and we will get the remainder as 1 and the last digit will be 3^{1} = 3

Question 2

What will be the unit digit when 45^{45}

A

5

B

0

C

1

D

9

Question 2 Explanation:

Here the last digit is depend upon the 5 The cyclicity of 5 is 1 so there is no need to divide the power with 1 because whatever is the power of 5 the last digit will remains 5 so the last digit of 45^{45} will be 5 . 5^{1} = 5 5^{2} = 25 5^{3 }= 125

Question 3

What will be the last digit of 3^{4 }x 4^{5} x 5^{6}

A

8

B

0

C

9

D

3

Question 3 Explanation:

Last digit of 3^{4 }= 1 Last digit of 4^{5} = 4 Last digit of 5^{6 }= 5 So as we discussed earlier that the last digit depends upon the last digits So 1 x 4 x 5 = 20 so the last digit is 0; also whenever 5 is multiplied by even number then last digit will be 0

Question 4

Identify the last digit of (79^{4 }+ 87^{5})

A

8

B

0

C

7

D

4

Question 4 Explanation:

Last digit of 79^{4} is depends upon the the 9^{4} i.e 1 Last digit of 87^{5} is depends upon the the 7^{5}i.e 7 So the last digit of the whole expression will be 1 +7 = 8 So the last digit will be 8

Question 5

What will be the last digit of 43^{56} x 5^{67 }x 45^{34}

A

8

B

5

C

7

D

4

Question 5 Explanation:

Last digit of 43^{56 }= 1 because cyclicity of 3 is 4 and 56 is completely divisible by 4 so the last term of 3^{4 }is 1. Last digit of 5^{67} is 5 and last digit of 45^{34} is also 5 so that means the last digit of whole of the expression is 1 x 5x 5 = 5 therefore the digit is 5.

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2 Comments

sandeep on July 23, 2014 at 3:47 pm

very awesme site it is, very useful for gre

satish on April 24, 2014 at 2:53 pm

good coverage of concepts.. you can add factorial questions also..!!

very awesme site it is, very useful for gre

good coverage of concepts..

you can add factorial questions also..!!