This set of Aptitude Questions and Answers (MCQs) focuses on “Power Cycle”.

1. Find the last digit of 4^{65}.

a) 4

b) 6

c) 2

d) 8

View Answer

Explanation: We know that, 4

^{odd}= 4 and 4

^{even}= 6.

Therefore, last digit of 4

^{65}is 4.

2. Find the last digit of 158967^{74}.

a) 3

b) 7

c) 9

d) 1

View Answer

Explanation: The last digit of 158967

^{74}depends on last digit of 7

^{74}.

We know that, unit digit of 7

^{4n}=1, 7

^{4n+1}=7, 7

^{4n+2}=9, 7

^{4n+3}=3.

The unit digit of 7

^{74}= 7

^{4*18+2}is 9.

Therefore, the last digit of 158967

^{74}is 9.

3. Find the last digit of 689968^{102}.

a) 2

b) 4

c) 6

d) 8

View Answer

Explanation The last digit of 689968

^{102}depends on last digit of 8

^{102}.

We know that, unit digit of 8

^{4n}=6, 8

^{4n+1}=8, 8

^{4n+2}=4, 8

^{4n+3}=2

The unit digit of 8

^{102}= 7

^{4*25+2}is 4.

Therefore, the last digit of 689968

^{102}is 4.

4. Find the rightmost non-zero integer of the expression 1340^{123}+1580^{153}.

a) 2

b) 4

c) 6

d) 8

View Answer

Explanation: The rightmost non-zero integer of the expression depends on the non-zero digit in the term with lowest power.

Here, 1340

^{123}is the term with lowest power and 4 is the rightmost non-zero term.

We know that, 4

^{odd}= 4 and 4

^{even}= 6.

Therefore, the rightmost non-zero integer of the expression 1340

^{123}+1580

^{153}is 4.

5. Find the last digit of 688^{102} + 753^{103}.

a) 4

b) 7

c) 1

d) 8

View Answer

Explanation: The last digit of 688

^{102}is 4.

The last digit of 753

^{103}of 7.

Hence, the last digit of 688

^{102}+ 753

^{103}is 7+4 i.e., 1.

6. Find the last digit of (67)^67^{12}.

a) 1

b) 6

c) 3

d) 7

View Answer

Explanation: The last two digits repeat itself after every 4 number for digit 7.

7

^{4n}= 01; 7

^{4n+1}= 07; 7

^{4n+2}= 49; 7

^{4n+3}= 43.

The last two digits of 67

^{12}is 01.

For a number to be divisible by 4, last two digits should be divisible by 4.

xxx01 on dividing by 4, we get 1 as remainder, i.e., it is of the form 67

^{4n+1}.

The last digit of 67

^{xxx01}= 67

^{4n+1}is 7.

Therefore, the last digit of (67)^67

^{12}is 7.

7. What is the frequency of digit 6 in power cycle?

a) 1

b) 2

c) 4

d) 8

View Answer

Explanation: We know that the unit digit of 6

^{any number}is 6 itself.

Therefore, the frequency of digit 6 in power cycle is 1.

8. Find the last digit in the sum of fourth power of the sum of first 100 natural numbers.

a) 1

b) 8

c) 5

d) 0

View Answer

Explanation: The unit digit of 1

^{4}+2

^{4}+3

^{4}+……+10

^{4}is same as 11

^{4}+12

^{4}+13

^{4}+……+20

^{4}and so on till 91

^{4}+92

^{4}+93

^{4}+……+100

^{4}.

Hence, it is sufficient to find the unit digit of first set and multiply it by 10 to get the overall answer.

The unit digit of 1

^{4}+2

^{4}+3

^{4}+……+10

^{4}is 5.

Therefore, last digit in the sum of fourth power of the sum of first 100 natural numbers is 5*10 i.e., 0.

9. Find the unit digit of 256^{789}*789^{356}.

a) 6

b) 1

c) 3

d) 9

View Answer

Explanation: The unit digit of 6

^{any number}is 6 and the unit digit of 9

^{odd}is 9 and 9

^{even}is 1.

Therefore, the unit digit of 256

^{789}*789

^{356}is 6*1 i.e., 6.

10. Find the unit digit of 258^{25}-364^{18}.

a) 2

b) 4

c) 6

d) 0

View Answer

Explanation: The unit digit of 4

^{odd}is 4 and 4

^{even}is 6.

The unit digit of 8

^{4n}=6, 8

^{4n+1}=8, 8

^{4n+2}=4, 8

^{4n+3}=2.

The unit digit of 258

^{25}= 8

^{4*6+1}is 8.

Therefore, the unit digit of 258

^{25}-364

^{18}is 8-6 i.e., 2.

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