This set of Aptitude Questions and Answers (MCQs) focuses on “Power Cycle”.
1. Find the last digit of 465.
a) 4
b) 6
c) 2
d) 8
View Answer
Explanation: We know that, 4odd = 4 and 4even = 6.
Therefore, last digit of 465 is 4.
2. Find the last digit of 15896774.
a) 3
b) 7
c) 9
d) 1
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Explanation: The last digit of 15896774 depends on last digit of 774.
We know that, unit digit of 74n=1, 74n+1=7, 74n+2=9, 74n+3=3.
The unit digit of 774 = 74*18+2 is 9.
Therefore, the last digit of 15896774 is 9.
3. Find the last digit of 689968102.
a) 2
b) 4
c) 6
d) 8
View Answer
Explanation The last digit of 689968102 depends on last digit of 8102.
We know that, unit digit of 84n=6, 84n+1=8, 84n+2=4, 84n+3=2
The unit digit of 8102 = 74*25+2 is 4.
Therefore, the last digit of 689968102 is 4.
4. Find the rightmost non-zero integer of the expression 1340123+1580153.
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, 1340123 is the term with lowest power and 4 is the rightmost non-zero term.
We know that, 4odd = 4 and 4even = 6.
Therefore, the rightmost non-zero integer of the expression 1340123+1580153 is 4.
5. Find the last digit of 688102 + 753103.
a) 4
b) 7
c) 1
d) 8
View Answer
Explanation: The last digit of 688102 is 4.
The last digit of 753103 of 7.
Hence, the last digit of 688102 + 753103 is 7+4 i.e., 1.
6. Find the last digit of (67)^6712.
a) 1
b) 6
c) 3
d) 7
View Answer
Explanation: The last two digits repeat itself after every 4 number for digit 7.
74n = 01; 74n+1 = 07; 74n+2 = 49; 74n+3 = 43.
The last two digits of 6712 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 674n+1.
The last digit of 67xxx01 = 674n+1 is 7.
Therefore, the last digit of (67)^6712 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 6any 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 14+24+34+……+104 is same as 114+124+134+……+204 and so on till 914+924+934+……+1004.
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 14+24+34+……+104 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 256789*789356.
a) 6
b) 1
c) 3
d) 9
View Answer
Explanation: The unit digit of 6any number is 6 and the unit digit of 9odd is 9 and 9even is 1.
Therefore, the unit digit of 256789*789356 is 6*1 i.e., 6.
10. Find the unit digit of 25825-36418.
a) 2
b) 4
c) 6
d) 0
View Answer
Explanation: The unit digit of 4odd is 4 and 4even is 6.
The unit digit of 84n=6, 84n+1=8, 84n+2=4, 84n+3=2.
The unit digit of 25825 = 84*6+1 is 8.
Therefore, the unit digit of 25825-36418 is 8-6 i.e., 2.
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