This set of Aptitude Questions and Answers (MCQs) focuses on “Remainder Theorem”.
1. Find the value of \(\frac{7^{301}}{4}\).
a) 3
b) 2
c) 1
d) 0
View Answer
Explanation: \(\frac{7^{odd}}{4}\)=3 and \(\frac{7^{even}}{4}\)=1
Therefore, \(\frac{7^{301}}{4}\)=3.
2. Find the remainder when 11526 is divided by 5.
a) 1
b) 2
c) 3
d) 4
View Answer
Explanation: The unit digit of 11526 depends on unit digit of 1526.
We know that, 1any number=1.
Therefore, the remainder when 11526 is divided by 5 is 1.
3. Which of the following divides 345+346+347+348+349?
a) 11
b) 3
c) 5
d) c
View Answer
Explanation: 345+346+347+348+349 = 345(1+3+32+33+34) = 345*121.
345*121 is divisible by 11.
4. What is the remainder when 2385+1585 is divisible by 19?
a) 0
b) 17
c) 7
d) 11
View Answer
Explanation: We know that xn+an is divisible by x+a for n being odd.
Therefore, 23+15= 38 is divisible by 19 and remainder is 0.
5. What is the remainder when 2565 is divided by 26?
a) 1
b) 25
c) 24
d) 2
View Answer
Explanation: We know that xn+an is divisible by x+a for n being odd.
2565+1 = 2565 + (26-25) is divisible 26.
2565 = 2565 + 1 – 1 = 2565 + (26-25) – (26-25) gives remainder 25 when divided by 26.
6. What is the remainder when a prime number greater than 6 is divided by 6?
a) 1 or 3
b) 1 or 5
c) 3 or 5
d) 3 or 4
View Answer
Explanation: Prime number greater than 6 are 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 ……
When 7, 13, 19, 31, 37, 43 …… is divisible by 6, we get 1 as remainder.
When 11, 17, 23, 41, 47 …… is divisible by 6, we get 5 as remainder.
Hence, when a prime number greater than 6 is divided by 6, the remainder is 1 or 5.
7. When 8255 is divided by 511, what is the remainder?
a) 500
b) 510
c) 10
d) 1
View Answer
Explanation: \(\frac{8^{255}}{511}=\frac{8^{3*85}}{511}=\frac{512^{85}}{511}=\frac{(511+1)^{85}}{511} \)
Therefore, 1 is the remainder.
8. What is the remainder when N=1521*1523*1525 is divisible by 12?
a) 3
b) 7
c) 5
d) 11
View Answer
Explanation: On multiplying the unit digit of N we get, 1*3*5=15.
15 when divided by 12 gives 3 as remainder.
Therefore, remainder when N=1521*1523*1525 is divisible by 12 is 3.
9. What is the remainder when 4156 is divided by 6?
a) 5
b) 3
c) 2
d) 4
View Answer
Explanation: The remainder of 41 when divided by 6 is 4.
The remainder of 42 when divided by 6 is 4.
The remainder of 43 when divided by 6 is 4.
The remainder of 44 when divided by 6 is 4.
We can infer that remainder of any power of 4 when divided by 6 is 4.
10. Find the last two digits of 72020.
a) 49
b) 43
c) 01
d) 07
View Answer
Explanation: 70 = 01; 71 = 07; 72 = 49; 73 = 343; 74 = 2401; 75 = 16807; 76 = 117649; 77= 823543.
The last two digits are repeating itself after every 4 number.
74n = 01; 74n+1 = 07; 74n+2 = 49; 74n+3 = 43.
Therefore, the last two digits of 72020 = 74*505 is 01.
To practice all aptitude questions, please visit “1000+ Quantitative Aptitude Questions”, “1000+ Logical Reasoning Questions”, and “Data Interpretation Questions”.
If you find a mistake in question / option / answer, kindly take a screenshot and email to [email protected]
