This set of Aptitude Questions and Answers (MCQs) focuses on “Division Algorithm”.
1. On dividing 30879 by a certain number, the quotient is 67 and the remainder is 327. Find the divisor.
a) 476
b) 456
c) 466
d) 444
View Answer
Explanation: Divisor=\(\frac{Dividend-Remainder}{Quotient}=\frac{30879-327}{67}\)=456.
2. In a division sum, the divisor is eleven times the quotient and six times the remainder. If the remainder is 55, determine the dividend.
a) 9955
b) 9855
c) 9985
d) 9965
View Answer
Explanation: Divisor = 6*Remainder = 6*55 = 330.
Quotient = Divisor/11 = 330/11 = 30.
Dividend = Divisor*Quotient + Remainder = 330*30 + 55 = 9955.
3. A number when divided by 91 leaves a remainder 65. If the same number is divided by 13, find the remainder.
a) 12
b) 5
c) 0
d) 7
View Answer
Explanation: On dividing the given number by 91, let k be the quotient and 65 the remainder.
Then, number = 91k + 65 = 13*7k + 13*5 = 13(7k + 5).
The number is completely divisible by 13. Hence the remainder is 0.
4. A number when divided by 9 leaves remainder 6. When square of the same number is divided by 9, find the remainder.
a) 7
b) 5
c) 3
d) 0
View Answer
Explanation: On dividing the given number by 9, let k be the quotient and 6 the remainder.
Then the number is 9k+6.
Square of the number = (9k+6)2 = 81k2 + 36 + 108k = 9(9k2 + 4 + 12k)
The square of the number is completely divisible by 9. Hence the remainder is 0.
5. Find the remainder when 718 + 6 is divided by 6.
a) 0
b) 1
c) 3
d) 5
View Answer
Explanation: (xn – an) is divisible by (x – a) for all values of n.
So, 718 – 1 is divisible by (7 – 1) = 6
718 + 6 = (718 – 1) + 7 = (718 – 1) + 6 + 1
i.e., when [(718 – 1) + 7] is divided by 6, the remainder is 1.
6. Find the remainder when 5892587 + 9 is divided by 590.
a) 8
b) 1
c) 6
d) 4
View Answer
Explanation: (xn + an) is divisible by (x + a) for all odd values of n.
So, 5892587 + 1 is divisible by (589+1) = 590
5892587 + 9 = (5892587 + 1) + 8 gives remainder 8 when divided by 590.
7. If 9126 is divided by 80, find the remainder.
a) 17
b) 29
c) 79
d) 1
View Answer
Explanation: 9126 = (92)63 = 8163.
(xn – an) is divisible by (x – a) for all values of n.
(8163 – 1) is divisible by 80.
(92)63 = 8163 = (8163 – 1) + 1, gives a remainder 1 when divided by 80.
8. Find the remainder when 367188 – 333188 is divided by 700.
a) 12
b) 0
c) 19
d) 1
View Answer
Explanation: (xn – an) is divisible by (x + a) for all even values of n.
367188 – 333188 is divisible by 367+333=700.
Hence, the remainder is 0.
9. For, what values of n, 32n – 1 is divisible by 2n+2.
a) 1
b) 3
c) Both 1 and 3
d) Both 1 and 2
View Answer
Explanation: 32n – 1 is divisible by 2n+2 for only n = 1 and 2.
When n = 1, 32-1 is divisible by 23.
When n = 2, 34-1 is divisible by 24.
10. For any natural number m, m3 – m is divisible by which of the following number?
a) 6
b) 12
c) 24
d) 48
View Answer
Explanation: m3 – m = (m – 1)*m*(m + 1)
We know that, any three consecutive natural number is always divisible by 6.
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