DXC Technology Divisibility Questions and Answers Quiz-1

Basically, we successively multiply the divisors with the result of the previous stage and add the corresponding remainder.
7 x 1 + 3 = 10
3 x 10 + 2 = 32
2 x 32 + 1 = 65
Thus, 65 is the required answer.
NOTE : The answer would differ if we change the order of divisors. For smallest number, arrange the divisors in decreasing order.

Solution : Proceeding in the similar manner as the above question,
8 x 1 + 0 = 8
4 x 8 + 1 = 33
2 x 33 + 1 = 67
Thus, 67 is the required answer.

The number is of the form 340a + 47 = 17 * (20a) + 17 * (2) + 13 = 17 * (20a + 2) + 13.
Therefore, on dividing this number by 17, we would get 13 as the remainder.

Solution : 3⁴ = 81. So, the unit’s digit of 3⁴ is 1.
Therefore, the unit’s digit of 3²⁰ = 1 and thus, the unit’s digit of 3²¹ = 1*3 = 3.
3 when divided by 5 gives 3 as the remainder.
So, the remainder when 3²¹ is divided by 5 is 3.

124 is divisible by 2 since the last digit is 4.
124 is not divisible by 3 since the sum of the digits is 7 (1+2+4 = 7), and 7 is not divisible by 3.
124 is divisible by 4 since 24 is divisible by 4.
124 is not divisible by 5 since the last digit is 4 it is neither 0 nor 5.
124 is divisible by 2 and 4 not by 3 and 5.

Let xy be the whole number with x and y the two digits that make up the number. The number is divisible by 3 may be written as follows

10 x + y = 3 k

The sum of x and y is equal to 9.

x + y = 9

Solve the above equation for y

y = 9 - x Substitute y = 9 - x in the equation 10 x + y = 3 k to obtain.

10 x + 9 - x = 3 k

Solve for x

x = (k - 3) / 3

x is a positive integer smaller than 10

Let k = 1, 2, 3, ... and select the first value that gives x as an integer. k = 6 gives x = 1

Find y using the equation y = 9 - x = 8

The number we are looking for is 18 and the answer is B. It is divisible by 3 and the sum of its digits is equal to 9 and it is the smallest and positive whole number with such properties.

Video solution:

When n is divided by 8, the remainder is 3 may be written as

n = 8 k + 3

multiply all terms by 6

6 n = 6(8 k + 3) = 8(6k) + 18

Write 18 as 16 + 2 since 16 = 8 * 2.

= 8(6k) + 16 + 2

Factor 8 out.

= 8(6k + 2) + 2

The above indicates that if 6n is divided by 8, the remainder is 2

If n is divisible by 3, 5 and 12 it must a multiple of the lcm of 3, 5 and 12 which is 60.

n = 60 k

n + 60 is also divisible by 60 since

n + 60 = 60 k + 60 = 60(k + 1)

Video solution:

We first expand (2n + 2)²

(2n + 2)² = 4n ² + 8 n + 4

Factor 4 out.

= 4(n ² + 2n + 1)

(2n + 2)² is divisible by 4 and the remainder is equal to 0.

divided by 5 yields a remainder equal to 3 is written as follows

n = 5 k + 3 , where k is an integer.

add 2 to both sides of the above equation to obtain

n + 2 = 5 k + 5 = 5(k + 1)

The above suggests that n + 2 divided by 5 yields a remainder equal to zero

Video solution: