Number System Questions and Answers with Solution

Remainder = 4

⇒ Divisor = 3 × 4 = 12

Again, divisor = 4 × quotient

⇒ 4 × quotient = 12

Quotient =$${12\over 4}=3$$

⇒ Dividend = 3 × 12 + 4 = 40

Let the required number of persons be x.

According to the question, 2x² = 3042

Or

or 

Number just greater than 3 which is divisible by 7 = 7

Number just smaller than 200 which is divisible by 7 = 196

Here, a = 7, a_n = 196,

d = 7, n = 8

a_n = a + (n –1)d

⇒196 = 7 + (n – 1) × 7

⇒ 

⇒ n = 27 + 1 = 28

Note : We can find the answer after dividing 200 by 7. The quotient is our answer.

Sum of first 60 numbers

The number 1830 is divisible by 61.

The least number (dividend) x is obtained as follows :

y = 2 × 1 + 1 = 3

x = 3 × 3 + 1 = 10

When we divide 10 by 6, the remainder = 4

Let the numbers be x and y and x is greater than y.

As given,

xy = 9375 ....(i)

Again,

∴ From equation (i),

15y × y = 9375

On dividing the given number by 119, let k be the quotient and 19 as remainder.

Then, number = 119k + 19

= 17 × 7k + 17 × 1 + 2

= 17 (7k + 1) + 2

Hence, the given number when divided by 17, gives (7k + 1) as quotient and 2 as remainder.

By the Binomial expansion we have

Here, each term except the last term contains x. Obviously, each term except the last term is exactly divisible by x.

Following the same logic,

7¹⁹ = (6 + 1)¹⁹ has each term except last term divisible by 6.

Hence, 7¹⁹ + 2 when divided by 6 leaves remainder =1 + 2 = 3

Here, 357 is exactly divisible by 17.

∴  Required remainder = Remainder obtained on dividing 39 by 17 = 5

Number = 269 × 68

= 269 × (67 + 1)

= 269 × 67 + 269

Clearly, remainder is obtained on dividing 269 by 67 that is 1.