Question 1

8988 ÷ 8 ÷ 4 =?

Accepted Answer

Given Exp. = 8988 x 1 x 1 = 2247 = 280.875 8 4 8

Question 2

5358 x 51 =?

Accepted Answer

5358 x 51 = 5358 x (50 + 1) = 5358 x 50 + 5358 x 1 = 267900 + 5358 = 273258.

Question 3

The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number?

Accepted Answer

Let the smaller number be x . Then larger number = ( x + 1365). ∴ x + 1365 = 6x + 15 ⟹ 5x = 1350 ⟹ x = 270 ∴Smaller number = 270.

Question 4

1397 x 1397 =?

Accepted Answer

1397 x 1397 = (1397)2 = (1400 - 3)2 = (1400)2 + (3)2 - (2 x 1400 x 3) = 1960000 + 9 - 8400 = 1960009 - 8400 = 1951609.

Question 5

{(476 + 424)2 - 4 x 476 x 424} =?

Accepted Answer

Given Exp. = [(a + b)2 - 4ab], where a = 476 and b = 424 = [(476 + 424)2 - 4 x 476 x 424] = [(900)2 - 807296] = 810000 - 807296 = 2704.

Question 6

If (64)2 - (36)2 = 20 x x, then x =?

Accepted Answer

20 x x = (64 + 36)(64 - 36) = 100 x 28 ⟹ x = 100 x 28 = 140 20

Question 7

If n is a natural number, then (6n2 + 6n) is always divisible by:

Accepted Answer

(6 n 2 + 6 n ) = 6 n ( n + 1), which is always divisible by 6 and 12 both, since n ( n + 1) is always even.

Question 8

Which of the following numbers will completely divide (4915 - 1)?

Accepted Answer

( x n - 1) will be divisibly by ( x + 1) only when n is even. (4915 - 1) = {(72)15 - 1} = (730 - 1), which is divisible by (7 +1), i.e., 8.

Question 9

The unit digit in the product (784 x 618 x 917 x 463) is:

Accepted Answer

Unit digit in the given product = Unit digit in (4 x 8 x 7 x 3) = (672) = 2

Question 10

Which natural number is nearest to 9217, which is completely divisible by 88?

Accepted Answer

On dividing we get, 

 88) 9217 (104
        88
        ----
          417
          352
          ----
          65
          ----
  
 Therefore, Required number = 9217 + (88 - 65) // Because (88 - 65) < 65.
                            = 9217 + 23
                            = 9240.

Question 11

107 x 107 + 93 x 93 =?

Accepted Answer

107 x 107 + 93 x 93 = (107)2 + (93)2 = (100 + 7)2 + (100 - 7)2 = 2 x [(100)2 + 72] [Ref: (a + b)2 + (a - b)2 = 2(a2 + b2) ] = 20098

Question 12

On dividing a number by 68, we get 269 as quotient and 0 as remainder. On dividing the same number by 67, what will the remainder?

Accepted Answer

Number = 269 x 68 + 0 = 18292

 67) 18292 (273
     134
     ----
      489
      469
      ----
       202
       201
       ---
         1
       ---
       
Therefore, Required remainder = 1

Question 13

What least number must be added to 1056, so that the sum is completely divisible by 23?

Accepted Answer

23) 1056 (45
      92
      ---
      136
      115
      ---
       21
      ---
     
 Required number = (23 - 21)    
                 = 2.

Question 14

Which one of the following can't be the square of natural number?

Accepted Answer

The square of a natural number nerver ends in 2. ∴ 143642 is not the square of natural number.

Question 15

Which one of the following is a prime number?

Accepted Answer

√551 > 22 All prime numbers less than 24 are : 2, 3, 5, 7, 11, 13, 17, 19, 23. 119 is divisible by 7; 187 is divisible by 11; 247 is divisible by 13 and 551 is divisible by 19. So, none of the given numbers is prime.

Question 16

The sum of first five prime numbers is:

Accepted Answer

Required sum = (2 + 3 + 5 + 7 + 11) = 28. Note: 1 is not a prime number. Definition: A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself.

Question 17

The sum all even natural numbers between 1 and 31 is:

Accepted Answer

Required sum = (2 + 4 + 6 + ... + 30) This is an A.P. in which a = 2, d = (4 - 2) = 2 and l = 30. Let the number of terms be n. Then, tn = 30 ⟹ a + (n - 1)d = 30 ⟹ 2 + (n - 1) x 2 = 30 ⟹ n - 1 = 14 ⟹ n = 15 ∴Sn = n (a + l) = 15 x (2 + 30) = 240. 2 2

Question 18

How many prime numbers are less than 50?

Accepted Answer

Prime numbers less than 50 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 Their number is 15

Question 19

(51 + 52 + 53 + ... + 100) =?

Accepted Answer

S n = (1 + 2 + 3 + ... + 50 + 51 + 52 + ... + 100) - (1 + 2 + 3 + ... + 50) = 100 x (1 + 100) - 50 x (1 + 50) 2 2 = (50 x 101) - (25 x 51) = (5050 - 1275) = 3775.

Question 20

How many of the following numbers are divisible by 132? 264, 396, 462, 792, 968, 2178, 5184, 6336

Accepted Answer

132 = 4 x 3 x 11 So, if the number divisible by all the three number 4, 3 and 11, then the number is divisible by 132 also. 264 → 11,3,4 (/) 396 → 11,3,4 (/) 462 → 11,3 (X) 792 → 11,3,4 (/) 968 → 11,4 (X) 2178 → 11,3 (X) 5184 → 3,4 (X) 6336 → 11,3,4 (/) Therefore the following numbers are divisible by 132 : 264, 396, 792 and 6336. Required number of number = 4.

Numbers Questions