Question 1

7589 -? = 3434

Accepted Answer

Let 7589 -x = 3434 Then, x = 7589 - 3434 = 4155

Question 2

A 3-digit number 4a3 is added to another 3-digit number 984 to give a 4-digit number 13b7, which is divisible by 11. Then, (a + b) =?

Accepted Answer

4 a 3  |
 9 8 4  }  ==> a + 8 = b  ==>  b - a = 8  
13 b 7  |
 Also, 13 b 7 is divisible by 11 ⟹ (7 + 3) - ( b + 1) = (9 - b ) ⟹ (9 - b) = 0 ⟹ b = 9 ∴ (b = 9 and a = 1) ⟹ (a + b) = 10.

Question 3

Which one of the following numbers is completely divisible by 45?

Accepted Answer

45 = 5 x 9, where 5 and 9 are co-primes. Unit digit must be 0 or 5 and sum of digits must be divisible by 9. Among given numbers, such number is 202860.

Question 4

If 1400 x x = 1050. Then, x =?

Accepted Answer

1400 x x = 1050 ⟹ x = 1050 = 3 1400 4

Question 5

The sum of the two numbers is 12 and their product is 35. What is the sum of the reciprocals of these numbers?

Accepted Answer

Let the numbers be a and b . Then, a + b = 12 and ab = 35. ∴ a + b = 12 ⟹ ❨ 1 + 1 ❩ = 12 ab 35 b a 35 ∴ Sum of reciprocals of given numbers = 12 35

Question 6

854 x 854 x 854 - 276 x 276 x 276 =? 854 x 854 + 854 x 276 + 276 x 276

Accepted Answer

Given Exp. = (a3 - b3) = (a - b) = (854 - 276) = 578 (a2 + ab + b2)

Question 7

The sum of first 45 natural numbers is:

Accepted Answer

Let S n = (1 + 2 + 3 + ... + 45) This is an A.P. in which a = 1, d = 1, n = 45 and l = 45 ∴Sn = n (a + l) = 45 x (1 + 45) = (45 x 23) = 1035 2 2 Required sum = 1035.

Question 8

n is a whole number which when divided by 4 gives 3 as remainder. What will be the remainder when 2n is divided by 4?

Accepted Answer

Let n = 4 q + 3. Then 2 n = 8 q + 6 = 4(2 q + 1 ) + 2. Thus, when 2n is divided by 4, the remainder is 2.

Question 9

What is the unit digit in (4137)754?

Accepted Answer

Unit digit in (4137) 754 = Unit digit in {[(4137) 4 ] 188 x (4137) 2 } =Unit digit in { 292915317923361 x 17114769 } = (1 x 9) = 9

Question 10

How many 3-digit numbers are completely divisible 6?

Accepted Answer

3-digit number divisible by 6 are: 102, 108, 114,... , 996 This is an A.P. in which a = 102, d = 6 and l = 996 Let the number of terms be n. Then tn = 996. ∴ a + (n - 1)d = 996 ⟹ 102 + (n - 1) x 6 = 996 ⟹ 6 x (n - 1) = 894 ⟹ (n - 1) = 149 ⟹ n = 150 ∴ Number of terms = 150.

Question 11

What is the unit digit in {(6374)1793 x (625)317 x (341491)}?

Accepted Answer

Unit digit in (6374) 1793 = Unit digit in (4) 1793 = Unit digit in [(42)896 x 4] = Unit digit in (6 x 4) = 4 Unit digit in (625)317 = Unit digit in (5)317 = 5 Unit digit in (341)491 = Unit digit in (1)491 = 1 Required digit = Unit digit in (4 x 5 x 1) = 0.

Question 12

(xn - an) is completely divisible by (x - a), when

Accepted Answer

For every natural number n , ( x n - a n ) is completely divisible by ( x - a ).

Question 13

(22 + 42 + 62 + ... + 202) =?

Accepted Answer

(2 2 + 4 2 + 6 2 + ... + 20 2 ) = (1 x 2) 2 + (2 x 2) 2 + (2 x 3) 2 + ... + (2 x 10) 2 = (22 x 12) + (22 x 22) + (22 x 32) + ... + (22 x 102) = 22 x [12 + 22 + 32 + ... + 102] [ Ref: (12 + 22 + 32 + ... + n2) = 1 n(n + 1)(2n + 1) ] 6 = ❨ 4 x 1 x 10 x 11 x 21 ❩ 6 = (4 x 5 x 77) = 1540.

Question 14

8796 x 223 + 8796 x 77 =?

Accepted Answer

8796 x 223 + 8796 x 77 = 8796 x (223 + 77) [Ref: By Distributive Law ] = (8796 x 300) = 2638800

Question 15

How many of the following numbers are divisible by 3 but not by 9? 2133, 2343, 3474, 4131, 5286, 5340, 6336, 7347, 8115, 9276

Accepted Answer

Marking (/) those which are are divisible by 3 by not by 9 and the others by (X), by taking the sum of digits, we get:s 2133 → 9 (X) 2343 → 12 (/) 3474 → 18 (X) 4131 → 9 (X) 5286 → 21 (/) 5340 → 12 (/) 6336 → 18 (X) 7347 → 21 (/) 8115 → 15 (/) 9276 → 24 (/) Required number of numbers = 6.

Question 16

(12345679 x 72) =?

Accepted Answer

12345679 x 72 = 12345679 x (70 +2) = 12345679 x 70 + 12345679 x 2 = 864197530 + 24691358 = 888888888

Question 17

If the number 97215 * 6 is completely divisible by 11, then the smallest whole number in place of * will be:

Accepted Answer

Given number = 97215 x 6 (6 + 5 + 2 + 9) - (x + 1 + 7) = (14 - x), which must be divisible by 11. ∴ x = 3

Question 18

What smallest number should be added to 4456 so that the sum is completely divisible by 6?

Accepted Answer

6) 4456 (742
    42
    ---
     25
     24        Therefore, Required number = (6 - 4) = 2.
     ---
      16
      12
      ---
       4

Question 19

The difference between the local value and the face value of 7 in the numeral 32675149 is

Accepted Answer

(Local value of 7) - (Face value of 7) = (70000 - 7) = 69993

Question 20

(112 + 122 + 132 + ... + 202) =?

Accepted Answer

(11 2 + 12 2 + 13 2 + ... + 20 2 ) = (1 2 + 2 2 + 3 2 + ... + 20 2 ) - (1 2 + 2 2 + 3 2 + ... + 10 2 ) [ Ref: (12 + 22 + 32 + ... + n2) = 1 n(n + 1)(2n + 1) ] 6 = ❨ 20 x 21 x 41 - 10 x 11 x 21 ❩ 6 6 = (2870 - 385) = 2485.

Numbers Questions