Question 1

2 + 22 + 23 + ... + 29 =?

Accepted Answer

This is a G.P. in which a = 2, r = 22 = 2 and n = 9. 2 ∴Sn = a(rn - 1) = 2 x (29 - 1) = 2 x (512 - 1) = 2 x 511 = 1022. (r - 1) (2 - 1)

Question 2

217 x 217 + 183 x 183 =?

Accepted Answer

(217)2 + (183)2 = (200 + 17)2 + (200 - 17)2 = 2 x [(200)2 + (17)2] [Ref: (a + b)2 + (a - b)2 = 2(a2 + b2)] = 2[40000 + 289] = 2 x 40289 = 80578.

Question 3

What will be remainder when (6767 + 67) is divided by 68?

Accepted Answer

( x n + 1) will be divisible by ( x + 1) only when n is odd. ∴(6767 + 1) will be divisible by (67 + 1) ∴(6767 + 1) + 66, when divided by 68 will give 66 as remainder.

Question 4

9 + 3 + 7 + 2 - ❨ 9 + 1 ❩ =? 4 17 15

Accepted Answer

Given sum = 9 + 3 + 7 + 2 - ❨ 9 + 1 ❩ 4 17 15 = (9 + 7 - 9) + ❨ 3 + 2 - 1 ❩ 4 17 15 = 7 + 765 + 120 - 68 1020 = 7 + 817 1020

Question 5

Which one of the following numbers is exactly divisible by 11?

Accepted Answer

(4 + 5 + 2) - (1 + 6 + 3) = 1, not divisible by 11. (2 + 6 + 4) - (4 + 5 + 2) = 1, not divisible by 11. (4 + 6 + 1) - (2 + 5 + 3) = 1, not divisible by 11. (4 + 6 + 1) - (2 + 5 + 4) = 0, So, 415624 is divisible by 11.

Question 6

3897 x 999 =?

Accepted Answer

3897 x 999 = 3897 x (1000 - 1) = 3897 x 1000 - 3897 x 1 = 3897000 - 3897 = 3893103.

Question 7

(800 / 64) x (1296 / 36) =?

Accepted Answer

Given Exp. = 800 x 1296 = 450 64 36

Question 8

2056 x 987 =?

Accepted Answer

2056 x 987 = 2056 x (1000 - 13) = 2056 x 1000 - 2056 x 13 = 2056000 - 26728 = 2029272.

Question 9

If a and b are odd numbers, then which of the following is even?

Accepted Answer

The sum of two odd number is even. So, a + b is even.

Question 10

How many natural numbers are there between 23 and 100 which are exactly divisible by 6?

Accepted Answer

Required numbers are 24, 30, 36, 42, ..., 96 This is an A.P. in which a = 24, d = 6 and l = 96 Let the number of terms in it be n. Then tn = 96 ⟹ a + (n - 1)d = 96 ⟹ 24 + (n - 1) x 6 = 96 ⟹ (n - 1) x 6 = 72 ⟹ (n - 1) = 12 ⟹ n = 13 Required number of numbers = 13.

Question 11

What least number must be subtracted from 13601, so that the remainder is divisible by 87?

Accepted Answer

87) 13601 (156
     87
     ----
      490
      435
      ----
       551
       522
       ---
        29
       ---
       
 Therefore, the required number = 29.

Question 12

If the product 4864 x 9 P 2 is divisible by 12, then the value of P is:

Accepted Answer

Clearly, 4864 is divisible by 4. So, 9P2 must be divisible by 3. So, (9 + P + 2) must be divisible by 3. ∴ P = 1.

Question 13

Which natural number is nearest to 8485, which is completely divisible by 75?

Accepted Answer

On dividing, we get

 75) 8485 (113
     75
     ---
      98
      75
      ----
       235
       225
       ---
        10
       ---
 
 Required number = (8485 - 10) // Because 10 < (75 - 10)
                 = 8475.

Question 14

❨ 1 - 1 ❩ + ❨ 1 - 2 ❩ + ❨ 1 - 3 ❩ + ... up to n terms =? n n n

Accepted Answer

Given sum = (1 + 1 + 1 + ... to n terms) - ❨ 1 + 2 + 3 + ... to n terms ❩ n n n = n - n ❨ 1 + 1 ❩ [ Ref: nth terms = (n/n) = 1] 2 n = n - n + 1 2 = 1 (n - 1) 2

Question 15

3 + 33 + 333 + 3.33 =?

Accepted Answer

3
+  33
+ 333
+   3.33
  ------
  372.33
  ------

Question 16

A boy multiplied 987 by a certain number and obtained 559981 as his answer. If in the answer both 9 are wrong and the other digits are correct, then the correct answer would be:

Accepted Answer

987 = 3 x 7 x 47 So, the required number must be divisible by each one of 3, 7, 47 553681 → (Sum of digits = 28, not divisible by 3) 555181 → (Sum of digits = 25, not divisible by 3) 555681 is divisible by 3, 7, 47.

Question 17

If 60% of 3/5 of a number is 36, then the number is:

Accepted Answer

Let the number be x . Then 60% of 3 of x = 36 5 ⟹ 60 x 3 x x = 36 100 5 ⟹ x = ❨ 36 x 25 ❩ = 100 9 ∴ Required number = 100

Question 18

768 x 768 x 768 + 232 x 232 x 232 =? 768 x 768 - 768 x 232 + 232 x 232

Accepted Answer

Given Exp. = (a3 + b3) = (a + b) = (768 + 232) = 1000 (a2 - ab + b2)

Question 19

476 ** 0 is divisible by both 3 and 11. The non-zero digits in the hundred's and ten's places are respectively:

Accepted Answer

Let the given number be 476 xy 0. Then (4 + 7 + 6 + x + y + 0) = (17 + x + y) must be divisible by 3. And, (0 + x + 7) - (y + 6 + 4) = (x - y -3) must be either 0 or 11. x - y - 3 = 0 ⟹ y = x - 3 (17 + x + y) = (17 + x + x - 3) = (2x + 14) ⟹ x= 2 or x = 8. ∴ x = 8 and y = 5.

Question 20

(4300731) -? = 2535618

Accepted Answer

Let 4300731 - x = 2535618 Then x, = 4300731 - 2535618 = 1765113

Numbers Questions