Question 1

What will be remainder when 17200 is divided by 18?

Accepted Answer

When n is even. ( x n - a n ) is completely divisibly by ( x + a ) (17200 - 1200) is completely divisible by (17 + 1), i.e., 18. ⟹ (17200 - 1) is completely divisible by 18. ⟹ On dividing 17200 by 18, we get 1 as remainder.

Question 2

Which of the following numbers will completely divide (325 + 326 + 327 + 328)?

Accepted Answer

(3 25 + 3 26 + 3 27 + 3 28 ) = 3 25 x (1 + 3 + 3 2 + 3 3 ) = 3 25 x 40 = 324 x 3 x 4 x 10 = (324 x 4 x 30), which is divisible by30.

Question 3

(489 + 375)2 - (489 - 375)2 =? (489 x 375)

Accepted Answer

Given Exp. = (a + b)2 - (a - b)2 = 4ab = 4 ab ab

Question 4

On dividing a number by 56, we get 29 as remainder. On dividing the same number by 8, what will be the remainder?

Accepted Answer

Formula: (Divisor*Quotient) + Remainder = Dividend. Soln: (56*Q)+29 = D -------(1) D%8 = R -------------(2) From equation(2), ((56*Q)+29)%8 = R. => Assume Q = 1. => (56+29)%8 = R. => 85%8 = R => 5 = R.

Question 5

Which one of the following is the common factor of (4743 + 4343) and (4747 + 4347)?

Accepted Answer

When n is odd, ( x n + a n ) is always divisible by ( x + a ). ∴Each one of (4743 + 4343) and (4747 + 4347) is divisible by (47 + 43).

Question 6

If the number 517*324 is completely divisible by 3, then the smallest whole number in the place of * will be:

Accepted Answer

Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = (22 + x ), which must be divisible by 3. ∴ x = 2.

Question 7

Which of the following is a prime number?

Accepted Answer

Clearly, 97 is a prime number.

Question 8

The difference between a positive proper fraction and its reciprocal is 9/20. The fraction is:

Accepted Answer

Let the required fraction be x. Then 1 - x = 9 x 20 ∴ 1 - x2 = 9 x 20 ⟹ 20 - 20x2 = 9x ⟹ 20x2 + 9x - 20 = 0 ⟹ 20x2 + 25x - 16x - 20 = 0 ⟹ 5x(4x + 5) - 4(4x + 5) = 0 ⟹ (4x + 5)(5x - 4) = 0 x = 4 5

Question 9

-84 x 29 + 365 =?

Accepted Answer

Given Exp. = -84 x (30 - 1) + 365 = -(84 x 30) + 84 + 365 = -2520 + 449 = -2071

Question 10

It is being given that (232 + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?

Accepted Answer

Let 2 32 = x . Then, (2 32 + 1) = ( x + 1). Let (x + 1) be completely divisible by the natural number N. Then, (296 + 1) = [(232)3 + 1] = (x3 + 1) = (x + 1)(x2 - x + 1), which is completely divisible by N, since (x + 1) is divisible by N.

Question 11

3251 + 587 + 369 -? = 3007

Accepted Answer

3251          Let 4207 - x = 3007
+ 587          Then,  x = 4207 - 3007 = 1200
+ 369
 ----
 4207
 ----

Question 12

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. Sn = n [2a + (n - 1)d] = 45 x [2 x 1 + (45 - 1) x 1] = ❨ 45 x 46 ❩ = (45 x 23) 2 2 2 = 45 x (20 + 3) = 45 x 20 + 45 x 3 = 900 + 135 = 1035. Shorcut Method: Sn = n(n + 1) = 45(45 + 1) = 1035. 2 2

Question 13

The difference between the place values of two sevens in the numeral 69758472 is

Accepted Answer

Required difference = (700000 - 70) = 699930

Question 14

If the number 653 xy is divisible by 90, then (x + y) =?

Accepted Answer

90 = 10 x 9 Clearly, 653xy is divisible by 10, so y = 0 Now, 653x0 is divisible by 9. So, (6 + 5 + 3 + x + 0) = (14 + x) is divisible by 9. So, x = 4. Hence, (x + y) = (4 + 0) = 4.

Question 15

The smallest 3 digit prime number is:

Accepted Answer

The smallest 3-digit number is 100, which is divisible by 2. ∴ 100 is not a prime number. √101 < 11 and 101 is not divisible by any of the prime numbers 2, 3, 5, 7, 11. ∴101 is a prime number. Hence 101 is the smallest 3-digit prime number.

Question 16

The difference between the place value and the face value of 6 in the numeral 856973 is

Accepted Answer

(Place value of 6) - (Face value of 6) = (6000 - 6) = 5994

Question 17

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

Accepted Answer

The square of a natural number never ends in 7. ∴42437 is not the square of a natural number.

Question 18

What is the unit digit in the product (365 x 659 x 771)?

Accepted Answer

Unit digit in 3 4 = 1 ⟹ Unit digit in (3 4 ) 16 = 1 ∴ Unit digit in 365 = Unit digit in [ (34)16 x 3 ] = (1 x 3) = 3 Unit digit in 659 = 6 Unit digit in 74 ⟹ Unit digit in (74)17 is 1. Unit digit in 771 = Unit digit in [(74)17 x 73] = (1 x 3) = 3 ∴ Required digit = Unit digit in (3 x 6 x 3) = 4.

Question 19

How many 3 digit numbers are divisible by 6 in all?

Accepted Answer

Required numbers 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, a + (n - 1)d = 996 ⟹ 102 + (n - 1) x 6 = 996 ⟹ 6 x (n - 1) = 894 ⟹ (n - 1) = 149 ⟹ n = 150.

Question 20

The smallest 6 digit number exactly divisible by 111 is:

Accepted Answer

The smallest 6-digit number 100000.

 111) 100000 (900
      999
      -----
        100
        ---

 Required number = 100000 + (111 - 100)
                 = 100011.

Numbers Questions