# Problems on Numbers for Exam

Q41. 352 * 9 is exactly divisible by 9, then the digit in place of * is

(a) 5

(b) 6

(c) 8

(d) 9

**Answer:** (c) 8

3+5+2+*+9 = 19 + * which is divisible by 9

=19 + 8 which is divisible by 9

=27

∴ * = 8

Q42. Which of the following numbers is exactly divisible by 15

(a) 52340

(b) 14720

(c) 91230

(d) 43810

**Answer:** (c) 91230

The unit digit of each number is 0

So, all number divisible by 5

Now the sum of the digit of number 91230 is 9+1+2+3+0 = 15

∴ 91230 is divisible by 15

Q43. The bigest number of 5 digits begining with 4 and ending with 6 is

(a) 49966

(b) 49996

(c) 60994

(d) 99466

**Answer:** (b) 49996

Q44. By how much is 2/3 rd of 99 is higher than 3/4 th of 52

(a) 19

(b) 22

(c) 24

(d) 27

**Answer:** (d) 27

2/3 rd of 99 = 2/3 X 99 = 66

3/4 th of 52 = 3/4 X 52 = 39

Higher = 66 - 39 = 27

Q45. If the difference between the reciprocal of a positive proper fraction and the fraction itself be 9/20, the fraction is

(a) 4/10

(b) 4/5

(c) 5/4

(d) 5/7

**Answer:** (b) 4/5

Let the fraction is 1/x

Nowx | - | 1 | = | 9 |

x | 20 |

=> | x^{2} - 1 |
= | 9 |

x | 20 |

=> 20x^{2} - 9x - 20 = 0

=> 20x^{2} - 25x + 16x - 20 = 0

=> 5x(4x - 5) + 4(4x-5) = 0

=> (4x - 5) (5x + 4) = 0

∴ 4x - 5 = 0 [x is positive]

=> x = 5/4

∴ Fraction 4/5

Q46. In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 46, the dividend is

(a) 5336

(b) 4363

(c) 5636

(d) 6343

**Answer:** (a) 5336

Remainder = 46

Divisor = 5 X 46 = 230

Quotient = (5 X 46)/10 = 230/10 = 23

Dividend = (Divisor X Quotient) + Remainder

= 230 X 23 + 46

= 5290 + 46

= 5336

Q47. What least number of five digits is exactly divisible by 52

(a) 12514

(b) 12008

(c) 10036

(d) 10006

**Answer:** (c) 10036

Least five digit number = 10000

=> 10000 ÷ 52 = 192 with remainder 16

∴ Required number = 10000 + (52 - 16)

=10036

Q48. The smallest 4 digit prime number is

(a) 1001

(b) 1003

(c) 1007

(d) 1009

**Answer:** (b) 1003

The smallest 4 digit number is 1000

1000 is divisible by 2

1003 is not divisible by 2, 3, 5, 7, 11, 13

∴ 1003 is the required number

Q49. If n is a natural number, then the largest number dividing (n^{3} - n) is

(a) 6

(b) 3

(c) 4

(d) 12

**Answer:** (a) 6

2^{3} - 2 = 6 is the largest natural number which divides (n^{3} - n) for ∀ n ∈ N

Q50. A number when divided by 5, leaves 3 as remainder. What will be the remainder when the square of this number is divided by 5

(a) 3

(b) 4

(c) 5

(d) 6

**Answer:** (b) 4

Let the number be x

Now x = 5v + 3

∴ x^{2} = (5v + 3)^{2} = 25v^{2} + 30q + 9

= 5 (5v^{2} + 6q + 1) + 4

∴ Remainder = 4