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 |
=> | x2 - 1 | = | 9 |
x | 20 |
=> 20x2 - 9x - 20 = 0
=> 20x2 - 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 (n3 - n) is
(a) 6
(b) 3
(c) 4
(d) 12
Answer: (a) 6
23 - 2 = 6 is the largest natural number which divides (n3 - 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
∴ x2 = (5v + 3)2 = 25v2 + 30q + 9
= 5 (5v2 + 6q + 1) + 4
∴ Remainder = 4