Problems on Numbers for Exam
Q31. The smallest whole number is
(a) 0
(b) 1
(c) 2
(d) None of the above
Answer: (a) 0
Q32. The smallest natural number is
(a) 0
(b) 1
(c) 2
(d) None of the above
Answer: (b) 1
Q33. The sum of first 6 prime number is
(a) 38
(b) 39
(c) 40
(d) 41
Answer: (d) 41
2+3+5+7+11+13
41
Q34. Which of the following is not a prime number
(a) 11
(b) 21
(c) 31
(d) 41
Answer: (b) 21
Q35. The difference between the square of two consecutive even integers is always divisible by
(a) 2
(b) 3
(c) 4
(d) 7
Answer: (c) 4
Let the two consucative even integers are 2x and 2x+2
Now (2x+2)2 - (2x)2 = 4x2 + 8x + 4 - 4x2
=8x + 4
= 4 (2x + 1) which is divisible by 4
Q36. There are four prime numbers written in ascending order. The product of first three is 385 and that of the last three is 1001. The first number is
(a) 3
(b) 4
(c) 5
(d) 10
Answer: (c) 5
Let the prime numbers be a, b, c, d
Now abc = 385
bcd = 1001
∴ | abc | = | 385 |
bcd | 1001 |
∴ | a | = | 5 |
d | 13 |
∴ a = 5 d = 13
∴ First number is 5
Q37. A number when divided by 6 leaves a remainder 3. When the square of the same number is divided by 6, the remainder is
(a) 0
(b) 1
(c) 2
(d) 3
Answer: (d) 3
Let the number is x
∴ x = 6k + 3
∴ x2 = (6k + 3)2 = 36k2 + 36k + 9
= 36k2 + 36k + 6 + 3
= 6 (6k2 + 6k + 1) + 3
∴ Remainder = 3
Q38. A number is divided by 56 gives 28 as remainder. If the same number is divided by 8, the remainder will be
(a) 2
(b) 3
(c) 4
(d) 5
Answer: (c) 4
Let the number is x
∴ x = 56k + 28
x = (8 X 7k) + (8 X 3) + 4
x = 8(7k + 3) + 4
Remainder = 4
Q39. In a question on division with zero remainder, a candidate took 21 as divisor instead of 12. The quotient obtained by him was 20. The correct quotient is
(a) 35
(b) 48
(c) 56
(d) 66
Answer: (a) 35
Divisor = 21
Quotient = 20
Remainder = 0
∴ Number = Divisor X Quotient + Remainder
= 21 X 20 + 0
= 420
Correct quotient = 420 ÷ 12
=35
Q40. If 27 * 324 is divisible by 3, then what is the smallest digit is there in place of *
(a) 0
(b) 3
(c) 5
(d) 7
Answer: (a) 0
2+7+*+3+2+4 = 18 + * which is divisible by 3
=18 + 0 which is divisible by 3
18
∴ * = 0
Practice Test Exam