Problems on Numbers for Exam

Answer: (a) 0

Product of unit digits are

= 5 X 2 X 6

=60

∴ Required digit =0

Answer: (d) 4

3⁶⁵ = (3⁴)¹⁶ X 3

The unit digit of 3⁴ is 1

∴ The unit digit of (3⁴)¹⁶ is 1

∴ The unit digit of 3⁶⁵ is 1 X 3 = 3

The unit digit of 6⁵⁹ is 6

The unit digit of 7⁴ is 1. So unit digit in (7⁴)¹⁷ is 1

Now 7⁷¹ = (7⁴)¹⁷ X 7³ and unit digit in 7³ is 3

∴ unit digit in 7⁷¹ is 3

∴ Required unit digit = Unit digit in (3 X 6 X 3)

=unit digit in 54

=4

Answer: (c) 5680

45 + 46 + 47 + ⋅ ⋅ ⋅ ⋅ ⋅ + 113 + 114 + 115

= (1 + 2 + ⋅ ⋅ ⋅ ⋅ ⋅ + 44 + 45 + 46 ⋅ ⋅ ⋅ ⋅ ⋅ + 115) - (1 + 2 + 3 + ⋅ ⋅ ⋅ ⋅ ⋅ + 44)

=115 X 58 - 22 X 45

=6670-990

=5680

Formula 1 + 2 + ⋅ ⋅ ⋅ ⋅ + n = n(n+1) ÷ 2

Answer: (a) 1085

Let the four integers are x+1, x+3, x+5, x+7

=> 4x = (32 X 4) - 16

=28

Now A = x+1 = 28+1 = 29

Now B = x+3 = 28+3 = 31

Now C = x+5 = 28+5 = 33

Now D = x+7 = 28+7 = 35

Product of B and D are 31 X 35 = 1085

Answer: (a) 3717

Let A =x+2, B=x+4, C=x+6, D=x+8

=> 4x = (62 X 4) - 20

=57

A = 57 + 2 = 59

C = 57 + 6 = 63

A X C = 59 X 63 = 3717

Answer: (b) 2400

106 X 106 - 94 X 94

=106² - 94²

=(106 + 94) (106 - 94)

=200 X 12

=2400

Answer: (c) 0.49

=0.49

Answer: (c) 280.875

8988 ÷ 8 ÷ 4

=8988 X (1/8) X (1/4)

=8988 ÷ 32

=280.875

Answer: (b) 1/3

Let the numbers are a and b.

Now a+b = 15 and ab = 45

Answer: (b) 2