If 43x = 16x+1, find the value of x
2
3
4
5
Correct answer is A
43x = 42(x+1)
3x = 2x + 2
3x - 2x = 2
x = 2
Given that A and B are sets such that n(A) = 8, n(B)=12 and n(AnB) =3, find n(AuB).
15
17
20
23
Correct answer is B
n(AuB) = n(A) + n(B) - n(AnB)
n(AuB) = 8 + 12 - 3
= 17
Change 432five to a number in base three.
10100three
11100three
11101three
10110three
Correct answer is B
Convert from base 5 to base 10
432five = (4 x 52) + (3 x 51) + (2 x 50)
= (4 x 25) + (3 x 5) + (2 x 1)
= 100 + 15 + 2
= 117ten
Then convert from base 10 to base 3
| 3 | 117 |
| 3 | 39 r 0 |
| 3 | 13 r 0 |
| 3 | 4 r 1 |
| 3 | 1 r 1 |
| 0 r 1 |
Selecting the remainders from bottom to top:
117ten = 11100three
Hence; 432five = 11100three
111101two
11111101two
1111101two
11001two
Correct answer is C
(101two)3 = (5ten)3
53 = 125
And 125 = 1111101two