1100002
1102
11000002
110002
Correct answer is C
101122 - 10122 = (1x23 + 0x22 + 1x21 + 1x20)2 - (1x22 + 0x21 + 1x22)2
(1x8 + 0x4 + 1x2 + 1x1) 2 - (1x4 + 0x2 + 1x1) 2)
= (8 + 0 + 2 + 1) 2 - (4 + 0 + 1) 2
= 112 - 52
= 16 x 6 = 96
9610 to base 2
2/96 = 48 R 0
2/48 = 24 R 0
2/24 = 12 R 0
2/12 = 6 R 0
2/6 = 3 R 0
2/3 = 1 R 1
2/1 = 0 R 1
11000002
P∩Q = ∅
P ⊂ Q
Q⊂P
P = Q
Correct answer is A
P = {1, 3, 5, 7, 9, 11}
Q = {2, 4, 6, 8, 1, 12}
P∩Q = {1, 3, 5, 7, 9, 11}∩{2, 4, 6, 8, 1, 12}
= {} = ∅
N68,000
N72,000
N65,000
N70,000
Correct answer is B
5% profit = 100 + 5 = 105%
26% profit = 100 + 26 = 126%
∴ 105% → N60,000
1% → 60000/15
126% = 1000/105 x 126/1
=N72,000
If log102 = x, express log1012.5 in terms of x
2(1 + x)
2 + 3x
2(1 - x)
2 - 3x
Correct answer is D
log1012.5 = log10 121/2
= log1025/2
= log1025 - log102
= log1052 - log102
= 2log105 - log102
= 2log1010/2 - log102
= 2(1-x)- x
= 2 - 2x – x
= 2 – 3x
Simplify \(\frac{3}{5} \div \left(\frac{2}{7} \times \frac{4}{3} \div \frac{4}{9}\right)\)
\(\frac{4}{5}\)
\(\frac{7}{10}\)
\(\frac{6}{6}\)
\(\frac{21}{6}\)
Correct answer is B
\(\frac{3}{5} \div \left(\frac{2}{7} \times \frac{4}{3} \div \frac{4}{9}\right)\\
=\frac{3}{5} \div \left(\frac{2}{7} \times \frac{4}{3} \times \frac{9}{4}\right)\\
=\frac{3}{5} \div \frac{6}{7}\\
=\frac{3}{5} \times \frac{7}{6}\\
=\frac{7}{10}\)