List all integer values of x satisfying the inequality -1 < 2x - 5 \(\leq\) 5
<2, 3, 4, 5
3, 4, 5
2, 3, 4
3, 4
Correct answer is B
\(-1 < 2x - 5 \leq 5\)
\(\implies -1 + 5 < 2x - 5 + 5 \leq 5 + 5\)
\(4 < 2x \leq 10\)
\(\implies 2 < x \leq 5 \)
= 3, 4, 5.
The median of the set of numbers 4, 9, 4, 13, 7, 14, 10, 17 is
13
7
\(\frac{19}{2}\)
\(\frac{39}{4}\)
10
Correct answer is C
Rearranging in increasing order 4, 4, 7, 9, 10, 13, 14, 17, the
median = \(\frac{(9 + 10)}{2}\)
= \(\frac{19}{2}\)
When a dealer sells a bicycle for N81 he makes a profit of 80%. What did he pay for the bicycle?
N73
N74.52
N75
N87.48
N75.52
Correct answer is C
Profit = 8%
\(\therefore S.P = N81 = (100 + 8)% = 108%\)
\(108% = N81\)
\(100% = \frac{81}{108} \times 100\)
= \(\frac{8100}{108} = N75\)
1 + 2a - 2\(\sqrt{a(1 + a)}\)
\(\sqrt{1(1 + a)}\)
2a - 2\(\sqrt{a(1 + a)}\)
1 + 2a - 2\(\sqrt{a + b}\)
Correct answer is A
\(\frac{\sqrt{1 + a} - \sqrt{a}}{1 + a + \sqrt{a}}\) = \(\frac{\sqrt{1 + a} - \sqrt{a}}{\sqrt{1 + a} + \sqrt{a}}\) x \(\frac{\sqrt{1 + a} - \sqrt{a}}{\sqrt{1 + a} - \sqrt{a}}\)
= \(\frac{\sqrt{1 + a + a}}{1 + a - a}\)
= 2a + a(1 + a)
= 1 + 2a - 2\(\sqrt{a(1 + a)}\)
Which of the following is NOT a factor of 12\(^{4}\) - 5\(^{4}\)?
7
13
17
49
169
Correct answer is D
124 - 54 = (122)2 - (52)2
= (122 + 52) x (122 - 52)
(144 + 25)(144 - 25)
= (169)(119)
Factors of above 169, 17, 13, 7