x < 5
x < 7\(\frac{1}{2}\)
x > 5
x > 7\(\frac{1}{2}\)
Correct answer is A
\(\frac{x}{2} - \frac{1}{3} < \frac{2x}{5} + \frac{1}{6}\)
\(\frac{x}{2} - \frac{2x}{5} < \frac{1}{6} + \frac{1}{3}\)
\(\frac{x}{10} < \frac{1}{2}\)
\(2x < 10 \implies x < 5\)
24
42
74
47
72
Correct answer is D
Let the tens digits of the number be x and the unit digit be y
3x = 2y - 2
3x - 2y = -2.......(i)
If the digits are interchanged, the tens digit becomes y, the unit digit becomes x. Hence 2(10x + y) = 10y + x + 20
(20x + 2y) - (10y + x) = 20
19x - 8y = 20.....(ii)
Multiply eqn.(i) by 8 and eqn.(ii) by 2
24x - 16y = -16......(iii)
38x - 16y = 40........(iv)
eqn(iv) - eqn(iii)
14x = 56
x = 4
Sub. for x = 4 in eqn(i)
3(4) - 2y = -2
14 = 2y
y = 7
So the original number is 10(4) + 7
i.e. 10x + y
= 47
40r:50t
44r : 50t
50r : 44t
44r:55t
55r:44t
Correct answer is C
Ratio of bread to sugar = r:t
25% increase in bread = \(\frac{125r}{100}\)
10% increase in sugar = \(\frac{100t}{100}\)
New ratio = \(\frac{125r}{100}\):\(\frac{110t}{100}\)
= 25r:22t
= 50r:44t
If sine x equals cosine x, what is x in radians?
\(\frac{\pi}{2}\)
\(\frac{\pi}{3}\)
\(\frac{\pi}{4}\)
\(\frac{\pi}{6}\)
\(\frac{\pi}{12}\)
Correct answer is C
\(\sin x = \cos x\)
\(\implies x = 45°\)
In radians, \(x = \frac{\pi}{4}\).
81
27
\(\frac{1}{9}\)
\(\frac{1}{27}\)
\(\frac{1}{81}\)
Correct answer is A
\(x \propto \frac{1}{y}\)
\(x = \frac{k}{y}\)
\(y \propto t^{2}\)
\(y = ct^{2}\)
k and c are constants.
\(x = \frac{k}{ct^{2}}\)
Let \(\frac{k}{c} = d\) (a constant)
\(x = \frac{d}{t^{2}}\)
\(1 = \frac{d}{3^{2}} \implies d = 9\)
\(\therefore x = \frac{9}{t^{2}}\)
\(x = 9 \div (\frac{1}{3})^{2} \)
= \( 9 \div \frac{1}{9} = 9 \times 9 = 81\)