Equations and Inequalities Aptitude Questions and Answers.
Number of Questions:
10 Questions with Solutions.
Directions: Two equations (I) and (II) are given in each question. On the basis of these equations, you have to decide the relation between \(x\) and \(y\).
\(x = y\) or No relation can be established between \(x\) and \(y\)
Answer: (a) \(x \gt y\)Solution: $$ 8x + 15y = 14......(I) $$ $$ 2x - 3y = 17......(II) $$ By multiplying equation (II) with 4, we get $$ 8x - 12y = 68......(III) $$ Now, by subtracting equation (III) from eqaution (I), we get $$ 8x + 15y - 8x + 12y = 14 - 68 $$ $$ 27y = -54 $$ $$ y = -2 $$ By putting the value of y in equation (I), we get $$ 8x + 15y = 14......(I) $$ $$ 8x + 15 \ (-2) = 14 $$ $$ 8x - 30 = 14 $$ $$ 8x = 44 $$ $$ x = 5.5 $$ $$ Hence, \ x \gt y $$
(I). \(x^2 = 529\), (II). \(y = \sqrt{529}\)
\(x \gt y\)
\(x \lt y\)
\(x \ge y\)
\(x \le y\)
\(x = y\) or No relation can be established between \(x\) and \(y\)
Answer: (d) \(x \le y\)Solution: $$ x^2 = 529......(I) $$ $$ x = \pm 23 $$ $$ y = \sqrt{529}......(II) $$ $$ y = 23 $$ $$ Hence, \ x \le y $$
(I). \(x^2 = 729\), (II). \(y = \sqrt{-729}\)
\(x \gt y\)
\(x \lt y\)
\(x \ge y\)
\(x \le y\)
\(x = y\) or No relation can be established between \(x\) and \(y\)
Answer: (e) No relation can be established between \(x\) and \(y\)Solution: $$ x^2 = 729......(I) $$ $$ x = \pm 27 $$ $$ y = \sqrt{-729}......(II) $$ $$ y = \sqrt{-729} $$ Hence, No relation can be established.