SBI PO Quadratic Equation Questions and Answers set - 8

1 . Directions (Q. 1-5): In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give answer (1) if x > y (2) if x $\geq$y (3) if x < y (4) if x $\leq$y (5) if x = y or a relationship between x and y cannot be established. $Q.$ I. $x^ 2$ + 3x = 28 II. $y^ 2$ + 16y + 63 = 0 A.   $ x > y$ B.   $ x \geq y $ C.   $ x < y$ D.   $ x \leq y$ 2 . I. x = $\sqrt[3]{2197}$ II. y$^2$ = 169 A.   $ x > y$ B.   $ x \geq y $ C.   $ x < y$ D.   $ x \leq y$ 3 . I. $8x^ 2 $ - 49x + 45 = 0 II.$ 8y^ 2 $ - y - 9 = 0 A.   $ x > y$ B.   $ x \geq y $ C.   $ x < y$ D.   $ x \leq y$ 4 . I. 42x - 17y = -67 II. 7x + 12y = -26 A.   $ x > y$ B.   $ x \geq y $ C.   $ x < y$ D.   $ x \leq y$ 5 . I. $x^ 2 $ - 8x + 15 = 0 II. $2y^ 2 $ - 21y + 55 = 0 A.   $ x > y$ B.   $ x \geq y $ C.   $ x < y$ D.   $ x \leq y$ 6 . Directions (Q. 6-10): In each of these questions two equations (I) and (II) are given. You have to solve both the equations and give answer (1) if p > q (2) if p $\geq$ q (3) if p < q (4) if p $\leq$ q (5) if p = q or no relation can be established between p and q. $Q.$ I. $2.3p - 20.01 = 0$ II. $2.9q - p = 0$ A.   $ p > q$ B.   $ p \geq q $ C.   $ p < q$ D.   $ p \leq q$ 7 . I. p = $\sqrt{1764}$ II. $q^2$ = 1764 A.   $ p > q$ B.   $ p \geq q $ C.   $ p < q$ D.   $ p \leq q$ 8 . I. $p^ 2 $ - 26p + 168 = 0 II. $q^ 2 $ - 25q + 156 = 0 A.   p = q or no relation can be established between ‘p’ and ‘q’. B.   $ p \leq q$ C.   $ p < q$ D.   $ p \geq q $ 9 . I. $p^ 2 $ - 13p + 42 = 0 II. $q^ 2$ + q - 42 = 0 A.   $ p > q$ B.   $ p \geq q $ C.   $ p < q$ D.   $ p \leq q$ 10 . I. 6p - 5q = -47 II. 5p + 3q = 11 A.   $ p > q$ B.   $ p \geq q $ C.   $ p < q$ D.   $ p \leq q$

Answers & Solutions   1 .     Answer : Option B Explanation : I. $x^ 2$ + 3x - 28 = 0 or, $ x^ 2$ + 7x - 4x - 28 = 0 or, x (x + 7) - 4 (x + 7) = 0 or, (x - 4) (x + 7) = 0 or, x = 4, -7 II. $y^ 2$ + 9y + 7y + 63 = 0 or, y(y + 9) + 7(y + 9) = 0 or, (y + 7)(y + 9) = 0 or, y = -7, -9 $x \geq y$ 2 .     Answer : Option B Explanation : I. x = $\sqrt[3]{2197}$ x = 13 II. y$^2$ = 169 y = ± 13 x $\geq$ y 3 .     Answer : Option B Explanation : I. $8x^ 2$ - 40x - 9x + 45 = 0 or, 8x (x - 5) -9 (x - 5) = 0 or, (8x - 9) (x - 5) = 0 or, x = 5, 9/8 II. $8y^ 2$ + 8y - 9y -9 = 0 or, 8y (y + 1) -9 (y + 1) = 0 or, (8y - 9) (y + 1) = 0 y = $9\over 8$, -1 x$\geq$y 4 .     Answer : Option C Explanation : 42x - 17y = -67 42x + 72y = -156$\,\,\,\,\,$$\longrightarrow$ eqn (II) × 6 -$\,\,\,\,\,\,\,$ -$\,\,\,\,\,\,\,\,\,\,\,\,\,$ + ---------------------- -89y = 89 y = -$89\over 89$ = -1 & x = -2 x < y 5 .     Answer : Option D Explanation : I. $x^ 2$ - 8x + 15 = 0 or, $x^ 2 $ - 3x - 5x + 15 = 0 or, x (x - 3) -5 (x - 3) = 0 or, (x - 3) (x - 5) = 0 or, x = 3, 5 II. $2y^ 2 $ - 10y + 55 = 0 or, 2y (y - 5) -11 (y - 5) = 0 or, (y - 5)(2y - 11) = 0 y = 5, $11\over 2$ x $\leq$ y 6 .     Answer : Option A Explanation : I. 2.3p - 20.01 = 0 p = $20.01\over 2.3$ = 8.7 II. $2.9q - p$ = 0 or, p = 2.9q q = $8.7\over 2.9$ = 8.7 ie,. p > q 7 .     Answer : Option B Explanation : I. p = $\sqrt{1764}$ p = 42 II. $q^2$ = 1764 q = ± 42 P$\geq$ q 8 .     Answer : Option A Explanation : I.$ p^ 2$ - 26p + 168 = 0 $p^ 2$ - 12p - 14p + 168 = 0 p(p - 12) - 14(p - 12) = 0 (p - 12) (p - 14) = 0 p = 12, 14 II. $q^ 2$ - 25q + 156 = 0 $q^ 2$ - 13q - 12q + 156 = 0 q(q - 13) - 12(q - 13) = 0 (q - 12) (q - 13) = 0 q = 12, 13 Hence, no relation can be established between p and q 9 .     Answer : Option B Explanation : I. $p^ 2$ - l3q + 42 = 0 $p^ 2$ - 6p - 7p + 42 = 0 p(p - 6) - 7(p - 6) = 0 (p - 6) (p - 7) = 0 p = 6, 7 II. $q^ 2$ + q - 42 = 0 $q^ 2$ + 7q - 6p - 42 = 0 q(q + 7) - 6(q + 7) = 0 (q - 6)(q + 7) = 0 q = 6, - 7 ie p $\geq$ q 10 .     Answer : Option C Explanation : eqn(I) × 3 $\,\,\,\,\,\,$ 18p - 15q = -141 eqn (II) × 5 $\,\,\,\,$ 25p + 15q = 55 $\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$----------------------- $\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$ 43p = - 86 p = -$86\over 43$ = -2 5p + 3q = 11 3q = 11 - 5p 3q = 11 + 10 3q = 21 q = 7 ie p < q