## Algebra For SBI PO : Set – 18

D.1-5) In the following questions two equations numbered I and II are given. You have to solve both the equations and Give answer:

(a) if x > y

(b) if x y

(c) if x < y

(d) if x y

(e) if x = y or the relationship cannot be established

1. I.

II.

(a) if x > y

(b) if x y

(c) if x < y

(d) if x y

(e) if x = y or the relationship cannot be established

(a) I.

or, 35x + 70 = 0 or, x =-70/35=2

II. 3y + 7 = 0 or y = -7/3

x > y

2. I.

II. y3 + 9.68+ 5.64 = 16.95

(a) if x > y

(b) if x y

(c) if x < y

(d) if x y

(e) if x = y or the relationship cannot be established

(e)

I.

II. y2 = 16.95 – 9.68 – 5.64 = 1.63

y = ±1.277

3. I.

II.4y3 = – (589 ÷ 4)+5y3

(a) if x > y

(b) if x y

(c) if x < y

(d) if x y

(e) if x = y or the relationship cannot be established

(a) I.

II. 5y3 – 4y3 =589/4

or y3 = 589/4

x > y

4. I. 12x2 + 11x + 12 = 10x2+22x

II. 13y2 – 18y + 3 = 9y2 – 10y

(a) if x > y

(b) if x y

(c) if x < y

(d) if x y

(e) if x = y or the relationship cannot be established

(b) I. 2x2 – 11x + 12 = 0

or, x = 4, 3/2

II. 4y2 – 8y + 3 = 0

y=3/2,1/2

x y

5. I.

II. y¼ × y¼ ×7 = 273 ÷ y½

(a) if x > y

(b) if x y

(c) if x < y

(d) if x y

(e) if x = y or the relationship cannot be established

(d)

I.

or,

or, or, x2 =1521

D.6-10): 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 and give answer

(a) if x > y

(b) if x y

(c) if x < y

(d) if x y

(e) if x = y or the relationship cannot be established

6. I.

II. 2y2 – 9y – 56 = 0

(a) if x > y

(b) if x y

(c) if x < y

(d) if x y

(e) if x = y or the relationship cannot be established

(e) I. x =

x = 7

II. 2y2 – 16y + 7y – 56 = 0

2y(y – 8) + 7(y – 8) = 0

(2y + 7) (y – 8) = 0

y=8,-7/2

7. I. 5x2 + 3x – 14 = 0

II. 2y2 – 9y + 10 = 0

(a) if x > y

(b) if x y

(c) if x < y

(d) if x y

(e) if x = y or the relationship cannot be established

(b) I. 5x2 + 10x – 7x – 14 = 0

or, 5x(x + 2) – 7(x + 2) = 0

or, (x + 2) (5x – 7) = 0

x=-2,7/5

II. 2y2 – 4y – 5y + 10 = 0

or, 2y(y – 2) – 5(y – 2) = 0

or, (2y – 5)(y – 2) = 0

or, y = 2,5/2

x < y

8. I. 8x2 + 31x + 21 = 0

II. 5y2 + 11y – 36 = 0

(a) if x > y

(b) if x y

(c) if x < y

(d) if x y

(e) if x = y or the relationship cannot be established

(e) I. 8x2 + 24x + 7x + 21 = 0

or, 8x(x + 3) + 7(x + 3) = 0

or, (x + 3) (8x + 7) = 0

x=-3.-7/8

II. 5y2 + 20y – 9y – 36 = 0

or, 5y(y + 4) – 9(y + 4) = 0

or, (y + 4) (5y – 9) = 0

y=-4,9/5

Hence, no relation exists between x and y.

9. I. 3x – y = 12

II. y =

(a) if x > y

(b) if x y

(c) if x < y

(d) if x y

(e) if x = y or the relationship cannot be established

(b) I. y =

or,  y = 33

II.

x y

10. I. 15x2 + 68x + 77 = 0

II. 3y2 + 29y + 68 = 0

(a) if x > y

(b) if x y

(c) if x < y

(d) if x y

(e) if x = y or the relationship cannot be established

(a) I. 15x2 + 68x + 77 = 0

or, 15x2 + 35x + 33x + 77 = 0

or, 5x(3x + 7) + 11(3x + 7) = 0

or, (5x + 11) (3x + 7) = 0

x=-7/3,-11/5

II. 3y2 + 29y + 68 = 0

or, 3y2 + 12y + 17y + 68 = 0

or, 3y(y + 4) + 17(y + 4) = 0

or, (y + 4) (3y + 17) = 0

y=4 , -17/3