Algebra For SBI PO : Set

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

(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

(d) if x ≤ y

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

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(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

(d) if x ≤ y

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

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(e)

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

(d) if x ≤ y

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

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(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

(d) if x ≤ y

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

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(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. y^¼ × y^¼ ×7 = 273 ÷ y^½

(a) if x > y

(b) if x ≥ y

(d) if x ≤ y

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

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(d)

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

(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

(d) if x ≤ y

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

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(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

(d) if x ≤ y

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

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(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

(d) if x ≤ y

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

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(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

(d) if x ≤ y

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

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(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

(d) if x ≤ y

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

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(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

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Algebra For SBI PO : Set – 18