Algebra For SBI PO : Set – 23

D.1-5): In each of these questions, two equations (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 a relationship between x and y cannot be established.

1) I. x2 + 3x = 28

II) y2 + 16y + 63 = 0

(a) if x > y

(b) if x ≥ y

(c)if x < y

(d) if x ≤ y

(e) if x = y or a relationship between x and y cannot be established.

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(b)

x2 + 3x – 28 = 0

or, x2 + 7x – 4x – 28 = 0

or, x (x + 7) – 4 (x + 7) = 0

or, (x – 4) (x + 7) = 0

or, x = 4, -7

II. y2 + 9y + 7y + 63 = 0

or, y(y + 9) + 7(y + 9) = 0

or, (y + 7)(y + 9) = 0

or, y = -7, -9

2) I. x = ∛2197

II) y2 = 169

(a) if x > y

(b) if x ≥ y

(c)if x < y

(d) if x ≤ y

(e) if x = y or a relationship between x and y cannot be established.

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(b)

x = ∛2197

x = 13

II. y2 = 169

y = ±13

3) I. 8x2 – 49x + 45 = 0

II) 8y2 – y – 9 = 0

(a) if x > y

(b) if x ≥ y

(c)if x < y

(d) if x ≤ y

(e) if x = y or a relationship between x and y cannot be established.

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(b)

8x2 – 40x – 9x + 45 = 0

or, 8x (x – 5) -9 (x – 5) = 0

or, (8x – 9) (x – 5) = 0

or, x = 5, 9/8

II. 8y2 + 8y – 9y -9 = 0

or, 8y (y + 1) -9 (y + 1) = 0

or, (8y – 9) (y + 1) = 0

∴y= 9/8, -1

4) I. 42x – 17y = -67

II) 7x + 12y = -26

(a) if x > y

(b) if x ≥ y

(c)if x < y

(d) if x ≤ y

(e) if x = y or a relationship between x and y cannot be established.

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(c)

42x – 17y = -67

42x + 72y = -156                    eqn (II) × 6

-89y = 89

∴y= (-89)/89= -1 and x= -2 

5) I. x2 – 8x + 15 = 0

II) 2y2 – 21y + 55 = 0

(a) if x > y

(b) if x ≥ y

(c)if x < y

(d) if x ≤ y

(e) if x = y or a relationship between x and y cannot be established.

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(d)

x2 – 8x + 15 = 0

or, x2 – 3x – 5x + 15 = 0

or, x (x – 3) -5 (x – 3) = 0

or, (x – 3) (x – 5) = 0

or, x = 3, 5

II. 2y2 – 10y + 55 = 0

or, 2y (y – 5) -11 (y – 5) = 0

or, (y – 5)(2y – 11) = 0

or y = 5, 11/2

D.6-10): In each of these questions two equations (I) and (II) are given. You have to solve both the equations and give answer

(a) if p > q

(b) if p ≥ q

(c)if p < q

(d) if p ≤ q

(e) if p = q or no relation can be established between p and q.

6) I. 2.3p – 20.01 = 0

II) 2.9q – p = 0

(a) if x > y

(b) if x ≥ y

(c)if x < y

(d) if x ≤ y

(e) if x = y or a relationship between x and y cannot be established.

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(a)

2.3p – 20.01 = 0

∴P= 20.01/2.3=8.7  

7) I. p = √1764

II) q2 = 1764

(a) if x > y

(b) if x ≥ y

(c)if x < y

(d) if x ≤ y

(e) if x = y or a relationship between x and y cannot be established.

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(b)

p = √1764

p = 42

II. q2 = 1764

q = + 42

ie p ≥ q

8) I. p2 – 26p + 168 = 0

II) q2 – 25q + 156 = 0

(a) if x > y

(b) if x ≥ y

(c)if x < y

(d) if x ≤ y

(e) if x = y or a relationship between x and y cannot be established.

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(e)

p2 – 26p + 168 = 0

p2 – 12p – 14p + 168 = 0

p(p – 12) – 14(p – 12) = 0

(p – 12) (p – 14) = 0

p = 12, 14

II. q2 – 25q + 156 = 0

q2 – 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) I. p2 – 13p + 42 = 0

II) q2 + q – 42 = 0

(a) if x > y

(b) if x ≥ y

(c)if x < y

(d) if x ≤ y

(e) if x = y or a relationship between x and y cannot be established.

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(b)

p2 – l3q + 42 = 0

p2 – 6p – 7p + 42 = 0

p(p – 6) – 7(p – 6) = 0

(p – 6) (p – 7) = 0

p = 6, 7

II. q2 + q – 42 = 0
q2 + 7q – 6p – 42 = 0

q(q + 7) – 6(q + 7) = 0
(q – 6)(q + 7) = 0

q = 6, – 7 ie p³ q

10) I. 6p – 5q = -47

II) 5p + 3q = 11

(a) if x > y

(b) if x ≥ y

(c)if x < y

(d) if x ≤ y

(e) if x = y or a relationship between x and y cannot be established.

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(c)

eqn(I) × 3             18p – 15q = -141

eqn (II) × 5 25p + 15q = 55

43p = -86

∴p= (-86)/43=-2

5p + 3q = 11

3q = 11 – 5p

3q = 11 + 10

3q = 21

q = 7 ie p < q

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