Algebra For SBI PO : Set – 30
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 p > q
(b) if p ≥ q
(c) if p < q
(d) if p ≤ q
(e) if p = q or there is no relation between ‘p’ and ‘q’.
1) I. (p + q)2 = 3136
II. q + 2513 = 2569
(a) if p > q
(b) if p ≥ q
(c) if p < q
(d) if p ≤ q
(e) if p = q or there is no relation between ‘p’ and ‘q’.
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(c)
1) I. (p + q)2 = 3136
p + q = 56
II. q + 2513 = 2569
or, q = 2569 – 2513 = 56
Putting the value of q in (I) we have,
p = 0. -112
p < q
2. I. 4p2– 16p +15 = 0
II . 2q2 + 5q – 7 = 0
(a) if p > q
(b) if p ≥ q
(c) if p < q
(d) if p ≤ q
(e) if p = q or there is no relation between ‘p’ and ‘q’.
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(a)
4p2 – 16p + 15 = 0
or, 4p2 – 10p – 6p + 15 = 0
or, 2p (2p – 5) – 3 (2p – 5) = 0 or, (2p – 3) (2p – 5) = 0 p =
p =3/2, 5/2
II. 2q2 + 5q – 7 = 0
or, 2q2 + 7q – 2q – 7 = 0
or, q (2q + 7) – 1(2q + 7) = 0
or, (q – 1) (2q + 7) = 0
q = 1, -7/2
3. I. p2 = 49
II . q2+15q + 56 = 0
(a) if p > q
(b) if p ≥ q
(c) if p < q
(d) if p ≤ q
(e) if p = q or there is no relation between ‘p’ and ‘q’.
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(b)
I. p2 = 49
P = ±7
II. q2 + 15q + 56 = 0
or, q2 + 8q + 7q + 56 = 0
or, q(q + 8) + 7(q + 8) = 0
or, (q + 7) (q + 8) = 0
q = -7, -8
p ≥ q
4) I. 2p2 + 5p – 12 = 0
II. 2q2 – q – 1 = 0
(a) if p > q
(b) if p ≥ q
(c) if p < q
(d) if p ≤ q
(e) if p = q or there is no relation between ‘p’ and ‘q’.
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(e)
I. 2p2 + 5p – 12 = 0
or, 2p2 + 8p – 3p – 12 = 0
or, 2p (p + 4) – 3(p + 4) = 0
or, (2p – 3) (p + 4) = 0
p = 3/2, -4
II. 2q2 – q – 1 = 0
or, 2q2 – 2q + q – 1 = 0
or, 2q (q – 1) + 1(q – 1) = 0
or, (2q + 1) (q – 1) = 0
q = 1, – 1/2
No reaction between ‘p ’and ‘q ’.
5) I. p2– 12p + 35 = 0
II. q2– 25 = 0
(a) if p > q
(b) if p ≥ q
(c) if p < q
(d) if p ≤ q
(e) if p = q or there is no relation between ‘p’ and ‘q’.
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(b)
p2 – 12p + 35 = 0 or p2 – 5p – 7p + 35 = 0
or p (p – 5) – 7(p – 5) = 0
or (p – 7) (p – 5) = 0
p = 5, 7
II. q2 – 25 = 0
or, q2 = 25
q = ± 5
p ≥ q
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 x > y
(b) if x < y
(c) if x ≥ y
(d) if x ≤ y
(e) if x = y or there is no relation between ‘x’ and ‘y’.
6) I. 3x2 + 7x + 2 = 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 there is no relation between ‘x’ and ‘y’.
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(c)
3x2 + 6x + x + 2 = 0
or 3x(x + 2) + 1(x + 2) = 0
or (x + 2) (3x + 1) = 0 x = –2, 1/3
II. 2y2 + 4y + 5y + 10 = 0
or 2y (y + 2) + 5 (y + 2) = 0
or (2y + 5) (y + 2) = 0
y = –2,- 5/2
x ≥ y
7) I. x2 + x – 2 = 0
II. y2 – 3y + 2 = 0
(a) if x > y
(b) if x < y
(c) if x ≥ y
(d) if x ≤ y
(e) if x = y or there is no relation between ‘x’ and ‘y’.
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(d)
x2 + 2x – x – 2 = 0 or x(x + 2)– 1(x + 2) = 0
or (x – 1)
(x + 2) = 0 x = 1, –2
II. y 2 – y – 2y + 2 = 0
or y (y – 1) – 2 (y – 1) = 0 or
(y – 1) (y – 2) y = 1, 2
x ≤ y
8) I. 20x2 – 51x + 27 = 0
II. 15y2 – 16y + 4 = 0
(a) if x > y
(b) if x < y
(c) if x ≥ y
(d) if x ≤ y
(e) if x = y or there is no relation between ‘x’ and ‘y’.
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(a)
20x2 – 15x – 36x + 27 = 0
or 5x(4x – 3) – 9(4x – 3) = 0
or (5x – 9) (4x – 3) = 0
x = 9/53/4
II. 5y2 – 10y – 6y + 4 = 0
or 5y (3y – 2) – 2(3y – 2) = 0
or (5y – 2) (3y – 2)
y= 2/5, 2/3
x > y
9. I. 7x2 + 16x – 15 = 0
II. y2 – 6y – 7 = 0
(a) if x > y
(b) if x < y
(c) if x ≥ y
(d) if x ≤ y
(e) if x = y or there is no relation between ‘x’ and ‘y’.
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(e)
7x2 + 21x – 5x – 15 = 0
or 7x(x + 3) – 5(x + 3) = 0
or (x + 3) (7x – 5) = 0
x = -3,
II. y2 – 7y + y – 7 = 0
or y (y – 7) + 1 (y – 7) = 0
or (y + 1) (y – 7)
y =– 1, 7
Therefore, no relation between ‘x ’and ‘y ’.
10) I. x2 = 729
II. y2 + 58y + 840 = 0
(a) if x > y
(b) if x < y
(c) if x ≥ y
(d) if x ≤ y
(e) if x = y or there is no relation between ‘x’ and ‘y’.
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(a)
I. x2 = 729
x = ±27
II. y2 + 58y + 840 = 0
or y2 + 28y + 30y + 840 = 0
or y (y + 28) + 30 (y + 28) = 0
or (y + 30) (y + 28) = 0
y = –30, –28
x > y
