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Solutions

S1. Ans.(c)

Sol.

? ≃ 1.8 × 25500 +50

100× 29000 ≃ 60,400

S2. Ans.(a)

Sol.

? ≃ 172 × 15 ÷ 25

≃ 103

S3. Ans.(b)

Sol.

? ≃ 175 × 28 + 275 × 28

≃ 12,600

S4. Ans.(c)

Sol.

? ≃ 325 × 16 ÷ 4 + 37

≃ 1337 ≃ 1340

S5. Ans.(c)

Sol.

? ≃ 1164 × 128 ÷ 8 + 969

≃ 19593

S6. Ans.(c)

Sol.

? ≃ 25 + 27

≃ 52

S7. Ans.(a)

Sol.

? ≃69

100× 700 +

33

100× 400

≃ 483 +132

≃ 615

S8. Ans.(d)

Sol.

? ≃(9320 + 5400 + 1000)

(500 + 930 + 660)≃ 7.5


S9. Ans.(d)

Sol.

64

100× 8924 +

?

100× 5324 ≃ 6828

⇒ ? ≃ 21

S10. Ans.(a)

Sol.

? ≈67×800

100− 231 +

23×790

100

≈ 536 − 231 + 181.7

≈ 490

S11. Ans.(c)

Sol.

? ≈ 500 + 50 × 50

≈ 3000

S12. Ans.(c)

Sol.

? ≈74×1300

100+

10×1900

100

≈ 960 + 190

≈1150

S13. Ans.(a)

Sol.

? ≈67×800

100− 231 +

23×790

100

≈ 536 − 231 + 181.7

≈ 490

S14. Ans.(b)

Sol. 129 − 224 = −95

S15. Ans.(b)

Sol. ? ≈ 1956 + 8.25 + 7.28 ≈ 1970

S16. Ans.(c)

Sol.

? ≃68

100× 1400 −

14

100× 1300

≃ 770


S17. Ans.(d)

Sol.

? ≃ 5467 – 3245 + 1123 – 2310

≃ 1035

S18. Ans.(d)

Sol.

? ≃6000

10+ 671 − 140

≃ 1131

≃ 1130

S19. Ans.(e)

Sol.

? ≃ 900 – 81 – 125

≃ 694

S20. Ans.(b)

Sol.

? ≃56 × 24 × 8

16

≃ 672

≃ 670

S21. Ans.(b)

Sol.

? ≈ 12 × 15 − 9 × 7

≈ 180 − 63 = 117

S22. Ans.(e)

Sol.

? ≈8400 × 105

100− 5600 ×

3

700+ 10

≈ 8820 − 24 + 10 = 8806

S23. Ans.(e)

Sol.

≈ 30² – 20² – ? = 22²

⇒ 900 – 400 – ? = 484

⇒ 500 – ? = 484

⇒ ? = 500 – 484 = 16


S24. Ans.(c)

Sol.

? ≈ (5)2 + (21)3 + √1089

≈ 25 + 9261 + 33 ≈ 9319

S25. Ans.(b)

Sol.

? = √653

× 23.93 − 31.04

≈ √643

× 24 − 31

≈ 4 × 24 − 31 ≈ 96 − 31 ≈ 65

S26. Ans.(a)

Sol. 56

100× 958 +

67

100× 1008 = ? × 20

⇒ ? = 60.592

S27. Ans.(c)

Sol.

(?)² = 77 + 92

= 169

⇒ ? = ± 13

S28. Ans.(c)

Sol.

? =47 × 588

28 × 120

= 8.225

S29. Ans.(d)

Sol.

? =5

8×

4

9×

3

5× 222

= 37

S30. Ans.(b)

Sol.

? = 4441

S31. Ans.(d)

Sol.

441 – 63 = ? × 8

? = 47.25


S32. Ans.(e)

Sol.

23

16=? −

7

64

? =23

16+

7

64=

92+7

64

? =99

64= 1

35

64

S33. Ans.(d)

Sol.

5.76 × 10−7 ÷ (0.000048) = 0.012

S34. Ans.(c)

Sol.

(58

7× 1568) + 265.75 − 2455.6 =?

? = 13257.75 – 2455.6

? = 10802.15

S35. Ans.(e)

Sol. (1.1)2 − (4.24 × 0.04) =?

Or, ?=1.0404

S36. Ans.(d)

Sol.

(? )1

2 = 4 + 6

= 10

? = 100


S37. Ans.(b)

Sol. ? = √169 + 7 − 27 + 107

= √256

= 16

S38. Ans.(b)

Sol. = (0.7)?+3 =(0.7)8×(0.7)12

(0.7)16

= (0.7)4

⇒ ? = 4 – 3

⇒ ? = 1

S39. Ans.(c)

Sol.

(? )2

25=

45

100× 45 × 100

⇒ ? = ± 225

S40. Ans.(a)

Sol. ? = 15.8

S41. Ans.(a)

Sol. ? =11

4×

4

15×

125

16× 256

=4400

3

= 14662

3

S42. Ans.(c)

Sol. ? = 101 × 73 + 251

= 7373 + 251

= 7624

S43. Ans.(e)

Sol.

? =(0.7 − 0.5)(0.7 + 0.5)(0.72 + 0.52)

(0.7 − 0.5)(0.72 + 0.7 × 0.5 + 0.52)

? =1.2 × 0.74

1.09

? =88.8

109

? =444

545


S44. Ans.(d)

Sol.

? =36

100× 545 +

32

100× 215 −

47

100× 1300

= 196.2 + 68.8 − 611 = −346

S45. Ans.(d)

Sol. ? = 35 ÷ 7 × 342 = 1710

S46. Ans.(b)

Sol.

35 ÷ 7 × 342 = ? Or, ? = 1710

S47. Ans.(a)

Sol.

805 + 187 + 2? = 1000

Or, 2? = 8

Or, ? = 3

S48. Ans.(d)

Sol.

18? = 187.9 × 180.1 ÷ 184 Or, ? = 7.9 + 0.1 - 4 = 4

S49. Ans.(b)

Sol. 35

?=

22

7+

13

5+

36

5−

38

7−

18

35=

245

35

Or, ? =35×35

245= 5

S50. Ans.(e)

Sol.

88.2 − 4 = 10−? Or, ? = -74.2

S51. Ans.(a)

Sol.

I. 2𝑥2 + 4𝑥 + 7𝑥 + 14 = 0

2𝑥(𝑥 + 2) + 7(𝑥 + 2) = 0 𝑥 = −2, −3.5

II. (2𝑦 + 3)2 = 0

𝑦 = −1.5, −1.5

x < y


S52. Ans.(b)

Sol.

I. 𝑥 = ±2

II. 𝑦2 + 3𝑦 + 3𝑦 + 9 = 0

𝑦 = −3, −3

x > y

S53. Ans.(d)

Sol.

I. 𝑥2 − 3𝑥 − 4𝑥 + 12 = 0

𝑥(𝑥 − 3) − 4(𝑥 − 3) = 0

𝑥 = 3, 4

II. 𝑦2 + 4𝑦 − 3𝑦 − 12 = 0

𝑦(𝑦 + 4) − 3(𝑦 + 4) = 0

𝑦 = 3, −4

x ≥ y

S54. Ans.(e)

Sol.

I. 𝑥 = ±27

II. 𝑦 = 23

∴ No relation

S55. Ans.(e)

Sol.

I. 𝑥4 = 398 + 227 = 625

𝑥 = ±5

II. 𝑦2 = 346 − 321

𝑦 = ±5

no relation

S56. Ans.(e)

Sol. 𝑥 =1

3,

−1

3

4𝑦2 + 12𝑦 − 𝑦 − 3 = 0

4𝑦(𝑦 + 3) − 1(𝑦 + 3) = 0

𝑦 =1

4, −3

So, no relation can be established

S57. Ans.(a)

Sol. 𝑥 = √5, −√5

4𝑦2 − 14𝑦 − 10𝑦 + 35 = 0

2𝑦(2𝑦 − 7) − 5(2𝑦 − 7) = 0

𝑦 =5

2,

7

2

𝑥 < 𝑦


S58. Ans.(d)

Sol. 𝑥2 − 7𝑥 + 2𝑥 − 14 = 0

𝑥(𝑥 − 7) + 2(𝑥 − 7) = 0

𝑥 = 7, −2

𝑦2 + 5𝑦 + 2𝑦 + 10 = 0

𝑦 = −2, −5

𝑥 ≥ y

S59. Ans.(d)

Sol. Solving these equations.

𝑥 = −3, 𝑦 = −4

𝑥 ≥ 𝑦

S60. Ans.(d)

Sol. 2𝑥2 − 4𝑥 − √13𝑥 + 2√13 = 0

2𝑥(𝑥 − 2) − √13(𝑥 − 2) = 0

𝑥 =√13

2, 2

10𝑦2 − 18𝑦 − 5√13𝑦 + 9√13 = 0

2𝑦(5𝑦 − 9) − √13(5𝑦 − 9) = 0

𝑦 =√13

2,

9

5

𝑥 ≥ 𝑦

S61. Ans.(c)

Sol. I. 3x² + 10x + 8 = 0

⇒ 3x² + 6x + 4x + 8 = 0

⇒ (x + 2) (3x + 4) = 0

⇒ x = –2, –4/3

II. 3y² + 7y + 4 = 0

⇒ 3y² + 3y + 4y + 4 = 0

⇒ (y + 1) (3y + 4) = 0

⇒ y = –1, –4/3

y ≥ x

S62. Ans.(e)

Sol. I. 2x² + 21x + 10 = 0

⇒ 2x² + 20 + x + 10 = 0

⇒ (x + 10) (2x + 1) = 0

⇒ x = –10, –1/2


II. 3y² + 13y + 14 = 0

⇒ 3y² + 6y + 7y + 14 = 0

⇒ (y + 2) (3y + 7) = 0

⇒ y = –2, –7/3

No relation

S63. Ans.(e)

Sol. I. x² + x – 12 = 0

⇒ x² + 4x – 3x – 12 = 0

⇒ (x + 4) (x – 3) = 0

⇒ x = 3, –4

II. y² + 2y – 8 = 0

⇒ y² + 4y – 2y – 8 = 0

⇒ (y + 4) (y – 2) = 0

⇒ y = – 4, 2

No relation

S64. Ans.(e)

Sol. I. 4x² – 13x + 9 = 0

⇒ 4x² – 4x – 9x + 9 = 0

⇒ (x – 1) (4x – 9) = 0

⇒ x = 1, 9/4

II. 3y² – 14y + 16 = 0

⇒ 3y² – 6y – 8y + 16 = 0

⇒ (y – 2) (3y – 8) = 0

⇒ y = 2, 8/3

No relation

S65. Ans.(b)

Sol. I. 8x² + 18x + 9 = 0

⇒ 8x² + 12x + 6x + 9 = 0

⇒ (2x + 3) (4x + 3) = 0

⇒ x = –3/2, –3/4

II. 4y² + 19y + 21 = 0

⇒ 4y² + 12y + 7y + 21 = 0

⇒ (y + 3) (4y + 7) = 0

⇒ x = –3, –7/4

x > y


S66. Ans.(a)

Sol. I. 3x² + 16x + 21 = 0

⇒ 3x² + 9x + 7x + 21 = 0

⇒ (x + 3) (3x + 7) = 0

⇒ x = –3, –7/3

II. 6y² + 17y + 12 = 0

⇒ 6y² + 9y + 8y + 12 = 0

⇒ 3y (2y + 3) + 4 (2y + 3) = 0

⇒ y = – 3/2, –4/3

y > x

S67. Ans.(b)

Sol. I. 16x² + 20x + 6 = 0

⇒ 8x² + 10x + 3 = 0

⇒ 8x² + 4x + 6x + 3 = 0

⇒ (2x + 1) (4x + 3) = 0

⇒ x = –1/2, –3/4

II. 10y² + 38y + 24 = 0

⇒ 5y² + 19y + 12 = 0

⇒ 5y² + 15y + 4y + 12 = 0

⇒ (y + 3) (5y + 4) = 0

y = –3, –4/5

x > y

S68. Ans.(c)

Sol. I. 8x² + 6x – 5 = 0

⇒ 8x² + 10x – 4x – 5 = 0

⇒ (4x + 5) (2x – 1) = 0

⇒ x = ½, –5/4

II. 12y² – 22y + 8 = 0

⇒ 6y² – 11y + 4 = 0

⇒ 6y² – 3y – 8y + 4 = 0

⇒ (2y – 1) (3y – 4) = 0

⇒ y = 1/2, 4/3

y ≥ x

S69. Ans.(a)

Sol. I. 17x² + 48x – 9 = 0

⇒ 17x² + 51x – 3x – 9 = 0

⇒ (x + 3) (17x – 3) = 0

⇒ x = 3/17, – 3


II. 13y² – 32y + 12 = 0

⇒ 13y² – 26y – 6y + 12 = 0

⇒ (y – 2) (13y – 6) = 0

⇒ y = 2, 6/13

y > x

S70. Ans.(d)

Sol. I. 8x² + 26x + 15 = 0

⇒ 8x² + 20x + 6x + 15 = 0

⇒ 4x (2x + 5) + 3(2x + 5) = 0

⇒ (2x + 5) (4x + 3) = 0

⇒ x = – 5/2, –3/4

II. 4y² + 24y + 35 = 0

⇒ 4y² + 10y + 14y + 35 = 0

⇒ 2y (2y + 5) + 7 (2y + 5) = 0

⇒ (2y + 5) (2y + 7) = 0

⇒ y = –5/2, –7/2

x ≥ y

S71. Ans.(a)

Sol. I. 6x² + 19x + 15 = 0

⇒ 6x² + 9x + 10x + 15 = 0

⇒ (2x + 3) (3x + 5) = 0

⇒ x = –3/2, –5/3

II. 24y² + 11y + 1 = 0

⇒ 24y² + 8y + 3y + 1= 0

⇒ (3y + 1) (8y + 1) = 0

⇒ y = –1/3, –1/8

y > x

S72. Ans.(e)

Sol. I. 2x² + 11x + 15 = 0

⇒ 2x² + 6x + 5x + 15 = 0

⇒ (x + 3) (2x + 5) = 0

⇒ x = – 3, –5/2

II. 4y² + 22y + 24 = 0

⇒ 2y² + 11y + 12 = 0

⇒ 2y² + 8y + 3y + 12 = 0

⇒ (y + 4) (2y + 3) = 0

⇒ y = –4, –3/2

No relation


S73. Ans.(b)

Sol. I. 2x² + 9x + 9 = 0

⇒ 2x² + 6x + 3x + 9 = 0

⇒ (x + 3) (2x + 3) = 0

⇒ x = –3, –3/2

II. 2y² + 17y + 36 = 0

⇒ 2y² + 8y + 9y + 36 = 0

⇒ (y + 4) (2y + 9) = 0

y = – 4, –9/2

x > y

S74. Ans.(a)

Sol.

I. 5x² + 29 + 20 = 0

⇒ 5x² + 25x + 4x + 20 = 0

⇒ (x + 5) (5x + 4) = 0

⇒ x = –5, –4/5

II. 25y² + 25y + 6 = 0

⇒ 25y² + 15y + 10y + 6 = 0

⇒ (5y + 3) (5y + 2) = 0

⇒ y = – 3/5, –2/5

y > x

S75. Ans.(a)

Sol.

I. 3x² – 16x + 21 = 0

⇒ 3x² – 9x – 7x + 21 = 0

⇒ (x – 3) (3x – 7) = 0

⇒ x = 3, 7/3

II. 3y² – 28y + 65 = 0

⇒ 3y² – 15y – 13y + 65 = 0

⇒ (y – 5) (3y – 13) = 0

⇒ y = 5, 13/3

y > x

S76. Ans.(b)

Sol. Series is × 1.5, × 2, × 2.5, × 3, × 3.5

∴ ? = 135 × 3.5 = 472.5

S77. Ans.(d)

Sol. Series is ÷ 2 + 2, × 2+ 2, ÷ 2 + 2, × 2 + 2, ÷ 2 + 2

∴ ? = 78 ÷ 2 + 2 = 41


S78. Ans.(c) Sol. Series is + 22, + 33, + 42, +53, + 62 ∴ ? = 201 + 62 = 237 S79. Ans.(e) Sol. Series is + 1.52, + 2.52, + 3.52, 4.52, + 5.52 ∴ ? = 46 + (5.5)2 = 76.25 S80. Ans.(d) Sol. Series is × 2 – 7, × 2 – 6, × 2 – 5, × 2 – 4, × 2 – 3 ∴ ? = 2114 × 2 – 3 = 4225 S81. Ans.(c) Sol. Pattern is +2², +3², +4², +5², +6² ∴ ? = 177 + 25 = 202 S82. Ans.(d) Sol. Pattern is +16, –32, +48, –64, +80 ∴ ? = 307 + 80 = 387 S83. Ans.(d) Sol. Pattern is × 3 – 1, × 3 – 2, × 3 –3, × 3 – 4, × 3 – 5, ∴ ? = 347 × 3 – 5 = 1036


S84. Ans.(d)

Sol. Patter is ×2, ×4, ×6, ×8, ×10

∴ ? = 576 × 8 = 4608

S85. Ans.(b)

Sol. Patter is +312, +312, +312, +312, ….

∴ ? = 780 + 312 = 1092

S86. Ans. (c)

Sol. Pattern is (÷ 2), (÷ 2), (÷ 2) ………………

∴ 474 ÷ 2 = 237

S87. Ans. (a)

Sol. Pattern is (−19 × 1), (−19 × 2), (−19 × 3) ……………

∴ 317 − 19 × 3 = 260

S88. Ans. (d)

Sol. Pattern is (× 1 − 2), (× 4 − 3), (× 9 − 4), (× 16 − 5), (× 25 − 6)

∴ 3353 × 16 − 5 = 53643

S89. Ans. (b)

Sol. Pattern is 14, 24, 34, 44, 54

54 = 625

S90. Ans. (e)

Sol. Pattern is (÷ 2 + 0.5), (÷ 2 + 0.5)……….

∴ 18.5 ÷ 2 + 0.5 = 9.75

S91. Ans.(b)

Sol. Pattern is × 2 + 1, × 4 + 3, × 6 + 5, × 8 + 7, × 10 + 9

∴ ? = 1151 × 10 + 9

= 11519

S92. Ans.(c)

Sol. Pattern is × 1 + 1, × 2 + 2, × 3 + 3, × 4 + 4, × 5 + 5, ….

∴ ? = 63 × 4 + 4

= 256

S93. Ans.(a)

Sol. Series is


S94. Ans.(b)

Sol. Pattern is × 0.5 + 2, × 1 + 2, × 1.5 + 2, × 2 + 2, × 2.5 + 2

∴ ? = 27 × 2.5 + 2

= 69.5

S95. Ans.(d)

Sol. Series is

S96. Ans.(d)

Sol. Series is

S97. Ans.(b)

Sol. Pattern is ÷8, ÷6, ÷4, ÷2

∴ ? = 12.5 ÷ 4

= 3.125

S98. Ans.(a)

Sol. Series is

S99. Ans.(d)

Sol. Pattern is + 14 × 1, + 14 × 3, + 14 × 9, + 14 × 27

∴ ? = 564 + 14 × 81

= 1698

S100. Ans.(b)

Sol. Pattern is × 1 + 1, × 2 + 2, × 3 + 3, × 4 + 4, × 5 + 5

∴ ? = 352 × 5 + 5

= 1765

| No. 1 APP for Banking & SSC Preparation Website: Email. I. x² + x – 12 = 0 ⇒ x² + 4x – 3x...

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