Correct Answer: (36, 223, 6)

Solution : Given:
(17, 126, 7); (31, 286, 9)

Here, (17, 126, 7)→(17 × 7) + 7 = 119 + 7 = 126
(31, 286, 9)→(31 × 9) + 7 = 279 + 7 = 286

Let's check each option –
First option: (29, 270, 9)→(29 × 9) + 7 = 261 + 7 = 268 ≠ 270
Second option: (36, 223, 6)→(36 × 6) + 7 = 216 + 7 = 223
Third option: (42, 173, 4)→(42 × 4) + 7 = 168 + 7 = 175 ≠ 173
Fourth option: (12, 117, 9)→(12 × 9) + 7 = 108 + 7 = 115 ≠ 117

So, only the second option follows the same pattern as followed by the sets given in question. Hence, the second option is correct.

Correct Answer: (99, 82, 71)

Solution : Given:
(53, 36, 25); (71, 54, 43)

In the above-given set of numbers, divide the sum of the first and third numbers by 2 and subtract 3 from the resultant to get the second number –
⇒(53, 36, 25)→{(53 + 25) ÷ 2} – 3 = {78 ÷ 2} – 3 = 39 – 3 = 36
⇒(71, 54, 43)→{(71 + 43) ÷ 2} – 3 = {114 ÷ 2} – 3 = 57 – 3 = 54
Let's check each option –

First option: (41, 23, 18)→{(41 + 18) ÷ 2} – 3 = {59 ÷ 2} – 3 = 29.5 – 3 = 26.5 ≠ 23
Second option: (99, 82, 71)→{(99 + 71) ÷ 2} – 3 = {170 ÷ 2} – 3 = 85 – 3 = 82
Third option: (66, 53, 41)→{(66 + 41) ÷ 2} – 3 = {107 ÷ 2} – 3 = 53.5 – 3 = 50.5 ≠ 53
Fourth option: (32, 14, 7)→{(32 + 7) ÷ 2} – 3 = {39 ÷ 2} – 3 = 19.5 – 3 = 16.5 ≠ 14

So, only the second option follows the same pattern as followed by the given set of numbers. Hence, the second option is correct.

Correct Answer: (36, 106, 17)

Solution : Given:
(26, 120, 34); (14, 110, 41)

Here, (26, 120, 34)→(26 + 34) × 2 = 60 × 2 = 120
(14, 110, 41)→(14 + 41) × 2 = 55 × 2 = 110

Now, let's check the given options –
First option: (36, 106, 17)→(36 + 17) × 2 = 53 × 2 = 106
Second option: (72, 240, 16)→(72 + 16) × 2 = 88 × 2 = 176 ≠ 240
Third option: (44, 114, 24)→(44 + 24) × 2 = 68 × 2 = 136 ≠ 114
Fourth option: (15, 450, 8)→(15 + 8) × 2 = 23 × 2 = 46 ≠ 450

So, only the first option follows the same pattern as followed by the given set of numbers. Hence, the first option is correct.

Correct Answer: (61, 54, 45)

Solution : Given:
(82, 75, 66); (69, 62, 53)

The pattern is as follows –
(82, 75, 66)→82 – 75 = 7; 75 – 66 = 9
(69, 62, 53)→69 – 62 = 7; 62 – 53 = 9

Let's check the options –
First option: (21, 16, 9)→21 – 16 = 5 ≠ 7; 16 – 9 = 7 ≠ 9
Second option: (49, 52, 35)→49 – 52 = –3 ≠ 7; 52 – 35 = 17 ≠ 9
Third option: (61, 54, 45)→61 – 54 = 7; 54 – 45 = 9
Fourth option: (36, 28, 21)→36 – 28 = 8 ≠ 7; 28 – 21 = 7 ≠ 9

So, only the third option follows the same pattern as followed by the given set of numbers. Hence, the third option is correct.

Correct Answer: (6, 8, 144)

Solution : Given:
(4, 6, 72); (5, 7,105)

Add 2 to the first number, to get the second number and multiply the product of the first and second numbers by 3, to get the third number –
(4, 6, 72)→4 + 2 = 6; 4 × 6 × 3 = 72
(5, 7, 105)→5 + 2 = 7; 5 × 7 × 3 = 105

Let's check each option –
First option: (6, 8, 144)→6 + 2 = 8; 6 × 8 × 3 = 144
Second option: (2, 5, 40)→2 + 2 = 4 ≠ 5; 2 × 5 × 3 = 30 ≠ 40
Third option: (3, 6, 36)→3 + 2 = 5 ≠ 6; 3 × 6 × 3 = 54 ≠ 36
Fourth option: (6, 9, 108)→6 + 2 = 8 ≠ 9; 6 × 9 × 3 = 162 ≠ 108

So, only the first option follows the same pattern as the given number pair. Hence the first option is correct.

Correct Answer: (30, 90, 270)

Solution : Given:
(10, 30, 90); (20, 60,180)

Multiply the first number by 3, to get the second number and multiply the second number by 3, to get the third number –
(10, 30, 90)→10 × 3 = 30; 30 × 3 = 90
(20, 60, 180)→20 × 3 = 60; 60 × 3 = 180

Let's check each option –
First option: (30, 45, 60)→30 × 3 = 90 ≠ 45; 45 × 3 = 135 ≠ 60
Second option: (30, 90, 270)→30 × 3 = 90; 90 × 3 = 270
Third option: (30, 60, 90)→30 × 3 = 90 ≠ 60; 60 × 3 = 180 ≠ 90
Fourth option: (30, 90, 310)→30 × 3 = 90; 90 × 3 = 270 ≠ 310

So, only the second option follows the same pattern as the given number pair. Hence, the second option is correct.

Correct Answer: (4, 18, 82)

Solution : Given:
(6, 12, 228); (8, 3, 515)

Here, (6, 12, 228)→(6)³ + 12 = 216 + 12 = 228
(8, 3, 515)→(8)³ + 3 = 512 + 3 = 515

Let's check the options –
First option: (3, 28, 56)→(3)³ + 28 = 27 + 28 = 55 ≠ 56
Second option: (13, 11, 172)→ (13)³ + 11 = 2197 + 11 = 2208 ≠ 172
Third option: (4, 18, 82)→(4)³ + 18 = 64 + 18 = 82
Fourth option: (9, 23, 119)→(9)³ + 23 = 729 + 23 = 752 ≠ 119

So, only the third option follows the same pattern as followed by the given set of numbers. Hence, the third option is correct. 

Correct Answer: (6, 144, 8)

Solution : Given:
(2, 114, 19); (12, 216, 6)

In the given sets, multiply the first and the third numbers by 3 to obtain the second number.
(2, 114, 19)→3 × 2 × 19 = 6 × 19 = 114
(12, 216, 6)→3 × 12 × 6 = 36 × 6 = 216
Now, let's check the options –
First option: (5, 20, 2)→3 × 5 × 2 = 15 × 2 = 30 ≠ 20
Second option: (6, 144, 8)→3 × 6 × 8 = 18 × 8 = 144
Third option: (11, 176, 4)→3 × 11 × 4 = 33 × 4 = 132 ≠ 176
Fourth option: (4, 128, 7)→3 × 4 × 7 = 12 × 7 = 84 ≠ 128

So, only the second option follows the same pattern as followed by the given set of numbers. Hence, the second option is correct.