Correct Answer: (88, 100, 50)

Solution : Given:
(72, 84, 42); (96,108, 54)

Add 12 to the first number, to get the second number, and divide the second number by 2, to get the third number –
⇒ (72, 84, 42)→17 + 12 = 84; 84 ÷ 2 = 42
⇒ (96,108, 54)→96 + 12 = 108; 108 ÷ 2 = 54

Let's check each option –
First option: (92, 102, 51)→92 + 12 = 104 ≠ 102; 102 ÷ 2 = 51
Second option: (112, 120, 60)→112 + 12 = 124 ≠ 120; 120 ÷ 2 = 60
Third option: (88, 100, 50)→88 + 12 = 100; 100 ÷ 2 = 50
Fourth option: (64, 86, 42)→64 + 12 = 74 ≠ 86; 86 ÷ 2 = 43

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

Correct Answer: (61, 57, 53)

Solution : Given:
(39, 81, 123); (56, 32, 8)

Here, (39, 81, 123)→123 – 81 = 42; 81 – 39 = 42
(56, 32, 8)→56 – 32 = 24; 32 – 8 = 24

Let's check the options –
First option: (61, 57, 53)→61 – 57 = 4; 57 – 53 = 4
Second option: (42, 33, 15)→42 – 33 = 9; 33 – 15 = 18
Third option: (97, 63, 38)→97 – 63 = 34; 63 – 38 = 25
Fourth option: (24, 35, 31)→35 – 24 = 11; 35 – 31 = 4

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: (33, 133, 1133)

Solution : Given:
(99,199,1199); (15,115,1115)

Here, (99, 199, 1199)→99 + (10)² = 199; 199 + (10)³ = 1199
(15, 115, 1115)→15 + (10)² = 115; 115 + (10)³ = 1115

Let's check each option –
First option: (11, 111, 1000)→11 + (10)² = 111; 111 + (10)³ = 1111 ≠ 1000
Second option: (33, 133, 1133)→33 + (10)² = 133; 133 + (10)³ = 1133
Third option: (22, 222, 2222)→22 + (10)² = 122 ≠ 222; 122 + (10)³ = 1122 ≠ 2222
Fourth option: (77, 717, 7117)→77 + (10)² = 177 ≠ 717; 177 + (10)³ = 1177 ≠ 7117

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

Correct Answer: (374, 22, 17)

Solution : Given:
(312, 24, 13); (645, 43, 15)

In the given sets, multiply the second and the third numbers to get the first number.
(312, 24, 13)→24 × 13 = 312
(645, 43, 15)→43 × 15 = 645
Let's check the options –
First option: (347, 27, 12)→27 × 12 = 324 ≠ 347
Second option: (347, 22, 17)→22 × 17 = 374 ≠ 347
Third option: (374, 17, 12)→12 × 17 = 204 ≠ 374
Fourth option: (374, 22, 17)→22 × 17 = 374

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

Correct Answer: (16, 17, 33)

Solution : Given:
(12, 22, 34); (14, 15, 29)

Add the first and second numbers, to get the third number –
(12, 22, 34)→12 + 22 = 34
(14, 15, 29)→14 + 15 = 29

Let's check each option –
First option: (10, 20, 24)→10 + 20 = 30 ≠ 24
Second option: (16, 17, 33)→16 + 17 = 33
Third option: (8, 9, 15)→8 + 9 = 17 ≠ 15
Fourth option: (14, 15, 19)→14 + 15 = 29 ≠ 19

So, only the first option follows the same pattern. Hence, the first option is correct.

Correct Answer: (7, 5, 318)

Solution : Given:
(8, 9, 431); (11, 8, 1267)

Here, (8, 9, 431)→(8)³ – (9)² = 512 – 81 = 431
(11, 8, 1267)→(11)³ – (8)² = 1331 – 64 = 1267

Let's check each option –
First option: (9, 12, 595)→(9)³ – (12)² = 729 – 144 = 585 ≠ 595
Second option: (13, 14, 2011)→(13)³ – (14)² = 2197 – 196 = 2001 ≠ 2011
Third option: (7, 5, 318)→(7)³ – (5)² = 343 – 25 = 318
Fourth option: (12, 10, 1528)→(12)³ – (10)² = 1728 – 100 = 1628 ≠ 1528

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: (13, 7, 218)

Solution : Given: 
(9, 3, 90); (5, 4, 41)

Add the squares of the first two numbers to obtain the third number —
⇒ (9, 3, 90)→9² + 3² = 81 + 9 = 90
⇒ (5, 4, 41)→5² + 4² = 25 + 16 = 41

Let's check the options —
First option: (13, 7, 218)→13² + 7² = 169 + 49 = 218
Second option: (7, 8,117)→7² + 8² = 49 + 64 = 113 ≠ 117
Third option: (11, 8,182)→11² + 8² = 121 + 64 = 185 ≠ 182
Fourth option: (4,12,162)→4² + 12² = 16 + 144 = 160 ≠ 162

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: (9, 81, 729)

Solution : Given:
(7, 49, 343); (8, 64, 512)

The second number is the square of the first number and the third number is the cube of the first number –
(7, 49, 343)→(7)² = 49; (7)³ = 343
(8, 64, 512)→(8)² = 64; (8)³ = 512

Let's check the options – 
First option: (6, 36, 206)→(6)² = 36; (6)³ = 216 ≠ 206
Second option: (5, 25, 225)→(5)² = 25; (5)³ = 125 ≠ 225
Third option: (11, 121, 1221)→(11)² = 121; (11)³ = 1331 ≠ 1221
Fourth option: (9, 81, 729)→(9)² = 81; (9)³ = 729

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

Correct Answer: (5, 14, 29)

Solution : Given:
(9, 26, 53); (8, 23, 47)

In the given sets, subtract the second number from the third number and divide the resultant by 3 to get the first number.
(9, 26, 53)→53 – 26 = 27; 27 ÷ 3 = 9
(8, 23, 47)→47 – 23 = 24; 24 ÷ 3 = 8
Let's check the options –
First option: (5, 14, 29)→29 – 14 = 15; 15 ÷ 3 = 5
Second option: (6, 17, 36)→36 – 17 = 19; 19 ÷ 3 = 6.3 ≠ 6
Third option: (11, 32, 56)→56 – 32 = 24; 24 ÷ 3 = 8 ≠ 11
Fourth option: (7, 20, 42)→42 – 20 = 22; 22 ÷ 3 = 7.3 ≠ 7

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: (18, 6, 110)

Solution : Given:
(8, 6, 50); (24, 4, 98)

Here, (8, 6, 50)→(8 × 6) + 2 = 48 + 2 = 50
(24, 4, 98)→(24 × 4) + 2 = 96 + 2 = 98

Let's check the options –
First option: (2, 48, 100)→(2 × 48) + 2 = 96 + 2 = 98 ≠ 100
Second option: (12, 8, 100)→(12 × 8) + 2 = 96 + 2 = 98 ≠ 100
Third option: (32, 3, 144)→(32 × 3) + 2 = 96 + 2 = 98 ≠ 144
Fourth option: (18, 6, 110)→(18 × 6) + 2 = 108 + 2 = 110

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