Olympiad Test: Pattern - 1

(5 + 6 + 7) × 3 = 18 × 3 = 54
(7 + 11 + 8) × 3 = 26 × 3 = 78
∴ ? = (8 + 12 + 9) × 3 = 29 × 3 = 87

4² + 5² = 16 + 25 = 41
12² + 8² = 144 + 64 = 208
⇒ 24² + x² = 832
⇒ x² = 832 – 576 = 256
x=16

(18 – 7)² = 11² = 121
(21 – 8)² = 13² = 169
∴ ? = (25 – 13)² = 12² = 144

(25) ² – (18) ² = 625 – 324 = 301
(27) ² – (16) ² = 729 - 256 = 473
∴ ? = (23) ² – (9) ² = 529 – 81 = 448

4² 6² = 1636
5² 4² = 2516
∴ ? = 7² 8² = 4964;

(96 ÷ 16) × 2 = 6 × 2 = 12
(162 ÷ 18) × 2 = 9 × 2 = 18
and (168 ÷ x) × 2 = 24

(112 ÷ 16) × 4 = 7 × 4 = 28
(276 ÷ 23) × 4 = 12 × 4 = 48
∴ ? = (304 ÷ 19) × 4 = 16 × 4 = 64

(7 × 4) + (8 × 13) = 28 + 104 = 132
(9 × 6) + (5 × 17) = 54 + 85 = 139
∴ ? = (6 × 7) + (6 × 23) = 42 + 138 = 180

(18 × 11) – (9 × 12) = 198 – 108 = 90
(25 × 13) – (15 × 13) = 325 – 195 = 130
∴ ? = (28 × 17) - (16 × 13) = 476 – 208 = 268

985 – 734 = 251; 869 – 578 = 291
∴ ? = 743 – 487 = 256

867 – 523 = 344; 675 – 414 = 261;
∴ ? = 784 – 662 = 122