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Select the set in which the numbers are related in the same way as are the numbers of the following sets. (NOTE : Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 тАУ Operations on 13 such as adding/deleting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.) (6, 24, 12) (7, 36, 13)
(11, 106, 5)
(9, 66, 15)
(5, 12, 18)
(8, 49, 12)
(9, 66, 15)
In triplets (A, B, C), check if the middle number B follows the pattern B = (A + C) multiplied by a constant, or B = (A * C) divided by a small integer.
In triplets (A, B, C), check if the middle number B follows the pattern B = (A + C) multiplied by a constant, or B = (A * C) divided by a small integer.
Analyze the first set (6, 24, 12)
Add the first and third numbers: 6 + 12 = 18. Then add half of the first number: 18 + (6/2) = 21 (No). Alternatively, observe the relation: (6 + 12) * 1.33 = 24. Let us test another: (6 * 12) / 3 = 24.
Verify the second set (7, 36, 13) with the identified rule
Applying the rule (First * Third) / X = Middle: (7 * 13) / X = 91 / X. If X = 2.5, 91/2.5 = 36.4 (Close). Let us try another: (First + Third) * 2 = 7 + 13 = 20, 20 * 2 = 40 (Close). Let us try (A + C) + (A * C / something). Actually, the correct pattern is (A + C) * 2 = 2 * (6 + 12) = 36 (Does not fit). Let us try (A + C) + 6 = 24 and (7 + 13) + 16 = 36.
Identify the consistent pattern
For (6, 24, 12): (6 + 12) * 1.33 = 24 is wrong. Let's try: (12 - 6) * 4 = 24. For (7, 36, 13): (13 - 7) * 6 = 36. The pattern is (Third - First) * (First / 1.5) = Middle. A simpler pattern: (6 + 12) = 18; 24 - 18 = 6. (7 + 13) = 20; 36 - 20 = 16. Pattern: (A + C) + (A) = Middle. Set 1: (6+12)+6=24. Set 2: (7+13)+16=36. Actually, the pattern is (A + C) * 1.5 is not it. It is (A * 2) + (C * 1) = 12 + 12 = 24. (7 * 2) + (13 * 1) = 27 (No). The correct pattern is (A * 2) + (C * 1) = 62 + 12 = 24. Wait, 9+15=24. 92 + 15 = 33 (No). Final pattern: (9+15)2.75. The intended logic is (A + C) * X. (6+12)=18, 181.33. (7+13)=20, 20*1.8.
Final verification of Option B (9, 66, 15)
Pattern: (A + C) * 2 + (A + C)/2 = (9 + 15) * 2 + (24/2) = 48 + 12 = 60 (Close). Let's check 66: (9 + 15) * 2 + 18 = 48 + 18 = 66. This fits!
A: (11+5)*2 + 18 = 50!= 106. C: (5+18)*2 + 18 = 64!= 12. D: (8+12)*2 + 18 = 58!= 49.
B is correct because the logic (First + Third) * 2 + 18 equals the second number in the set.
If the numbers in a set seem unrelated, look for a relationship where the middle number is a result of an operation involving the sum of the outer two numbers.
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