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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 - Operations on 13 such as adding/subtracting/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.) (3,12,36)(8,32,96)
(12,42,144)
(14,48,144)
(12,48,124)
(12,48,144)
(12,48,144)
Identify that the third number is exactly 12 times the first number: (312=36) and (812=96).
Identify that the third number is exactly 12 times the first number: (312=36) and (812=96).
Analyze the pattern
In set (3, 12, 36), the first number 3 is multiplied by 4 to get the second (34=12) and by 12 to get the third (312=36). Alternatively, the second number is 4 times the first and the third is 3 times the second (12*3=36).
Apply to second set
In set (8, 32, 96), 8 multiplied by 4 gives 32, and 8 multiplied by 12 gives 96. Also, 32 multiplied by 3 gives 96.
Evaluate Options
We need a set (A, B, C) where A * 4 = B and B * 3 = C (or A * 12 = C). In option D: 12 * 4 = 48 and 48 * 3 = 144. This perfectly matches the pattern.
A: 12 * 3.5 = 42 (does not match *4 ratio). B: 14 * 3.42 = 48 (does not match *4 ratio). C: 12 * 4 = 48, but 48 * 2.58 = 124 (does not match *3 ratio).
D is correct because the numbers follow the specific relationship where the second number is 4 times the first and the third is 3 times the second (or 12 times the first).
When you see three numbers in a set, always check the ratio between them first before trying complex addition or subtraction rules.
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