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Two sets of numbers are given below. In each set of numbers, certain mathematical operation(s) on the first number result(s) in the second number. Similarly, certain mathematical operation(s) on the second number result(s) in the third number and so on. Which of the given options follows the same set of operations as in the given sets? (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 тАУ Operations on 13 such as adding / subtracting /multiplying to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.) 8-24-72-216; 6-18-54-162
12-36-108-216
7-21-63-189
11-33-99-287
9-27-81-343
7-21-63-189
Observe the progression: Each number is multiplied by 3 to get the next number in the sequence (n, n3, n9, n*27).
Observe the progression: Each number is multiplied by 3 to get the next number in the sequence (n, n3, n9, n*27).
Analyze Given Sets
Set 1: 8, 24, 72, 216. Operations: 83=24, 243=72, 723=216. Set 2: 6, 18, 54, 162. Operations: 63=18, 183=54, 543=162. The pattern is multiplying the previous number by 3.
Verify Option B
For 7-21-63-189: 73=21, 213=63, 63*3=189. This perfectly matches the rule of multiplication by 3.
A: 123=36, 363=108, but 1082=216 (Incorrect). C: 113=33, 333=99, but 992.9 approx = 287 (Incorrect). D: 93=27, 273=81, but 81*4.2 approx = 343 (Incorrect).
B is correct because the sequence follows a constant multiplication factor of 3 for every transition (73=21, 213=63, 63*3=189).
In number series, always check the ratio between consecutive terms first. If the ratio is constant, it is a Geometric Progression.
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