(NOTE – A two/three-digit number cannot be broken into individual digits for operations. E.g. if 37 is followed by 10, the operation cannot be 3+7 as a two-digit number cannot be broken into individual digits.)
5 – 20 – 60 – 120
8 – 32 – 96 – 192
Identifying Number Sequence Operations
The question asks us to find the consistent mathematical pattern used in the given number sequences and identify which option follows the same pattern. We must ensure that operations are performed on the entire number, not its individual digits.
Analyzing the Pattern in Given Sets
Let's examine the operations between consecutive numbers in the provided sets:
Set 1: 5 – 20 – 60 – 120
- To get from 5 to 20: Multiply by 4. Calculation: $5 \times 4 = 20$
- To get from 20 to 60: Multiply by 3. Calculation: $20 \times 3 = 60$
- To get from 60 to 120: Multiply by 2. Calculation: $60 \times 2 = 120$
The pattern observed is: Multiply by 4, then by 3, then by 2.
Set 2: 8 – 32 – 96 – 192
- To get from 8 to 32: Multiply by 4. Calculation: $8 \times 4 = 32$
- To get from 32 to 96: Multiply by 3. Calculation: $32 \times 3 = 96$
- To get from 96 to 192: Multiply by 2. Calculation: $96 \times 2 = 192$
This set confirms the pattern: Multiply by 4, then by 3, then by 2.
Evaluating the Options
We will now test each option using the identified pattern (x4, x3, x2):
| Option | Sequence | Operation 1 (x4) | Operation 2 (x3) | Operation 3 (x2) | Matches Pattern? |
| 1 | 24 – 48 – 96 – 120 | $24 \times 4 = 96$ (Expected 48) | - | - | No |
| 2 | 10 – 40 – 120 – 240 | $10 \times 4 = 40$ (Matches) | $40 \times 3 = 120$ (Matches) | $120 \times 2 = 240$ (Matches) | Yes |
| 3 | 60 – 240 – 80 – 160 | $60 \times 4 = 240$ (Matches) | $240 \times 3 = 720$ (Expected 80) | - | No |
| 4 | 12 – 48 – 144 – 248 | $12 \times 4 = 48$ (Matches) | $48 \times 3 = 144$ (Matches) | $144 \times 2 = 288$ (Expected 248) | No |
Conclusion
Option 2 is the only sequence that follows the mathematical operations of multiplying by 4, then 3, then 2 consistently.
Important Questions from Number Based
- Below are given two sets of numbers. In each set of numbers, a certain mathematical operation on the first number results in the second number. Similarly, certain mathematical operations on the second number result in the third number and so on. Which of the given options follows the same set of operations as in question?
(NOTE – A two/three-digit number cannot be broken into individual digits for operations, e.g., if 37 is followed by 10, the operation cannot be 3+7 as a two-digit number cannot be broken into individual digits.)
12 – 26 – 46 – 70; 20 – 34 – 54 – 78 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 their constituent digits. E.g. 13 – 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.
(15, 7, 100)
(25, 8, 195)- Select the set in which the numbers are related in the same way as are the numbers of the following sets.
5-7-9
11-13-15
(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) - Replace the question mark with an option that follows the same logic applied in the first pair.
$21027:12::32576:?$ Replace the question mark with an option that follows the same logic applied in the first pair.
58:40::86:?
