(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
Number Series Pattern Analysis
The question requires identifying a consistent mathematical pattern across two number sequences and applying it to find the correct option.
We need to determine the operation linking each consecutive pair of numbers in the given sequences: 12 – 26 – 46 – 70 and 20 – 34 – 54 – 78.
Mathematical Operations Identification
Let's calculate the difference between consecutive numbers in the first set:
- $26 - 12 = 14$
- $46 - 26 = 20$
- $70 - 46 = 24$
The pattern of additions is +14, +20, +24.
Now, let's check the second set to confirm if it follows the same pattern:
- $34 - 20 = 14$
- $54 - 34 = 20$
- $78 - 54 = 24$
Both sets use the same sequence of operations: add 14 to the first number, add 20 to the result, and then add 24 to that result.
Option Sequence Verification
We will now test each option to see which one adheres to the '+14, +20, +24' pattern:
- Option 1: 25 – 39 – 59 – 83
- First number: 25
- $25 + 14 = 39$
- $39 + 20 = 59$
- $59 + 24 = 83$
- Option 2: 28 – 42 – 52 – 76
- First number: 28
- $28 + 14 = 42$
- $42 + 20 = 62$. The sequence has 52, which is incorrect.
- Option 3: 34 – 48 – 78 – 102
- First number: 34
- $34 + 14 = 48$
- $48 + 20 = 68$. The sequence has 78, which is incorrect.
- Option 4: 15 – 30 – 50 – 74
- First number: 15
- $15 + 14 = 29$. The sequence has 30, which is incorrect.
Final Conclusion
Option 1 is the only choice that consistently applies the identified mathematical operations (+14, +20, +24) to generate the number sequence.
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 the 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.)
5 – 20 – 60 – 120
8 – 32 – 96 – 192 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:?
