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)
Identifying the Number Pattern
The problem asks to find a set of numbers exhibiting the same relationship as the given examples: 5-7-9 and 11-13-15.
Let's analyze the relationship within the first set (5-7-9):
- The difference between the second and first number is $7 - 5 = 2$.
- The difference between the third and second number is $9 - 7 = 2$.
The pattern observed is an arithmetic progression where each subsequent number increases by a constant difference of 2. The sequence can be represented as $x, x+2, x+4$.
Let's verify this pattern with the second set (11-13-15):
- $13 - 11 = 2$
- $15 - 13 = 2$
This set also follows the arithmetic progression with a common difference of 2.
Analyzing the Options
Now, we check which option follows the same pattern ($x, x+2, x+4$):
- Option 1: 4-39-61
- Difference 1: $39 - 4 = 35$
- Difference 2: $61 - 39 = 22$
- Option 2: 21-23-25
- Difference 1: $23 - 21 = 2$
- Difference 2: $25 - 23 = 2$
- Option 3: 18-15-12
- Difference 1: $15 - 18 = -3$
- Difference 2: $12 - 15 = -3$
- Option 4: 4-30-84
- Difference 1: $30 - 4 = 26$
- Difference 2: $84 - 30 = 54$
Conclusion
Option 2 (21-23-25) is the only set that maintains the arithmetic progression with a common difference of 2, consistent with the initial sets 5-7-9 and 11-13-15.
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 - 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)- 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:?
