Find the odd one out: 1, 8, 9, 36, 25, 216, 49
36
Finding the Odd One Out in the Sequence
To find the odd one out in the sequence 1, 8, 9, 36, 25, 216, 49, we need to look for a pattern or a rule that applies to most of the numbers, but not to one particular number. Let's examine the properties of each number in the given sequence.
Let's try to express each number as a power (a base raised to an exponent).
| Number | Can be written as |
|---|---|
| 1 | \(1^2\) or \(1^3\) |
| 8 | \(2^3\) |
| 9 | \(3^2\) |
| 36 | \(6^2\) |
| 25 | \(5^2\) |
| 216 | \(6^3\) |
| 49 | \(7^2\) |
Analyzing the Number Pattern
From the table above, we can see that most numbers are either a perfect square (raised to the power of 2) or a perfect cube (raised to the power of 3).
- Numbers that are perfect squares: 1 ($1^2$), 9 ($3^2$), 36 ($6^2$), 25 ($5^2$), 49 ($7^2$)
- Numbers that are perfect cubes: 1 ($1^3$), 8 ($2^3$), 216 ($6^3$)
Let's look closely at the bases of these powers, especially distinguishing between squares and cubes.
- For the perfect squares: The bases are 1, 3, 6, 5, and 7.
- For the perfect cubes: The bases are 1, 2, and 6.
Identifying the Odd One Out
Let's consider the bases used for the perfect squares in the sequence:
- 1 is \(1^2\). The base is 1, which is an odd number.
- 9 is \(3^2\). The base is 3, which is an odd number.
- 36 is \(6^2\). The base is 6, which is an even number.
- 25 is \(5^2\). The base is 5, which is an odd number.
- 49 is \(7^2\). The base is 7, which is an odd number.
Notice a pattern here. All the perfect squares in the list (1, 9, 25, 49) are squares of odd numbers (1, 3, 5, 7). However, the number 36 is the square of the number 6, which is an even number.
Now let's look at the bases for the perfect cubes:
- 1 is \(1^3\). The base is 1.
- 8 is \(2^3\). The base is 2.
- 216 is \(6^3\). The base is 6.
The pattern for the bases of the cubes doesn't show a consistent odd or even property like the squares do (they are 1, 2, 6).
Based on the observation regarding the bases of the perfect squares, the number 36 stands out. It is the only number in the sequence that is a perfect square of an even number, while all other perfect squares in the list are squares of odd numbers.
Therefore, 36 is the odd one out in the sequence.
Important Questions from Number Series
Select the number from among the given options that can replace the question mark (?) in the following series.
37, 52, 74, 104, 143, ?
Select the number that can replace the question mark (?) in the following series.
17, 19, 22, 27, 34, 45, 58,?Select the number from among the given options that can replace the question mark (?) in the following series.
10, 14, 31, 35, 73, 77, ?
Select the number from among the given options that can replace the question mark (?) in the following series.
215, 231, 256, 292, ?
Select the number from among the given options that can replace the question mark (?) in the following series.
6, 6, 8, 24, 28, 140, ?
