Four numbers have been given, out of which three are alike in some manner and one is different. Select the one that is different.
676
Finding the Different Number in the Series
In this question, we are given four numbers: 676, 216, 125, and 729. Our task is to identify the one number that is different from the other three, based on some common property shared by the three numbers. This type of problem is common in reasoning and quantitative aptitude sections, requiring us to find the underlying pattern or rule.
Analyzing Each Number for Patterns
Let's examine each number to see if it possesses any specific mathematical properties, such as being a perfect square or a perfect cube.
- 676: Let's check if it's a perfect square or cube. \[ \sqrt{676} = 26 \] So, \( 676 = 26^2 \). 676 is a perfect square. \[ \sqrt[3]{676} \approx 8.77 \] 676 is not a perfect cube.
- 216: Let's check if it's a perfect square or cube. \[ \sqrt{216} \approx 14.69 \] 216 is not a perfect square. \[ \sqrt[3]{216} = 6 \] So, \( 216 = 6^3 \). 216 is a perfect cube.
- 125: Let's check if it's a perfect square or cube. \[ \sqrt{125} \approx 11.18 \] 125 is not a perfect square. \[ \sqrt[3]{125} = 5 \] So, \( 125 = 5^3 \). 125 is a perfect cube.
- 729: Let's check if it's a perfect square or cube. \[ \sqrt{729} = 27 \] So, \( 729 = 27^2 \). 729 is a perfect square. \[ \sqrt[3]{729} = 9 \] So, \( 729 = 9^3 \). 729 is also a perfect cube.
Identifying the Common Property and the Outlier
Let's summarize our findings in a table:
| Number | Perfect Square? | Perfect Cube? | Value (if applicable) |
|---|---|---|---|
| 676 | Yes | No | \(26^2\) |
| 216 | No | Yes | \(6^3\) |
| 125 | No | Yes | \(5^3\) |
| 729 | Yes | Yes | \(27^2\) and \(9^3\) |
Looking at the properties, we can see a pattern among three of the numbers.
- 216 is a perfect cube.
- 125 is a perfect cube.
- 729 is a perfect cube (and also a perfect square).
The number 676 is a perfect square, but it is not a perfect cube.
Therefore, the property shared by three numbers (216, 125, and 729) is that they are all perfect cubes. The number 676 does not share this property.
Thus, 676 is the number that is different from the other three.
Conclusion
Based on the analysis of the mathematical properties of the given numbers, 216, 125, and 729 are all perfect cubes, while 676 is not. This makes 676 the different number among the set.
Revision Table: Perfect Squares and Cubes
Understanding perfect squares and perfect cubes is crucial for solving such number series reasoning problems.
| Number | Perfect Square (n²) | Perfect Cube (n³) |
|---|---|---|
| 1 | \(1^2 = 1\) | \(1^3 = 1\) |
| 4 | \(2^2 = 4\) | |
| 8 | \(2^3 = 8\) | |
| 9 | \(3^2 = 9\) | |
| 16 | \(4^2 = 16\) | |
| 25 | \(5^2 = 25\) | |
| 27 | \(3^3 = 27\) | |
| 36 | \(6^2 = 36\) | |
| 49 | \(7^2 = 49\) | |
| 64 | \(8^2 = 64\) | \(4^3 = 64\) |
| 81 | \(9^2 = 81\) | |
| 100 | \(10^2 = 100\) | |
| 121 | \(11^2 = 121\) | |
| 125 | \(5^3 = 125\) | |
| 144 | \(12^2 = 144\) | |
| 169 | \(13^2 = 169\) | |
| 196 | \(14^2 = 196\) | |
| 216 | \(6^3 = 216\) | |
| 225 | \(15^2 = 225\) | |
| 256 | \(16^2 = 256\) | |
| 289 | \(17^2 = 289\) | |
| 324 | \(18^2 = 324\) | |
| 361 | \(19^2 = 361\) | |
| 400 | \(20^2 = 400\) | |
| 441 | \(21^2 = 441\) | |
| 484 | \(22^2 = 484\) | |
| 512 | \(8^3 = 512\) | |
| 529 | \(23^2 = 529\) | |
| 576 | \(24^2 = 576\) | |
| 625 | \(25^2 = 625\) | |
| 676 | \(26^2 = 676\) | |
| 729 | \(27^2 = 729\) | \(9^3 = 729\) |
| 1000 | \(10^3 = 1000\) |
Additional Information on Number Series Reasoning
Odd one out or different number reasoning questions test your ability to identify patterns. These patterns can be based on various properties:
- Mathematical Operations: Numbers following a specific arithmetic or geometric progression.
- Digit Properties: Sum of digits, product of digits, even/odd digits, specific digits present or absent.
- Divisibility Rules: Numbers divisible by a particular number (e.g., 3, 5, 11).
- Prime and Composite Numbers: Three primes and one composite, or vice versa.
- Squares and Cubes: As seen in this problem, numbers being perfect squares or cubes.
- Other Sequences: Fibonacci series, etc.
To solve these effectively, it's helpful to be familiar with squares and cubes of numbers up to a certain extent and practice identifying different types of patterns.
Important Questions from Number Based
In the following question, four number pairs are given. The number on left side of (-) is related to the number of the right side of (-) with some Logic/Rule/Relation. Three are similar on basis of same Logic/Rule/Relation. Select the odd one out from the given alternatives.
Select the set in which the numbers are related in the same way as are the number of the following set.
(3, 7, 58)
Find the odd number/letters from the given alternatives.
Find the odd number/letters from the given alternatives.
Identify the number which is different from the other.
