Out of the given options, three are alike in a certain way. However, one option is not like the other three. Select the option which is different from the others.
144
Identifying the Odd Number Out Among Numbers
The question asks us to find the number that is different from the other three options provided. We are given four numbers: 144, 343, 512, and 729. To solve this, we need to examine the mathematical properties of each number and look for a pattern that is shared by three numbers but not by the fourth one.
Analyzing Number Properties: Perfect Squares and Perfect Cubes
Let's look at each number and check if it is a perfect square or a perfect cube.
- A perfect square is an integer that is the square of an integer; in other words, it is the product of an integer with itself (e.g., $4 = 2^2$, $9 = 3^2$).
- A perfect cube is an integer that is the cube of an integer; in other words, it is the product of an integer multiplied by itself three times (e.g., $8 = 2^3$, $27 = 3^3$).
Let's evaluate each number:
- 144: We know that $12 \times 12 = 144$. So, $144 = 12^2$. It is a perfect square. Is it a perfect cube? $5^3 = 125$ and $6^3 = 216$. So, 144 is not a perfect cube.
- 343: Let's check for perfect cubes. $7 \times 7 = 49$, and $49 \times 7 = 343$. So, $343 = 7^3$. It is a perfect cube. Is it a perfect square? $18^2 = 324$ and $19^2 = 361$. So, 343 is not a perfect square.
- 512: Let's check for perfect cubes. $8 \times 8 = 64$, and $64 \times 8 = 512$. So, $512 = 8^3$. It is a perfect cube. Is it a perfect square? $22^2 = 484$ and $23^2 = 529$. So, 512 is not a perfect square.
- 729: Let's check for perfect cubes. $9 \times 9 = 81$, and $81 \times 9 = 729$. So, $729 = 9^3$. It is a perfect cube. Is it a perfect square? $27 \times 27 = 729$. So, $729 = 27^2$. It is also a perfect square.
We can summarize these findings in a table:
| Number | Calculation | Property |
|---|---|---|
| 144 | $12^2$ | Perfect Square (not a perfect cube) |
| 343 | $7^3$ | Perfect Cube (not a perfect square) |
| 512 | $8^3$ | Perfect Cube (not a perfect square) |
| 729 | $9^3$ or $27^2$ | Perfect Cube and Perfect Square |
Finding the Different Number
Looking at the properties, we see that:
- 343 is a perfect cube.
- 512 is a perfect cube.
- 729 is a perfect cube (and also a perfect square).
- 144 is a perfect square but NOT a perfect cube.
Three of the numbers (343, 512, and 729) are perfect cubes. The number 144 is the only one among the options that is not a perfect cube. Therefore, 144 is the number that is different from the others based on the property of being a perfect cube.
Thus, the option which is different from the others is 144.
Revision Table: Odd Number Out Properties
| Number | Is it a Perfect Square? | Is it a Perfect Cube? | Distinct Property |
|---|---|---|---|
| 144 | Yes ($12^2$) | No | Only Perfect Square (among common integer powers) |
| 343 | No | Yes ($7^3$) | Perfect Cube |
| 512 | No | Yes ($8^3$) | Perfect Cube |
| 729 | Yes ($27^2$) | Yes ($9^3$) | Both Perfect Square and Cube |
Additional Information: Number Classification and Odd One Out Questions
Odd one out questions involving numbers often test your understanding of number properties like prime numbers, composite numbers, even/odd numbers, multiples, factors, perfect squares, perfect cubes, and sometimes specific sequences. It's helpful to be familiar with the squares and cubes of small integers. Recognizing these patterns quickly helps in solving such reasoning problems.
In this specific case, while 729 is unique for being both a perfect square and a perfect cube, the property shared by the majority (3 out of 4) is being a perfect cube. The number 144 is the only one that does not share this property with the other three, making it the odd one out based on this common pattern.
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.
Identify the number which is different from the other.
Three of the given options are alike in a certain way. However, one option is not like the other three. Select the option that is different from the rest.
