Identify the number that is different from the rest.
252
Understanding the Question: Identifying the Different Number
The question asks us to examine a given set of four numbers and identify which one is different from the others based on a common mathematical property or pattern shared by the rest.
The numbers provided are:
- 196
- 256
- 252
- 121
Analyzing the Given Numbers
Let's look at each number individually and see if we can find a common property:
| Number | Analysis |
|---|---|
| 196 | Let's check if 196 is a perfect square. We know that $10^2 = 100$ and $20^2 = 400$. The number ends in 6, so its square root might end in 4 or 6. Let's try 14: $14 \times 14 = 196$. So, 196 is a perfect square, specifically $14^2$. |
| 256 | Let's check if 256 is a perfect square. It ends in 6. We know $15^2 = 225$. Let's try 16: $16 \times 16 = 256$. So, 256 is a perfect square, specifically $16^2$. |
| 252 | Let's check if 252 is a perfect square. $15^2 = 225$ and $16^2 = 256$. 252 is between 225 and 256. Therefore, its square root would be between 15 and 16, which means it's not a whole number. 252 is not a perfect square. |
| 121 | Let's check if 121 is a perfect square. We know $10^2 = 100$. Let's try 11: $11 \times 11 = 121$. So, 121 is a perfect square, specifically $11^2$. |
Identifying the Pattern and the Different Number
Based on our analysis:
- 196 is a perfect square ($14^2$).
- 256 is a perfect square ($16^2$).
- 252 is not a perfect square.
- 121 is a perfect square ($11^2$).
We can see that three of the numbers (196, 256, and 121) share the property of being a perfect square, while 252 does not possess this property. Therefore, 252 is the number that is different from the rest.
Conclusion: The Number That Is Different
Comparing all the numbers, the number 252 stands out because it is not a perfect square, unlike the other three numbers provided. The property of being a perfect square serves as the basis for distinguishing one number from the others in this set.
The number that is different from the rest is 252.
Revision Table: Perfect Squares Analysis
| Number | Is it a Perfect Square? | Square Root (if integer) |
|---|---|---|
| 196 | Yes | 14 |
| 256 | Yes | 16 |
| 252 | No | N/A |
| 121 | Yes | 11 |
Additional Information: Understanding Perfect Squares
A perfect square is an integer that is the square of an integer. In other words, it is the product of some integer with itself. For example, 9 is a perfect square because $3 \times 3 = 9$.
Examples of perfect squares:
- $1^2 = 1$
- $2^2 = 4$
- $3^2 = 9$
- $4^2 = 16$
- $5^2 = 25$
- $10^2 = 100$
- $11^2 = 121$
- $12^2 = 144$
- $13^2 = 169$
- $14^2 = 196$
- $15^2 = 225$
- $16^2 = 256$
Identifying perfect squares is a common technique used in number pattern questions like this one. When faced with a list of numbers, checking for properties like being a perfect square, an even/odd number, a prime number, or divisibility by certain numbers can help reveal the pattern and identify the outlier.
Important Questions from Number Based
Four number triads have been given, out of which three are alike in some manner and one is different. Select the number triad that is different.
Choose the odd number out of the given options.
Identify the odd one from the following.
Four numbers have been given out of which three are alike in some manner, while one is different. Choose the odd one.
Four numbers have been given out of which three are alike in some manner, while one is different. Choose the odd one.
