Three of the following four number-pairs are alike in a certain way and one is different. Pickthe odd pair out.
49 : 218
Finding the Odd Number Pair Pattern
This question presents four pairs of numbers, and we need to find the one pair that is different from the other three. This usually means there is a pattern or rule that applies to three of the pairs, but not to the fourth one.
To solve this, we need to examine the relationship between the two numbers in each pair and try to find a consistent rule.
Analyzing the Given Number Pairs
Let's list the four number pairs:
- Pair 1: 4 : 27
- Pair 2: 16 : 125
- Pair 3: 9 : 64
- Pair 4: 49 : 218
We can often find patterns involving basic mathematical operations, powers, or relationships between the numbers.
Identifying the Number Pattern
Let's look at the numbers themselves. Many are perfect squares or perfect cubes:
- 4 is $2^2$
- 27 is $3^3$
- 16 is $4^2$
- 125 is $5^3$
- 9 is $3^2$
- 64 is $4^3$ or $8^2$
- 49 is $7^2$
- 218 is not a common power.
Let's try to find a relationship between the first and second number in each pair using these powers.
| Pair | First Number | Second Number | Observation |
|---|---|---|---|
| 4 : 27 | 4 $= 2^2$ |
27 $= 3^3$ |
The base of the cube (3) is one more than the base of the square (2). This suggests a pattern like $n^2 : (n+1)^3$. Here $n=2$. |
| 16 : 125 | 16 $= 4^2$ |
125 $= 5^3$ |
The base of the cube (5) is one more than the base of the square (4). This fits the pattern $n^2 : (n+1)^3$. Here $n=4$. |
| 9 : 64 | 9 $= 3^2$ |
64 $= 4^3$ |
The base of the cube (4) is one more than the base of the square (3). This fits the pattern $n^2 : (n+1)^3$. Here $n=3$. Note that 64 is also $8^2$, but $3^2 : 8^2$ doesn't fit the $(n+1)$ relationship seen in the first two pairs. |
| 49 : 218 | 49 $= 7^2$ |
218 |
The first number is $7^2$. If the pattern $n^2 : (n+1)^3$ holds, the second number should be $(7+1)^3 = 8^3$. |
Let's calculate $8^3$ for the fourth pair:
$8^3 = 8 \times 8 \times 8 = 64 \times 8 = 512$.
So, if the fourth pair followed the same pattern $n^2 : (n+1)^3$ with $n=7$, it should be 49 : 512. However, the given pair is 49 : 218.
Therefore, the first three pairs follow the pattern $n^2 : (n+1)^3$, while the fourth pair does not.
Conclusion: Identifying the Odd Pair
Based on our analysis, the pair 49 : 218 is the one that is different from the other three, as it does not fit the $n^2 : (n+1)^3$ pattern.
Thus, the odd pair out is 49 : 218.
Revision Table: Analyzing Odd Number Pairs
| Pair | First Number Form ($n^2$) | Second Number Form ($(n+1)^3$) | Expected Second Number | Actual Second Number | Fits Pattern? |
|---|---|---|---|---|---|
| 4 : 27 | $2^2$ | $(2+1)^3 = 3^3$ | 27 | 27 | Yes |
| 16 : 125 | $4^2$ | $(4+1)^3 = 5^3$ | 125 | 125 | Yes |
| 9 : 64 | $3^2$ | $(3+1)^3 = 4^3$ | 64 | 64 | Yes |
| 49 : 218 | $7^2$ | $(7+1)^3 = 8^3$ | 512 | 218 | No |
Additional Information: Number Pattern Questions
Odd pair out questions involving numbers test your ability to find logical rules or patterns. These can be based on various mathematical concepts:
- Arithmetic/Geometric Progressions: Looking at differences or ratios between numbers.
- Powers: Identifying squares, cubes, or other powers.
- Prime/Composite Numbers: Checking if numbers are prime or composite.
- Digit Properties: Sum of digits, product of digits, etc.
- Mathematical Operations: Addition, subtraction, multiplication, division, or a combination of these applied between the numbers in a pair or sequence.
To improve at these questions, practice recognizing common sequences and properties of numbers quickly.
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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.
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(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.
