The second number in the given number pairs is obtained by performing certain mathematical operation(s) on the first number. The same operation(s) are followed in all the number pairs except one. Find that odd number pair. (NOTE: Operations should be performed on whole numbers, without breaking down the numbers into their constituent digits. E.g. 13-Operations on 13 such as adding/ subtracting/multiplying, etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
25 : 177
Understanding the Number Pattern Problem
The problem asks us to identify a number pair that doesn't follow the same mathematical operation linking the first number to the second number, unlike the other pairs. We are specifically instructed to perform operations on the whole numbers provided, not on their individual digits.
Analyzing Number Patterns: Finding the Rule
Let's look closely at the given number pairs and try to find a consistent relationship between the first number (let's call it $x$) and the second number (let's call it $y$). The pairs are:
- 31 : 215
- 29 : 201
- 21 : 145
- 25 : 177
We need to find an operation or a series of operations performed on the first number ($x$) that results in the second number ($y$). Let's test a few common relationships, like multiplication and addition/subtraction.
If we divide the second number by the first number for each pair, we get values around 7:
- $215 \div 31 \approx 6.93$
- $201 \div 29 \approx 6.93$
- $145 \div 21 \approx 6.90$
- $177 \div 25 = 7.08$
Since the values are close to 7, let's explore if multiplication by 7 is part of the pattern.
- For 31 : 215: $31 \times 7 = 217$. The second number is 215. $215 = 217 - 2$. This suggests the pattern might be $y = 7x - 2$.
- For 29 : 201: Let's test the pattern $y = 7x - 2$. $29 \times 7 - 2 = 203 - 2 = 201$. This matches the second number.
- For 21 : 145: Let's test the pattern $y = 7x - 2$. $21 \times 7 - 2 = 147 - 2 = 145$. This also matches the second number.
- For 25 : 177: Let's test the pattern $y = 7x - 2$. $25 \times 7 - 2 = 175 - 2 = 173$. This does not match the second number, which is 177.
It appears that the first three pairs follow the mathematical operation $y = 7x - 2$, while the fourth pair (25 : 177) does not follow this rule. Let's check what rule the fourth pair follows: $25 \times 7 = 175$. $177 = 175 + 2$. So, the fourth pair follows the rule $y = 7x + 2$.
Therefore, the odd number pair out is the one that does not follow the $y = 7x - 2$ rule.
Step-by-Step Number Pattern Identification
Here's how we can systematically identify the odd number pair:
- Examine the given number pairs and observe the relationship between the first and second numbers.
- Hypothesize a mathematical operation or pattern that might connect the numbers in the first pair.
- Test this hypothesized pattern on the remaining pairs.
- Identify the pair that does not fit the pattern observed in the majority of the pairs.
| Number Pair | First No. ($x$) | Operation ($7x - 2$) | Calculated Value | Given Second No. ($y$) | Matches Pattern ($y = 7x - 2$)? |
|---|---|---|---|---|---|
| 31 : 215 | 31 | $7 \times 31 - 2$ | $217 - 2 = 215$ | 215 | Yes |
| 29 : 201 | 29 | $7 \times 29 - 2$ | $203 - 2 = 201$ | 201 | Yes |
| 21 : 145 | 21 | $7 \times 21 - 2$ | $147 - 2 = 145$ | 145 | Yes |
| 25 : 177 | 25 | $7 \times 25 - 2$ | $175 - 2 = 173$ | 177 | No |
As the table shows, the pair 25 : 177 is the only one where applying the rule $7x - 2$ to the first number does not result in the second number.
Conclusion: Identifying the Odd Pair
Based on our analysis, the number pair 25 : 177 is the odd one out because it does not follow the pattern $y = 7x - 2$ which is observed in the other three pairs.
Revision Table: Number Pattern Analysis
| Number Pair | First Number ($x$) | Second Number ($y$) | Rule Tested ($7x - 2$) | Result of Rule | Consistency |
|---|---|---|---|---|---|
| 31 : 215 | 31 | 215 | $7 \times 31 - 2$ | 215 | Follows pattern |
| 29 : 201 | 29 | 201 | $7 \times 29 - 2$ | 201 | Follows pattern |
| 21 : 145 | 21 | 145 | $7 \times 21 - 2$ | 145 | Follows pattern |
| 25 : 177 | 25 | 177 | $7 \times 25 - 2$ | 173 | Does not follow pattern |
Additional Information: Solving Number Pattern Problems
Number pattern and number series problems are common in reasoning tests. They require you to identify the underlying rule that connects the numbers. Here are some tips for solving such problems:
- Look for simple arithmetic operations: addition, subtraction, multiplication, division.
- Consider combinations of operations, like multiplication followed by addition or subtraction, or squaring/cubing numbers.
- Check for patterns involving the position of the number in the sequence (though not applicable here as we have pairs).
- Test your hypothesized rule rigorously on all the given examples.
- If one rule doesn't fit, try to find another potential pattern.
- Sometimes the pattern might involve prime numbers, composite numbers, squares, cubes, etc.
Practice with various types of number pattern questions helps in quickly recognizing common patterns and developing strategies to identify the relationship between numbers.
Important Questions from Number Based
Four number-pairs have been given, out of which three are alike in some manner and one is different. Select the number-pair that is different. (Any operation on digits is not allowed)
Four number-pairs have been given, out of which three are alike in some manner and one is different. Select the number-pair that is different.
Four number-pairs have been given, out of which three are alike in some manner and one is different. Select the number-pair that is different.
Four number-pairs have been given, out of which three are alike in some manner and one is different. Select the number-pair that is different.
Four number-pairs have been given, out of which three are alike in some manner and one is different. Select the number-pair that is different.
