The second number in the given number-pairs is obtained by performing certain mathematical operation(s) on the first number. The same operation(s) is/are followed in all the number-pairs except one. Find that odd number-pair.
350 : 15
Finding the Odd Number Pair by Identifying Mathematical Patterns
The question asks us to find the number pair that does not follow the same mathematical operation as the others. We are given four number pairs, and we need to discover the relationship between the first and second numbers in each pair.
Let's examine the given number pairs:
- 128 : 8
- 288 : 12
- 350 : 15
- 18 : 3
We need to find a consistent rule that applies to three of these pairs. Let's try to find a relationship where the first number is derived from the second number using a mathematical operation.
Let's consider operations involving squaring or cubing the second number, possibly combined with multiplication or addition/subtraction. Looking at the pairs, especially 18:3 and 128:8, the first number seems significantly larger than the second number, suggesting operations beyond simple multiplication.
Let's test the hypothesis that the first number is related to the square of the second number. We can try multiplying the square of the second number by a constant.
Let the second number be $x$ and the first number be $y$. We are looking for a pattern like $y = a \cdot x^2$ or $y = a \cdot x^2 + b$, or similar.
Consider the pair 18 : 3. If $x=3$, $x^2 = 9$. $18 / 9 = 2$. So, $18 = 2 \times 3^2$. This suggests the pattern might be $y = 2x^2$.
Let's test this pattern with the other pairs:
| Number Pair (y : x) | Second Number (x) | $x^2$ | $2 \times x^2$ | First Number (y) | Does it fit $y = 2x^2$? |
|---|---|---|---|---|---|
| 128 : 8 | 8 | $8^2 = 64$ | $2 \times 64 = 128$ | 128 | Yes, $128 = 2 \times 8^2$ |
| 288 : 12 | 12 | $12^2 = 144$ | $2 \times 144 = 288$ | 288 | Yes, $288 = 2 \times 12^2$ |
| 350 : 15 | 15 | $15^2 = 225$ | $2 \times 225 = 450$ | 350 | No, $350 \neq 2 \times 15^2$ (since $450 \neq 350$) |
| 18 : 3 | 3 | $3^2 = 9$ | $2 \times 9 = 18$ | 18 | Yes, $18 = 2 \times 3^2$ |
Based on this analysis, the pattern $y = 2x^2$ holds true for the number pairs 128:8, 288:12, and 18:3. However, the pair 350:15 does not follow this pattern, as $2 \times 15^2 = 450$, which is not equal to 350.
Therefore, the odd number-pair that does not follow the same operation as the others is 350 : 15.
Revision Table: Checking the Pattern
| Pair | First Number | Second Number | Check $2 \times (\text{Second Number})^2$ | Matches First Number? | Follows Pattern? |
|---|---|---|---|---|---|
| 128 : 8 | 128 | 8 | $2 \times 8^2 = 2 \times 64 = 128$ | Yes | Yes |
| 288 : 12 | 288 | 12 | $2 \times 12^2 = 2 \times 144 = 288$ | Yes | Yes |
| 350 : 15 | 350 | 15 | $2 \times 15^2 = 2 \times 225 = 450$ | No ($350 \neq 450$) | No |
| 18 : 3 | 18 | 3 | $2 \times 3^2 = 2 \times 9 = 18$ | Yes | Yes |
The pair 350 : 15 is the one that stands out as it does not fit the established mathematical relationship.
Additional Information: Understanding Number Pattern Problems
Number pattern problems are common in logical reasoning and quantitative aptitude tests. They require identifying a rule or sequence that connects the numbers in a set or pairs of numbers. Common patterns involve:
- Arithmetic Progression (addition/subtraction of a constant difference).
- Geometric Progression (multiplication/division by a constant ratio).
- Squares, Cubes, or their roots.
- Combinations of operations (e.g., multiply and add, square and multiply).
- Differences between consecutive terms forming their own pattern.
- Alternating patterns.
To solve these problems, it is helpful to:
- Look at the differences or ratios between numbers.
- Consider squares, cubes, and prime numbers.
- Test simple hypotheses first before moving to more complex ones.
- Check the pattern with all given examples to ensure consistency.
- Identify the one element that breaks the discovered rule.
In this specific problem, the pattern involved the square of the second number multiplied by a constant, demonstrating a non-linear relationship between the numbers in the pair.
Similar Questions
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)
In the following question, four number pairs are given. In each pair the number on left side of (-) is related to the number of the right side of (-) with some Logic/Rule/Relation. Three pairs are similar on basis of same Logic/Rule/Relation. Select the odd one out from the given alternatives. (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its 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)
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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.
Select the number-pair in which the two numbers share a different relationship from that shared by the two numbers in the rest of the number-pairs.
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.
Three of the following four number-pairs are alike in a certain way and one is different. Pickthe odd pair out.
Three of the following four numbers are alike in a certain way and one is different. Pick the number that is different from the rest.
Four numbers-pair have been given, out of which three are alike in some manner and is different. Select the number-pair that is different from the rest
Select the option is which the numbers are related in the same way as are the numbers in the given set.
(45, 24, 441)
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.
