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 from the rest.
8-138
Finding the Different Number Pair
In this question, we are given four number pairs and asked to identify the one that is different from the others. This type of question tests our ability to identify patterns and relationships between numbers.
Let's examine each number pair and see if we can find a common pattern or rule that applies to three of the pairs, but not the fourth.
Analyzing Each Number Pair
We have the following four number pairs:
- 8-138
- 5-155
- 6-174
- 11-143
Let's investigate the relationship between the first number and the second number in each pair. A common relationship in such problems is multiplication or division. Let's see if the second number is an integer multiple of the first number.
| Pair | First Number (a) | Second Number (b) | Ratio (b ÷ a) | Is the ratio an integer? |
|---|---|---|---|---|
| 1. 8-138 | 8 | 138 | $\frac{138}{8} = 17.25$ | No |
| 2. 5-155 | 5 | 155 | $\frac{155}{5} = 31$ | Yes |
| 3. 6-174 | 6 | 174 | $\frac{174}{6} = 29$ | Yes |
| 4. 11-143 | 11 | 143 | $\frac{143}{11} = 13$ | Yes |
Identifying the Pattern and the Different Pair
From the analysis above, we can observe the following:
- For the pair 5-155, the second number (155) is an integer multiple of the first number (5), specifically $155 = 5 \times 31$.
- For the pair 6-174, the second number (174) is an integer multiple of the first number (6), specifically $174 = 6 \times 29$.
- For the pair 11-143, the second number (143) is an integer multiple of the first number (11), specifically $143 = 11 \times 13$.
- For the pair 8-138, the second number (138) is NOT an integer multiple of the first number (8), as the division $138 \div 8$ results in a decimal value of 17.25.
Three of the given number pairs (5-155, 6-174, and 11-143) share the common property that the second number is perfectly divisible by the first number. The pair 8-138 does not share this property, as 138 is not divisible by 8 without leaving a remainder.
Therefore, the number-pair that is different from the rest is 8-138 based on the property of divisibility.
Revision Table: Number Pair Analysis
| Number Pair | Relationship Found |
|---|---|
| 8-138 | Second number is not an integer multiple of the first number ($\frac{138}{8}$ is not an integer). |
| 5-155 | Second number is an integer multiple of the first number ($155 = 5 \times 31$). |
| 6-174 | Second number is an integer multiple of the first number ($174 = 6 \times 29$). |
| 11-143 | Second number is an integer multiple of the first number ($143 = 11 \times 13$). |
Additional Information: Number Analogy Reasoning
Number analogy questions require identifying the relationship or pattern between two numbers in a pair. This pattern is then expected to be present in other pairs. The goal is to find the pair that does not follow the same pattern.
Common types of relationships in number analogies include:
- Arithmetic operations (addition, subtraction, multiplication, division).
- Operations involving squares, cubes, or other powers.
- Relationships involving digits of the numbers.
- Divisibility rules or properties.
- Prime or composite numbers.
When solving such problems, it is helpful to test simple relationships first, such as divisibility, before moving to more complex patterns. Identifying a consistent pattern across most options and finding the one that breaks the pattern is key to finding the different pair.
Similar Questions
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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.
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.
