In the following question, select the odd number pair from the given alternatives.
4 – 63
Selecting the Odd Number Pair
This question asks us to identify the number pair from the given alternatives that does not follow the same logical pattern as the others. To solve this, we need to carefully examine the relationship between the two numbers in each pair and find the one that deviates from the common pattern.
Analysis of Number Pairs
Let's analyze each pair to find a consistent relationship. We will denote the first number in a pair as '\(n\)'.
| Option | Number Pair | Analysis | Relationship |
|---|---|---|---|
| 1 | 6 – 217 | Consider the cube of the first number: \(6^3 = 6 \times 6 \times 6 = 216\). The second number is 217. The relationship is \(217 = 216 + 1\). | \(n^3 + 1\) |
| 2 | 5 – 126 | Consider the cube of the first number: \(5^3 = 5 \times 5 \times 5 = 125\). The second number is 126. The relationship is \(126 = 125 + 1\). | \(n^3 + 1\) |
| 3 | 4 – 63 | Consider the cube of the first number: \(4^3 = 4 \times 4 \times 4 = 64\). The second number is 63. The relationship is \(63 = 64 - 1\). | \(n^3 - 1\) |
| 4 | 3 – 28 | Consider the cube of the first number: \(3^3 = 3 \times 3 \times 3 = 27\). The second number is 28. The relationship is \(28 = 27 + 1\). | \(n^3 + 1\) |
Identifying the Pattern and the Odd Pair
By analyzing the pairs, we observe a pattern in three of the options:
- In pair 1 (6 – 217), the second number (217) is \(6^3 + 1\).
- In pair 2 (5 – 126), the second number (126) is \(5^3 + 1\).
- In pair 4 (3 – 28), the second number (28) is \(3^3 + 1\).
These pairs follow the rule where the second number is obtained by cubing the first number (\(n\)) and adding 1, expressed mathematically as \(n^3 + 1\).
Now let's look at pair 3 (4 – 63):
- In pair 3 (4 – 63), the second number (63) is \(4^3 - 1\). This follows the pattern \(n^3 - 1\).
Since the relationship \(n^3 - 1\) is different from the \(n^3 + 1\) pattern followed by the other pairs, the pair 4 – 63 is the odd one out.
Final Answer Determination
The common pattern identified in the majority of the pairs is \(n^3 + 1\). The pair 4 – 63 breaks this pattern, as it follows \(n^3 - 1\). Therefore, 4 – 63 is the odd number pair.
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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.
