In the following question, select the odd number pair from the given alternatives.
13 – 199
Finding the Odd Number Pair Based on Pattern
The question asks us to identify the number pair that is different from the others among the given alternatives. This usually involves finding a mathematical or logical pattern that applies to three pairs but not the fourth one.
Let's examine each given number pair:
- Pair 1: 11 – 121
- Pair 2: 13 – 199
- Pair 3: 14 – 196
- Pair 4: 15 – 225
We need to look for a relationship between the first number and the second number in each pair. A common relationship in such problems is squaring the first number to get the second number. Let's test this hypothesis:
- For the pair 11 – 121: Let's square the first number, 11.
\(\text{11}^2 = 11 \times 11 = 121\)
The calculated value 121 matches the second number in the pair. - For the pair 13 – 199: Let's square the first number, 13.
\(\text{13}^2 = 13 \times 13 = 169\)
The calculated value 169 does not match the second number in the pair, which is 199. - For the pair 14 – 196: Let's square the first number, 14.
\(\text{14}^2 = 14 \times 14 = 196\)
The calculated value 196 matches the second number in the pair. - For the pair 15 – 225: Let's square the first number, 15.
\(\text{15}^2 = 15 \times 15 = 225\)
The calculated value 225 matches the second number in the pair.
From this analysis, we can see that pairs 1, 3, and 4 follow the pattern where the second number is the square of the first number. Pair 2 (13 – 199) does not follow this pattern, as \(13^2\) is 169, not 199.
Therefore, the odd number pair among the given alternatives is 13 – 199 because it does not fit the pattern of the second number being the square of the first number, unlike the other three pairs.
The final answer is the pair 13 – 199.
Revision Table: Checking the Number Pair Pattern
| Number Pair | First Number | Second Number | First Number Squared (\(\text{n}^2\)) | Does Second Number Match \(\text{n}^2\)? | Follows Pattern? |
|---|---|---|---|---|---|
| 11 – 121 | 11 | 121 | \(\text{11}^2 = 121\) | Yes | Yes |
| 13 – 199 | 13 | 199 | \(\text{13}^2 = 169\) | No (199 ≠ 169) | No |
| 14 – 196 | 14 | 196 | \(\text{14}^2 = 196\) | Yes | Yes |
| 15 – 225 | 15 | 225 | \(\text{15}^2 = 225\) | Yes | Yes |
Additional Information on Number Patterns
Finding the odd number pair or term in a series often requires recognizing various mathematical patterns. Some common patterns include:
- Arithmetic Progression: Adding or subtracting a constant value each time. Example: 2, 4, 6, 8... (adding 2)
- Geometric Progression: Multiplying or dividing by a constant value each time. Example: 3, 9, 27, 81... (multiplying by 3)
- Square Numbers: The sequence is formed by squaring consecutive integers (\(1^2, 2^2, 3^2, ...\)). Example: 1, 4, 9, 16...
- Cube Numbers: The sequence is formed by cubing consecutive integers (\(1^3, 2^3, 3^3, ...\)). Example: 1, 8, 27, 64...
- Prime Numbers: Numbers greater than 1 that have only two divisors: 1 and themselves. Example: 2, 3, 5, 7, 11, 13...
- Differences: Finding the pattern in the differences between consecutive terms.
- Alternating Patterns: Two different patterns interleaved.
- Sum/Product of Digits: The next number is based on the sum or product of the digits of the previous number.
In number pair questions, the relationship can be between the two numbers in the pair (like squaring, cubing, addition, subtraction, etc.) or the pairs themselves might follow a sequence.
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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.
