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)
Understanding the Number Pair Relationship
The question asks us to identify the number pair that does not follow the same rule or logic as the other three pairs. We are given four pairs of numbers, separated by a hyphen (left number - right number). The rule applies to the whole numbers, not their individual digits.
Analyzing Each Number Pair
Let's examine each number pair to find a possible mathematical relationship between the number on the left and the number on the right.
- Pair 1: 11 - 23
- Pair 2: 9 - 16
- Pair 3: 25 - 51
- Pair 4: 13 - 27
We need to look for a consistent operation (like addition, subtraction, multiplication, division, or a combination of these) that connects the first number to the second number in at least three of these pairs.
Discovering the Common Logic
Let's try a common type of relationship: multiplying the left number by a constant and then adding or subtracting a constant. Let the left number be $L$ and the right number be $R$. We are looking for a relationship like $R = aL + b$ or similar.
Consider the first pair: 11 - 23. If we multiply 11 by 2, we get 22. Adding 1 to 22 gives us 23. So, a possible rule is $R = 2L + 1$.
Let's test this rule on the other pairs:
| Pair | Left Number (L) | Applying Rule R = 2L + 1 | Calculated Right Number | Given Right Number (R) | Does it fit? |
|---|---|---|---|---|---|
| 1 | 11 | $2 \times 11 + 1$ | $22 + 1 = 23$ | 23 | Yes |
| 2 | 9 | $2 \times 9 + 1$ | $18 + 1 = 19$ | 16 | No |
| 3 | 25 | $2 \times 25 + 1$ | $50 + 1 = 51$ | 51 | Yes |
| 4 | 13 | $2 \times 13 + 1$ | $26 + 1 = 27$ | 27 | Yes |
As shown in the table, the rule $R = 2L + 1$ holds true for pairs 11 - 23, 25 - 51, and 13 - 27.
Identifying the Odd Pair
The pair 9 - 16 is the only one that does not follow the rule $R = 2L + 1$. According to this rule, if the left number is 9, the right number should be $2 \times 9 + 1 = 19$. However, the given pair is 9 - 16.
Conclusion: The Odd One Out
Based on the consistent logic found in three of the pairs, the pair 9 - 16 is the odd one out because it does not fit the rule $R = 2L + 1$.
Number Pair Analysis Revision Table
| Pair | Left Number (L) | Right Number (R) | Observed Relation | Fits Rule (R = 2L + 1)? | Odd One Out Status |
|---|---|---|---|---|---|
| 11 - 23 | 11 | 23 | $2 \times 11 + 1 = 23$ | Yes | Regular Pair |
| 9 - 16 | 9 | 16 | $2 \times 9 + 1 = 19 \neq 16$ | No | Odd Pair |
| 25 - 51 | 25 | 51 | $2 \times 25 + 1 = 51$ | Yes | Regular Pair |
| 13 - 27 | 13 | 27 | $2 \times 13 + 1 = 27$ | Yes | Regular Pair |
Additional Information on Number Patterns
Identifying patterns in number sequences or pairs is a common skill tested in various exams. These patterns can be based on arithmetic operations, algebraic expressions, squares, cubes, or other mathematical properties.
- Common Pattern Types: Look for arithmetic progressions (constant difference), geometric progressions (constant ratio), patterns involving squares or cubes, or linear relationships like $aL + b$.
- Tips for Finding Patterns:
- Calculate the difference or ratio between consecutive numbers (or numbers in a pair).
- Try simple operations: add, subtract, multiply, divide.
- Consider squaring or cubing the numbers.
- Test linear relationships like $aL + b$ by using two pairs to solve for $a$ and $b$.
- Once a potential rule is found, test it on all other items to confirm.
Important Questions from Classification
Three of the following four are alike in a certain way and thus form a group. Which is the one that does NOT belong to that group?
(Note: The odd one out is not based on the number of consonants/vowels or their position in the letter cluster.)Three of the following numbers are alike in a certain way and one is different. Pick the odd one out.
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – Operations on 13 such as adding/deleting/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.)
The following contains two pairs of words which are related to each other in a certain way. Three of the following four word-pairs are alike as these have the same relationship and thus form a group. Which word-pair does NOT belong to that group?
(The words must be considered as meaningful English words and must not be grouped based on the number of letters/number of consonants/vowels in the word)Three of the following four options are alike in a certain way and thus form a group. Which is the one that does NOT belong to that group?
(NOTE: Operations should be performed on the 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.)
The following contains two pairs of words which are related to each other in a certain way. Three of the following four word-pairs are alike as these have the same relationship and thus form a group. Which word-pair does NOT belong to that group?
(The words must be considered as meaningful English words and must not be grouped based on the number of letters/number of consonants/vowels in the word)
