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: 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)
27 - 53
Finding the Odd One Out in Number Pairs
This question asks us to identify the pair of numbers that doesn't follow the same rule or pattern as the other three pairs. We are specifically told that operations should be performed on the whole numbers provided, not on their individual digits.
Analyzing the Number Pairs
Let's look at the given options and try to find a relationship between the first number and the second number in each pair.
The pairs are presented as First Number - Second Number:
- 18 - 37
- 33 - 67
- 29 - 59
- 27 - 53
We need to find a pattern that applies to three of these pairs, while one pair deviates from it.
Identifying the Pattern
Let's explore possible relationships between the two numbers in each pair. A common type of pattern involves multiplication or addition/subtraction.
Consider a pattern where the second number is derived from the first number using simple arithmetic operations.
Let's test a possible pattern: the second number is equal to twice the first number plus a constant.
Let \(N_1\) be the first number and \(N_2\) be the second number.
Test Pattern 1: \(N_2 = 2 \times N_1 + C\), where C is a constant.
- For 18 - 37: \(37 = 2 \times 18 + C \implies 37 = 36 + C \implies C = 1\). So, \(N_2 = 2 \times N_1 + 1\).
- For 33 - 67: \(67 = 2 \times 33 + C \implies 67 = 66 + C \implies C = 1\). So, \(N_2 = 2 \times N_1 + 1\).
- For 29 - 59: \(59 = 2 \times 29 + C \implies 59 = 58 + C \implies C = 1\). So, \(N_2 = 2 \times N_1 + 1\).
- For 27 - 53: \(53 = 2 \times 27 + C \implies 53 = 54 + C \implies C = -1\). So, \(N_2 = 2 \times N_1 - 1\).
From this analysis, we can see that three of the pairs (18-37, 33-67, and 29-59) follow the pattern where the second number is twice the first number plus 1 (\(N_2 = 2 \times N_1 + 1\)).
The fourth pair (27-53) follows a different pattern, where the second number is twice the first number minus 1 (\(N_2 = 2 \times N_1 - 1\)).
Step-by-Step Verification
Let's verify the pattern for each option:
| Option | First Number (\(N_1\)) | Second Number (\(N_2\)) | Check \(2 \times N_1 + 1\) | Matches? | Check \(2 \times N_1 - 1\) | Matches? |
|---|---|---|---|---|---|---|
| 18 - 37 | 18 | 37 | \(2 \times 18 + 1 = 36 + 1 = 37\) | Yes | \(2 \times 18 - 1 = 36 - 1 = 35\) | No |
| 33 - 67 | 33 | 67 | \(2 \times 33 + 1 = 66 + 1 = 67\) | Yes | \(2 \times 33 - 1 = 66 - 1 = 65\) | No |
| 29 - 59 | 29 | 59 | \(2 \times 29 + 1 = 58 + 1 = 59\) | Yes | \(2 \times 29 - 1 = 58 - 1 = 57\) | No |
| 27 - 53 | 27 | 53 | \(2 \times 27 + 1 = 54 + 1 = 55\) | No | \(2 \times 27 - 1 = 54 - 1 = 53\) | Yes |
Conclusion
The pairs 18-37, 33-67, and 29-59 all follow the same rule: the second number is obtained by doubling the first number and adding 1. The pair 27-53 follows a different rule: the second number is obtained by doubling the first number and subtracting 1.
Therefore, the pair 27 - 53 does NOT belong to the group formed by the other three.
Revision Table: Number Pattern Analysis
| Option | Pattern \(N_2 = 2 \times N_1 + 1\) | Pattern \(N_2 = 2 \times N_1 - 1\) | Belongs to Group (\(2N_1+1\))? |
|---|---|---|---|
| 18 - 37 | Yes | No | Yes |
| 33 - 67 | Yes | No | Yes |
| 29 - 59 | Yes | No | Yes |
| 27 - 53 | No | Yes | No |
Additional Information: Types of Reasoning Patterns
Number pattern questions are common in logical reasoning and aptitude tests. They test your ability to observe, identify, and apply rules to numbers. Some common types of number patterns include:
- Arithmetic Progressions: Each term increases or decreases by a constant difference (e.g., 2, 4, 6, 8...).
- Geometric Progressions: Each term is multiplied or divided by a constant ratio (e.g., 3, 6, 12, 24...).
- Mixed Operations: Patterns involving a combination of operations, like the \(2N_1+1\) pattern seen here.
- Square or Cube Series: Patterns based on squares (\(1^2, 2^2, 3^2\)...) or cubes (\(1^3, 2^3, 3^3\)...), possibly with additions or subtractions.
- Prime Numbers: Sequences involving only prime numbers (2, 3, 5, 7, 11...).
- Fibonacci Series: Each term is the sum of the two preceding terms (1, 1, 2, 3, 5, 8...).
Solving these questions often involves trial and error to find the specific rule that connects the numbers.
Important Questions from Number Based
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)
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.
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.
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.
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.
