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.
33 : 109
Analyzing Number Pairs for Patterns
The question asks us to identify the number-pair that is different from the other three based on a hidden pattern or rule connecting the two numbers in each pair. We are given four number pairs:
- 27 : 85
- 33 : 109
- 44 : 136
- 30 : 94
We need to look for a consistent mathematical relationship between the first number and the second number in each pair. Let's test common relationships like multiplication and addition/subtraction.
Discovering the Number Pair Pattern
Let's examine each pair to find a potential rule. Often, these patterns involve multiplying the first number by a constant and then adding or subtracting another constant. Let's try multiplying the first number by a small integer and see if we can reach the second number by adding a constant.
Let's test the first number pair, 27 : 85. We can see that 85 is roughly three times 27 ($3 \times 27 = 81$). The difference is $85 - 81 = 4$. So, the relationship could be $3 \times \text{First Number} + 4 = \text{Second Number}$.
Let's test this potential pattern ($y = 3x + 4$) on the other pairs:
- Pair 1: 27 : 85
Applying the rule: $3 \times 27 + 4 = 81 + 4 = 85$.
This matches the given second number.
- Pair 2: 33 : 109
Applying the rule: $3 \times 33 + 4 = 99 + 4 = 103$.
The given second number is 109. $103 \neq 109$. This pair does not follow the pattern $y = 3x + 4$.
- Pair 3: 44 : 136
Applying the rule: $3 \times 44 + 4 = 132 + 4 = 136$.
This matches the given second number.
- Pair 4: 30 : 94
Applying the rule: $3 \times 30 + 4 = 90 + 4 = 94$.
This matches the given second number.
Based on this analysis, three of the number pairs (27:85, 44:136, and 30:94) follow the rule where the second number is obtained by multiplying the first number by 3 and adding 4. The number pair 33 : 109 does not follow this rule; instead, $109 = 3 \times 33 + 10$.
Identifying the Different Pair
Since the pair 33 : 109 is the only one that does not fit the identified pattern ($y = 3x + 4$), it is the number-pair that is different from the rest.
| Number Pair (x : y) | Calculation (3x + 4) | Result | Matches y? | Follows Pattern? |
|---|---|---|---|---|
| 27 : 85 | $3 \times 27 + 4$ | 85 | Yes | Yes |
| 33 : 109 | $3 \times 33 + 4$ | 103 | No | No |
| 44 : 136 | $3 \times 44 + 4$ | 136 | Yes | Yes |
| 30 : 94 | $3 \times 30 + 4$ | 94 | Yes | Yes |
The analysis confirms that 33 : 109 is the pair that is different.
Revision Table: Number Pair Patterns
| Number Pair | Relationship Found | Fits Pattern ($3x+4$)? |
|---|---|---|
| 27 : 85 | $3 \times 27 + 4 = 85$ | Yes |
| 33 : 109 | $3 \times 33 + 10 = 109$ | No (from $3x+4$) |
| 44 : 136 | $3 \times 44 + 4 = 136$ | Yes |
| 30 : 94 | $3 \times 30 + 4 = 94$ | Yes |
Additional Information: Types of Number Patterns
Problems involving finding the odd one out based on number pairs often rely on recognizing common mathematical patterns. Here are a few types you might encounter:
- Linear Relationships: $y = ax + b$ (like in this problem)
- Quadratic Relationships: $y = ax^2 + bx + c$ or involving squares/cubes
- Multiplicative Relationships: $y = a \times x$
- Divisibility Rules: Both numbers share a common factor, or one is a multiple of the other.
- Sum/Difference/Product of Digits: Relationship based on the digits of the numbers.
- Prime/Composite Numbers: One number is prime, the other composite, or both belong to a specific set.
- Specific Number Properties: Perfect squares, perfect cubes, triangular numbers, etc.
Solving these problems requires systematic testing of potential rules and careful calculation.
Similar Questions
What comes next?
AJ, BL, CN, ?
In the word "FUNDAMENTAL", if we assign even numbers to vowels (A=2, E=4, I=6, O=8, U=10), what is the sum of all vowel values?
Select the term from among the given options that can replace the question mark (?) in the following series.
YL 93, XK 88, WJ 83, VI 78, ?
Select the set in which the numbers are related in the same way as are the numbers of the following sets.
(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)
(49, 63, 441)
(7, 14, 14)
Select the set in which the numbers are related in the same way as are the numbers of the following sets. (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.)
(15, 20, 4)
(30, 30, 3)
Select the set in which the numbers are related in the same way as the numbers of the given sets. (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.)
(4, 6, 8)
(6, 8, 10)
Select the option that is related to the fifth term in the same way as the second term is related to the first term and the fourth term is related to the third term.
132 : 10 :: 42 : 5 :: 272 : ?
Study the given pattern carefully and select the number that can replace the question mark (?) in it.
(6, 2, 34)
(1, 5, 13)
(9, 1, ?)
(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)
Select the set in which the numbers are related in the same way as are the numbers of the following set.
(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)
(2, 114, 19)
(12, 216, 6)
Select the option that is related to the third term in the same way as the second term is related to the first term and the sixth term is related to the fifth term.
6 : 646 :: 5 : ? :: 4 : 190
Important Questions from Letter and Number Based
Select the option that is related to the third number in the same way as the second number is related to the first number.
22 : 441 :: 13 : ?Select the option that is related to the third number in the same way as the second number is related to the first number.
31 : 90 :: 43 : ?
Select the option which is related to the third number in the same way as the second number is related to the first number.
7 : 56 :: 13 : ?
Select the option that is related to the third number in the same way as the second number is related to the first number.
77 : 11 :: 259 : ?
Select the option that is related to the third number in the same way as the second number is related to the first number.
15 : 270 :: 13 : ?
