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. For 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.) (3, 6, 54) (4, 2, 24)
(3, 4, 36)
Solving Number Set Analogy Problems
This question asks us to find a set of numbers from the given options that shares the same relationship or pattern as the numbers in the two provided sets: (3, 6, 54) and (4, 2, 24). The key rule is that operations must be performed on the whole numbers themselves, not on their individual digits.
Analyzing the Given Number Sets
Let's look closely at the two example sets to uncover the pattern:
- Set 1: (3, 6, 54)
- Set 2: (4, 2, 24)
We need to find a rule that connects the first two numbers to the third number in both sets. Let's try various common arithmetic operations:
- Addition/Subtraction: 3+6=9 (not 54), 6-3=3 (not 54); 4+2=6 (not 24), 4-2=2 (not 24). This doesn't seem to be the direct relation.
- Multiplication: 3 * 6 = 18 (not 54); 4 * 2 = 8 (not 24). Simple multiplication isn't the full pattern.
Let's consider combining multiplication with another operation. Look at the results of the initial multiplication (18 and 8) and the third numbers (54 and 24).
- From 18 to 54: We can multiply 18 by 3 (\(18 \times 3 = 54\)).
- From 8 to 24: We can multiply 8 by 3 (\(8 \times 3 = 24\)).
It appears that the pattern is: Multiply the first number by the second number, and then multiply the result by 3 to get the third number.
Let's verify this pattern with both given sets:
- For Set (3, 6, 54): \((3 \times 6) \times 3 = 18 \times 3 = 54\). This matches the third number.
- For Set (4, 2, 24): \((4 \times 2) \times 3 = 8 \times 3 = 24\). This also matches the third number.
The pattern is consistently applying to both example sets. The rule is: Third number = (First number \(\times\) Second number) \(\times\) 3.
Testing the Options Based on the Pattern
Now, let's apply this rule to each of the given options to see which set follows the same pattern.
- Option 1: (9, 6, 60) Calculation: \((9 \times 6) \times 3 = 54 \times 3 = 162\). Expected third number is 162, but the given third number is 60. This set does not follow the pattern.
- Option 2: (5, 3, 30) Calculation: \((5 \times 3) \times 3 = 15 \times 3 = 45\). Expected third number is 45, but the given third number is 30. This set does not follow the pattern.
- Option 3: (3, 4, 36) Calculation: \((3 \times 4) \times 3 = 12 \times 3 = 36\). Expected third number is 36, and the given third number is 36. This set follows the pattern.
- Option 4: (2, 6, 48) Calculation: \((2 \times 6) \times 3 = 12 \times 3 = 36\). Expected third number is 36, but the given third number is 48. This set does not follow the pattern.
Only option 3 follows the identified pattern: the third number is the product of the first two numbers multiplied by 3.
Conclusion
Based on the analysis of the given sets and the application of the derived pattern to the options, the set (3, 4, 36) is related in the same way as the numbers in the sets (3, 6, 54) and (4, 2, 24).
| Set | Pattern Check: (First \(\times\) Second) \(\times\) 3 | Result | Matches Third Number? |
|---|---|---|---|
| (3, 6, 54) | \((3 \times 6) \times 3 = 18 \times 3\) | 54 | Yes |
| (4, 2, 24) | \((4 \times 2) \times 3 = 8 \times 3\) | 24 | Yes |
| (9, 6, 60) | \((9 \times 6) \times 3 = 54 \times 3\) | 162 | No (60) |
| (5, 3, 30) | \((5 \times 3) \times 3 = 15 \times 3\) | 45 | No (30) |
| (3, 4, 36) | \((3 \times 4) \times 3 = 12 \times 3\) | 36 | Yes |
| (2, 6, 48) | \((2 \times 6) \times 3 = 12 \times 3\) | 36 | No (48) |
Revision Table: Number Set Analogy Pattern
| Concept | Description | Application in this Problem |
|---|---|---|
| Number Set Analogy | Finding a hidden mathematical relationship between numbers in a set and applying it to other sets. | Identifying the rule connecting the first two numbers to the third number in the given sets. |
| Pattern Recognition | Observing patterns and regularities in numerical data. | Discovering that \((A \times B) \times 3 = C\) was the consistent pattern. |
| Rule Adherence | Following specific constraints given in the question (e.g., operations on whole numbers). | Ensuring calculations used entire numbers (3, 6, 54) rather than digits (1, 3 for 13). |
Additional Information: Mastering Number Patterns
Number pattern and analogy questions are common in logical reasoning sections of competitive exams. Success often depends on systematically trying different relationships between the numbers. Here are some common patterns to look for:
- Arithmetic Progressions: Numbers increasing or decreasing by a constant difference.
- Geometric Progressions: Numbers increasing or decreasing by a constant ratio (multiplication or division).
- Squares and Cubes: Numbers related to squares (\(n^2\)) or cubes (\(n^3\)) of other numbers in the set.
- Sum/Difference/Product/Quotient: The third number is a direct result of adding, subtracting, multiplying, or dividing the first two.
- Combined Operations: A combination of the above, such as \((A+B) \times C = D\) or \((A \times B) - C = D\), etc.
- Digit Operations: Although explicitly disallowed in this specific question, sometimes patterns involve sums or products of digits within the numbers.
- Position-Based Operations: The operation might depend on the position of the number in the set (e.g., multiplying the first number by 2, the second by 3, etc.).
Practice with various types of number pattern problems helps in quickly identifying the potential relationship and applying it correctly.
Important Questions from Letter and Number Based
Select the option in which the numbers are related in the same way as are the numbers of the following set.
(4, 8, 16)
Select the option that is related to the third number in the same way as the second number is related to the first number.
23 : 441 : : 28 : ?
Select the option that is related to the third number in the same way as the second number is related to the first number and the sixth number is related to the fifth number.
12 : 72 ∷ 18 : ? ∷22 : 242Select the option that is related to the third number in the same way as the second number is related to the first number.
7 : 56 :: 11 : ?
Select the option in which the numbers are related in the same way as are the numbers of the following set.
(12, 60, 84)
