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) (60, 15, 40) (100, 50, 20)
(200, 40, 50)
Analyzing the Relationship in the Given Number Sets
The question asks us to identify the set of numbers among the options that shares the same mathematical relationship as the two given sets: (60, 15, 40) and (100, 50, 20). The rule is that operations must be performed on the whole numbers as they are, without breaking them down into individual digits.
Let's examine the relationship between the numbers in the given sets. Let the three numbers in a set be A, B, and C.
For the first set (60, 15, 40):
- A = 60
- B = 15
- C = 40
Let's look for a pattern:
- If we divide the first number (A) by the second number (B): \( \frac{60}{15} = 4 \)
- Now, let's see if there is a relationship between this result (4) and the third number (C), which is 40. We notice that \( 4 \times 10 = 40 \).
- This suggests a possible rule: \( C = \left( \frac{A}{B} \right) \times 10 \)
Let's verify this rule with the second given set (100, 50, 20):
- A = 100
- B = 50
- C = 20
Applying the proposed rule \( C = \left( \frac{A}{B} \right) \times 10 \):
- \( \left( \frac{100}{50} \right) \times 10 = 2 \times 10 = 20 \)
The result, 20, matches the third number (C) in the second set. So, the relationship \( C = \left( \frac{A}{B} \right) \times 10 \) appears to be the pattern for the given number sets.
Applying the Number Set Pattern to Options
Now, we will apply this identified relationship to the numbers in each option to find the set that follows the same rule.
| Option Set (A, B, C) | Calculation: \( \left( \frac{A}{B} \right) \times 10 \) | Does it equal C? |
|---|---|---|
| (200, 40, 50) | \( \left( \frac{200}{40} \right) \times 10 = 5 \times 10 = 50 \) | Yes, \( 50 = 50 \). This set follows the pattern. |
| (12, 45, 89) | \( \left( \frac{12}{45} \right) \times 10 = \frac{4}{15} \times 10 = \frac{40}{15} = \frac{8}{3} \) | No, \( \frac{8}{3} \neq 89 \). This set does not follow the pattern. |
| (10, 5, 30) | \( \left( \frac{10}{5} \right) \times 10 = 2 \times 10 = 20 \) | No, \( 20 \neq 30 \). This set does not follow the pattern. |
| (40, 8, 10) | \( \left( \frac{40}{8} \right) \times 10 = 5 \times 10 = 50 \) | No, \( 50 \neq 10 \). This set does not follow the pattern. |
From the analysis, only the set (200, 40, 50) follows the same relationship \( C = \left( \frac{A}{B} \right) \times 10 \) as the given number sets.
Revision Table: Number Set Analogy
| Concept | Description | Key Takeaway |
|---|---|---|
| Number Analogy | Identifying the mathematical or logical relationship between numbers in a set or between sets. | Look for consistent patterns (arithmetic operations, ratios, etc.). |
| Pattern Identification | Analyzing given examples to deduce a rule or formula that connects the elements. | Test the potential rule against all given examples before applying it to options. |
| Applying the Rule | Using the identified pattern to evaluate the options and find the one that matches. | Be careful with calculations and ensure the rule holds true for the matching option. |
Additional Information: Logical Reasoning with Numbers
Logical reasoning questions often involve identifying patterns and relationships. In number-based reasoning, these relationships can be simple arithmetic operations (addition, subtraction, multiplication, division), ratios, squares, cubes, or more complex combinations. The key is to systematically analyze the given examples to find a consistent rule that applies to all of them.
When tackling such problems:
- Examine the relationship between pairs of numbers within a set.
- Consider relationships involving all numbers in the set.
- Test potential rules with all given examples.
- Once a rule is confirmed, apply it rigorously to the options.
- Pay attention to any specific constraints mentioned, like operating only on whole numbers.
Practice with various types of number series and analogies helps in quickly recognizing common patterns and developing a systematic approach to problem-solving.
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)
