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.) (14, 60, 16) (12, 40, 8)
(19, 80, 21)
Understanding Number Set Relationships
The question asks us to identify a set of three numbers that shares the same relationship as the numbers in the given sets: (14, 60, 16) and (12, 40, 8). We are instructed to perform operations on the whole numbers as they are, without breaking them down into individual digits.
Analyzing the Given Number Sets
Let's examine the relationship between the numbers in the provided sets.
- Set 1: (14, 60, 16)
Let the numbers be A=14, B=60, C=16. We need to find a relationship between A, B, and C. Consider the sum of the first and third numbers: A + C = 14 + 16 = 30. Now, let's see how this sum relates to the middle number, B=60. We observe that 60 is double of 30. So, a possible relationship is B = 2 * (A + C). Let's verify this: 2 * (14 + 16) = 2 * 30 = 60. This holds true for Set 1. - Set 2: (12, 40, 8)
Let the numbers be A=12, B=40, C=8. Let's test the relationship B = 2 * (A + C). A + C = 12 + 8 = 20. 2 * (A + C) = 2 * 20 = 40. This matches the middle number B=40. The relationship holds true for Set 2 as well.
The identified rule or pattern relating the three numbers (A, B, C) in the sets is:
The middle number (B) is equal to twice the sum of the first number (A) and the third number (C). Mathematically, this can be written as:
\(B = 2 \times (A + C)\)
Applying the Pattern to Options
Now, we will apply this established relationship to each of the given options to find the set that follows the same rule.
- Option 1: (19, 80, 21)
Let A=19, B=80, C=21. Calculate A + C = 19 + 21 = 40. Calculate 2 * (A + C) = 2 * 40 = 80. The calculated value (80) matches the middle number B (80). This set follows the pattern. - Option 2: (15, 45, 30)
Let A=15, B=45, C=30. Calculate A + C = 15 + 30 = 45. Calculate 2 * (A + C) = 2 * 45 = 90. The calculated value (90) does not match the middle number B (45). This set does not follow the pattern. - Option 3: (25, 120, 15)
Let A=25, B=120, C=15. Calculate A + C = 25 + 15 = 40. Calculate 2 * (A + C) = 2 * 40 = 80. The calculated value (80) does not match the middle number B (120). This set does not follow the pattern. - Option 4: (20, 30, 40)
Let A=20, B=30, C=40. Calculate A + C = 20 + 40 = 60. Calculate 2 * (A + C) = 2 * 60 = 120. The calculated value (120) does not match the middle number B (30). This set does not follow the pattern.
Based on the analysis, only Option 1 follows the same pattern as the given sets.
Conclusion
The set in which the numbers are related in the same way as the numbers of the given sets (14, 60, 16) and (12, 40, 8) is (19, 80, 21).
| Set | A | B | C | A + C | 2 × (A + C) | Is B = 2 × (A + C)? |
|---|---|---|---|---|---|---|
| (14, 60, 16) | 14 | 60 | 16 | 30 | 60 | Yes |
| (12, 40, 8) | 12 | 40 | 8 | 20 | 40 | Yes |
| (19, 80, 21) | 19 | 80 | 21 | 40 | 80 | Yes |
| (15, 45, 30) | 15 | 45 | 30 | 45 | 90 | No |
| (25, 120, 15) | 25 | 120 | 15 | 40 | 80 | No |
| (20, 30, 40) | 20 | 30 | 40 | 60 | 120 | No |
Revision Table: Number Set Pattern
| Concept | Description | Application in Problem |
|---|---|---|
| Identifying Pattern | Finding a mathematical relationship between numbers in a set. | Discovering \(B = 2 \times (A + C)\) from given sets. |
| Applying Pattern | Testing if other sets follow the identified relationship. | Checking each option against the rule \(B = 2 \times (A + C)\). |
| Whole Number Operations | Performing operations (addition, multiplication etc.) on the full numbers, not digits. | Calculating sums and products using numbers like 14, 16, 60 as they are. |
Additional Information: Reasoning with Number Sets
Reasoning questions involving number sets often require identifying a specific mathematical rule or pattern that connects the numbers within the set. These patterns can involve basic arithmetic operations like addition, subtraction, multiplication, division, squaring, cubing, or combinations of these operations.
Key strategies for solving such problems include:
- Look for relationships between the first, middle, and last numbers (A, B, C).
- Test simple operations first, such as sums, differences, products, or ratios.
- Consider relationships between sums/differences/products of pairs of numbers and the third number.
- Check if the pattern is consistent across all the given example sets.
- Apply the confirmed pattern to each option provided.
- Pay close attention to any specific constraints mentioned in the question, such as the rule about using whole numbers directly.
Practicing different types of number pattern problems helps in quickly identifying common relationships and improving logical reasoning skills.
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Important Questions from Analogy
Select the option that is related to the third term in the same way as the second term is related to the first term.
Day: Night :: Morning : ?Select the option that is related to the third term in the same way as the second term is related to the first term.
India : Country :: Delhi : ..........Select the option that is related to the third term in the same way as the second term is related to the first term.
MATE: NATE :: FATE: ?Select the option that is related to the third term in the same way as the second term is related to the first term.
13 : 196 :: 9 : .......
Select the related word pair from the given alternatives. Afghanistan : Kabul :: ....... : .........
