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) (75, 55, 70) (65, 55, 68)
(95, 85, 104)
Finding the Number Pattern in Sets
The question asks us to identify the set of numbers that shares the same relationship as the numbers in the given sets: (75, 55, 70) and (65, 55, 68). The key constraint is that operations must be performed on the whole numbers, not their individual digits.
Let's analyze the given sets. We can denote the numbers in each set as A, B, and C, where A is the first number, B is the second, and C is the third.
Analyzing the Given Sets
Let's look for a consistent pattern or rule that connects A, B, and C in both sets.
| Set | A | B | C | Observations / Calculations |
|---|---|---|---|---|
| (75, 55, 70) | 75 | 55 | 70 | $A - B = 75 - 55 = 20$ $C - B = 70 - 55 = 15$ $A/5 = 75/5 = 15$ |
| (65, 55, 68) | 65 | 55 | 68 | $A - B = 65 - 55 = 10$ $C - B = 68 - 55 = 13$ $A/5 = 65/5 = 13$ |
From the analysis, we can observe a pattern related to the second number (B) and the first number (A) to get the third number (C).
In the first set, we see that $C - B = 15$, and $A/5 = 15$. So, $C - B = A/5$.
In the second set, we see that $C - B = 13$, and $A/5 = 13$. So, $C - B = A/5$.
The pattern seems to be: The difference between the third number (C) and the second number (B) is equal to the first number (A) divided by 5. This can be written as:
\(C - B = \frac{A}{5}\)
Rearranging this formula to find C, we get:
\(C = B + \frac{A}{5}\)
For this rule to work with whole numbers as per the question's constraint, A must be divisible by 5.
Let's verify this rule with the given sets:
- For (75, 55, 70): $C = 55 + 75/5 = 55 + 15 = 70$. This matches the set.
- For (65, 55, 68): $C = 55 + 65/5 = 55 + 13 = 68$. This matches the set.
The rule \(C = B + \frac{A}{5}\) holds true for the given sets.
Applying the Pattern to the Options
Now, let's apply this rule to the given options to find the set that follows the same pattern.
| Option Set (A, B, C) | A | B | C (Given) | Calculate $B + A/5$ | Does $B + A/5$ equal C? |
|---|---|---|---|---|---|
| (95, 85, 124) | 95 | 85 | 124 | $85 + 95/5 = 85 + 19 = 104$ | $104 \neq 124$ (No) |
| (95, 85, 104) | 95 | 85 | 104 | $85 + 95/5 = 85 + 19 = 104$ | $104 = 104$ (Yes) |
| (95, 80, 104) | 95 | 80 | 104 | $80 + 95/5 = 80 + 19 = 99$ | $99 \neq 104$ (No) |
| (90, 85, 104) | 90 | 85 | 104 | $85 + 90/5 = 85 + 18 = 103$ | $103 \neq 104$ (No) |
Based on the calculations, only the set (95, 85, 104) follows the rule \(C = B + \frac{A}{5}\).
Therefore, the set (95, 85, 104) is related in the same way as the numbers of the given sets.
Revision Table: Key Concepts
| Concept | Description | Application in Problem |
|---|---|---|
| Number Analogy / Set Pattern | Identifying a mathematical or logical relationship between numbers in a set and applying it to find a similar set. | We found the rule \(C = B + \frac{A}{5}\) governing the numbers in the example sets. |
| Whole Number Operations | Calculations must use the full numbers provided, not their individual digits. Division must result in a whole number if used in the core pattern. | Our rule involves division by 5, which yields a whole number result for A in the example sets and the correct option. |
| Pattern Recognition | The process of observing given examples to deduce an underlying rule or relationship. | Comparing (75, 55, 70) and (65, 55, 68) helped uncover the \(C - B = A/5\) relationship. |
Additional Information: Solving Number Reasoning Problems
Number reasoning questions often involve finding a hidden pattern based on basic arithmetic operations, squares, cubes, ratios, or differences between numbers within a set or series. Here are some common strategies:
- Look at Differences: Check the difference between consecutive numbers, or the first and third, or differences from the middle number. See if these differences follow a pattern (arithmetic progression, geometric progression, constant difference, etc.).
- Look at Sums: Check the sum of numbers. Maybe the third number is the sum or a transformation of the sum of the first two.
- Look at Products/Ratios: Explore multiplication and division. Is one number a multiple of another? Is there a constant ratio between differences?
- Look at Squares/Cubes: Sometimes numbers are related to squares or cubes of other numbers or their differences/sums.
- Combine Operations: The pattern might involve a combination of operations, like \(C = 2A + B/3\) or \(C = (A+B) \times k\).
- Check Constraints: Always remember any specific rules given, like the 'whole number operations' rule in this problem.
- Test Options: Once a potential rule is found, test it rigorously on all given examples and then apply it to the options to find the match.
Practicing various types of number analogy and pattern questions helps develop the intuition to quickly spot potential relationships between numbers.
Similar Questions
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)
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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.
16 : 50 :: 49 : ? :: 144 : 338
Important Questions from Letter and Number Based
Select the related number from the given alternatives that will complete the series:
Y 2 : 4 : : V 2 : ?Select the related number from the given alternatives:
F : 216 : : L : ?Select the option in which the numbers are related in the same way as are the numbers of the following set.
(12, 60, 84)
Three of the following four number-pairs ale alike in a certain way and one is different. Find the odd one out.
In the following question, select the related number from the given alternatives.
52 : 57 ∷ 46 : ?
