Select the set in which the numbers are related in the same way as are 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.) (5, 60, 70) (9, 108, 126)
Solving Number Set Relation Reasoning Questions
This question asks us to identify the set of numbers that shares the same mathematical relationship as the two given sets: (5, 60, 70) and (9, 108, 126). The rule is that operations should be performed on the whole numbers themselves, not on their individual digits.
Analyzing the Given Number Sets
Let's look closely at the two given sets and try to find a consistent pattern relating the three numbers in each set. We can denote the numbers in a set as A, B, and C.
For the first set (5, 60, 70):
- The first number is 5.
- The second number is 60. Let's see how 60 relates to 5. $60 = 5 \times 12$.
- The third number is 70. Let's see how 70 relates to 5. $70 = 5 \times 14$.
The relationship seems to be that the second number is 12 times the first number, and the third number is 14 times the first number.
Let's check if this pattern holds true for the second given set (9, 108, 126):
- The first number is 9.
- The second number is 108. Let's see how 108 relates to 9. $108 = 9 \times 12$. This matches the pattern.
- The third number is 126. Let's see how 126 relates to 9. $126 = 9 \times 14$. This also matches the pattern.
The consistent pattern observed in both given sets is:
- Second Number = First Number $\times$ 12
- Third Number = First Number $\times$ 14
Applying the Pattern to the Options
Now, we will apply this pattern to each of the given options to find the set that follows the same rule.
Option 1: (7, 84, 98)
- First number = 7
- Check the second number: $7 \times 12 = 84$. This matches the second number in the set.
- Check the third number: $7 \times 14 = 98$. This matches the third number in the set.
Option 1 follows the established pattern.
Option 2: (4, 48, 52)
- First number = 4
- Check the second number: $4 \times 12 = 48$. This matches the second number in the set.
- Check the third number: $4 \times 14 = 56$. This does not match the third number (52) in the set.
Option 2 does not follow the pattern.
Option 3: (6, 72, 74)
- First number = 6
- Check the second number: $6 \times 12 = 72$. This matches the second number in the set.
- Check the third number: $6 \times 14 = 84$. This does not match the third number (74) in the set.
Option 3 does not follow the pattern.
Option 4: (8, 84, 112)
- First number = 8
- Check the second number: $8 \times 12 = 96$. This does not match the second number (84) in the set.
- Check the third number: $8 \times 14 = 112$. This matches the third number in the set, but the second number does not fit the pattern.
Option 4 does not follow the pattern.
Based on the analysis, only Option 1 follows the same mathematical relationship as the given sets.
Conclusion
The set (7, 84, 98) is related in the same way as the given sets (5, 60, 70) and (9, 108, 126), where the second number is 12 times the first, and the third number is 14 times the first.
Revision Table - Number Set Pattern
| Set | First Number (A) | Second Number (B) | Third Number (C) | Relationship B to A | Relationship C to A | Follows Pattern? |
|---|---|---|---|---|---|---|
| (5, 60, 70) | 5 | 60 | 70 | $60 = 5 \times 12$ | $70 = 5 \times 14$ | Yes (Reference) |
| (9, 108, 126) | 9 | 108 | 126 | $108 = 9 \times 12$ | $126 = 9 \times 14$ | Yes (Reference) |
| (7, 84, 98) | 7 | 84 | 98 | $84 = 7 \times 12$ | $98 = 7 \times 14$ | Yes |
| (4, 48, 52) | 4 | 48 | 52 | $48 = 4 \times 12$ | $52 \ne 4 \times 14$ | No |
| (6, 72, 74) | 6 | 72 | 74 | $72 = 6 \times 12$ | $74 \ne 6 \times 14$ | No |
| (8, 84, 112) | 8 | 84 | 112 | $84 \ne 8 \times 12$ | $112 = 8 \times 14$ | No |
Additional Information - Reasoning Concepts
Number set relation questions are common in logical reasoning and aptitude tests. They assess your ability to identify patterns and relationships between numbers. These relationships can involve various mathematical operations like addition, subtraction, multiplication, division, squares, cubes, or a combination of these.
Key strategies for solving such problems include:
- Look for patterns: Examine the relationship between the first and second numbers, first and third numbers, and second and third numbers.
- Consider operations: Test simple operations like addition, subtraction, multiplication, or division.
- Check for consistent rules: The pattern must apply consistently across all given examples.
- Apply to options: Once a potential rule is found, apply it to each option to see which one fits.
These types of questions help improve analytical thinking and problem-solving skills needed for various competitive exams.
Important Questions from Number Arrangement
Six friends A, B, C, D, E and F are sitting in two lines, facing the north. Three persons are sitting in each line. F is sitting in the middle. C is just behind B. D is to the immediate right of E. B is to the immediate left of F. Which three persons are sitting in the same line?
In the series 5442673314884743581, the number of 4s that are completely divisible by the number on their right but not divisible by the number on their left is:
Refer to the following series and answer the question (all numbers are single digit numbers only).
(Left) 1 2 6 5 6 8 1 5 8 6 9 8 3 3 5 8 9 4 7 8 (Right)
How many such even digits are there, each of which is immediately preceded by an odd digit and also immediately followed by an odd digit?
Each of the digits in the number 9362145 is arranged in ascending order from left to right. What will be the sum of the digits which are second from the left and third from the right in the number thus formed?
If 1 is added to each odd digit and 2 is subtracted from each even digit in the number 3842675, how many digits will appear more than once in the new number thus formed?
