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) (6, 14, 40) (10, 14, 48)
(5, 9, 28)
Solving Number Set Relationship Problems
This question asks us to identify the logical relationship connecting the numbers within the given sets and then find an option set that follows the exact same rule. We are provided with two example sets: (6, 14, 40) and (10, 14, 48).
The key rule is that operations must be performed on the whole numbers themselves, not their individual digits.
Analyzing the Given Number Sets
Let's examine the first set: (6, 14, 40).
Let the numbers be represented as a, b, and c, where a = 6, b = 14, and c = 40. We need to find a relationship between a, b, and c.
Let's try common mathematical operations:
- Adding the first two numbers: $6 + 14 = 20$. How is 20 related to 40? $20 \times 2 = 40$.
- This suggests a possible rule: $(a + b) \times 2 = c$. Let's test this rule.
- For $(6, 14, 40)$: $(6 + 14) \times 2 = 20 \times 2 = 40$. This matches the third number, 40.
Now, let's test this potential rule on the second given set: (10, 14, 48).
Here, a = 10, b = 14, and c = 48.
- Using the rule $(a + b) \times 2 = c$: $(10 + 14) \times 2 = 24 \times 2 = 48$. This also matches the third number, 48.
Since the rule $(a + b) \times 2 = c$ works for both the given sets, it is highly likely to be the correct relationship.
Testing the Options
We will now apply the rule $(a + b) \times 2 = c$ to each of the provided options to see which one follows the same pattern.
Option 1: (11, 5, 87)
Here, a = 11, b = 5, c = 87.
Applying the rule: $(11 + 5) \times 2 = 16 \times 2 = 32$.
Since $32 \neq 87$, this option does not follow the rule.
Option 2: (5, 9, 28)
Here, a = 5, b = 9, c = 28.
Applying the rule: $(5 + 9) \times 2 = 14 \times 2 = 28$.
Since $28 = 28$, this option follows the rule.
Option 3: (5, 6, 45)
Here, a = 5, b = 6, c = 45.
Applying the rule: $(5 + 6) \times 2 = 11 \times 2 = 22$.
Since $22 \neq 45$, this option does not follow the rule.
Option 4: (10, 5, 91)
Here, a = 10, b = 5, c = 91.
Applying the rule: $(10 + 5) \times 2 = 15 \times 2 = 30$.
Since $30 \neq 91$, this option does not follow the rule.
Conclusion
Based on our analysis, only option (5, 9, 28) follows the same relationship $(a + b) \times 2 = c$ as the given sets (6, 14, 40) and (10, 14, 48).
Revision Table: Relationship Verification
| Set | a | b | c | $(a+b) \times 2$ Calculation | Result | Follows Rule? |
|---|---|---|---|---|---|---|
| Given Set 1 | 6 | 14 | 40 | $(6+14) \times 2 = 20 \times 2 = 40$ | 40 | Yes |
| Given Set 2 | 10 | 14 | 48 | $(10+14) \times 2 = 24 \times 2 = 48$ | 48 | Yes |
| Option 1 | 11 | 5 | 87 | $(11+5) \times 2 = 16 \times 2 = 32$ | 32 | No |
| Option 2 | 5 | 9 | 28 | $(5+9) \times 2 = 14 \times 2 = 28$ | 28 | Yes |
| Option 3 | 5 | 6 | 45 | $(5+6) \times 2 = 11 \times 2 = 22$ | 22 | No |
| Option 4 | 10 | 5 | 91 | $(10+5) \times 2 = 15 \times 2 = 30$ | 30 | No |
Additional Information on Number Analogy
Number analogy questions are a common type in reasoning tests. They assess your ability to identify patterns and relationships between numbers in a set. The relationships can involve various arithmetic operations, squares, cubes, multiples, or combinations of these. Here are some strategies to find the relationship:
- Look for basic arithmetic operations: addition, subtraction, multiplication, division between the numbers.
- Check for relationships involving squares or cubes of the numbers.
- Consider relationships between the first and third numbers based on the second, or vice versa.
- Sometimes, the relationship involves the sum or difference of the first two numbers predicting the third (as seen in this problem).
- Always test your hypothesized rule on all the given example sets before applying it to the options.
- Remember the constraint: operations on whole numbers only, no breaking down digits.
Practicing different types of number analogy problems helps in quickly identifying common patterns and relationships.
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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 :: ....... : .........
