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.) (13, 52, 91) (19, 76, 133)
(17, 68, 119)
Understanding Number Set Relations
The question asks us to identify a set of numbers that shares the same relationship between its elements as the two given sets: (13, 52, 91) and (19, 76, 133). We are specifically told that operations must be performed on the whole numbers themselves, not their individual digits.
Analyzing the Given Number Sets
Let's examine the first given set: (13, 52, 91).
- Compare the second number (52) to the first number (13). We can see that \(52 = 13 \times 4\).
- Compare the third number (91) to the first number (13). We can see that \(91 = 13 \times 7\).
So, for the first set, the relationship appears to be \((x, x \times 4, x \times 7)\), where \(x\) is the first number in the set.
Now, let's test this potential relationship with the second given set: (19, 76, 133).
- The first number is 19. Let's check if the second number (76) is \(19 \times 4\). \(19 \times 4 = 76\). This matches.
- Let's check if the third number (133) is \(19 \times 7\). \(19 \times 7 = 133\). This also matches.
The relationship \((x, x \times 4, x \times 7)\) holds true for both given sets. This is the pattern we need to find in the options.
| Set | First Number (\(x\)) | Second Number | Relation to \(x\) | Third Number | Relation to \(x\) | Pattern |
|---|---|---|---|---|---|---|
| (13, 52, 91) | 13 | 52 | \(13 \times 4\) | 91 | \(13 \times 7\) | \((x, x \times 4, x \times 7)\) |
| (19, 76, 133) | 19 | 76 | \(19 \times 4\) | 133 | \(19 \times 7\) | \((x, x \times 4, x \times 7)\) |
Testing the Options
We will now test each option to see which one follows the pattern \((x, x \times 4, x \times 7)\), where \(x\) is the first number in the set.
Option 1: (17, 68, 119)
- First number \(x = 17\).
- Check the second number: \(17 \times 4 = 68\). This matches the second number in the set.
- Check the third number: \(17 \times 7 = 119\). This matches the third number in the set.
Option 1 follows the pattern \((x, x \times 4, x \times 7)\).
Option 2: (11, 55, 99)
- First number \(x = 11\).
- Check the second number: \(11 \times 4 = 44\). The second number is 55, which is not 44. This option does not follow the pattern. (Note: The pattern here is actually \(11 \times 5 = 55\) and \(11 \times 9 = 99\), i.e., \((x, x \times 5, x \times 9)\)).
Option 3: (9, 45, 63)
- First number \(x = 9\).
- Check the second number: \(9 \times 4 = 36\). The second number is 45, which is not 36. This option does not follow the pattern. (Note: The pattern here is actually \(9 \times 5 = 45\) and \(9 \times 7 = 63\), i.e., \((x, x \times 5, x \times 7)\)).
Option 4: (12, 48, 96)
- First number \(x = 12\).
- Check the second number: \(12 \times 4 = 48\). This matches the second number.
- Check the third number: \(12 \times 7 = 84\). The third number is 96, which is not 84. This option does not follow the pattern. (Note: The pattern here is actually \(12 \times 4 = 48\) and \(12 \times 8 = 96\), i.e., \((x, x \times 4, x \times 8)\)).
Based on our analysis, only Option 1 follows the identified pattern \((x, x \times 4, x \times 7)\).
Conclusion
The pattern observed in the given sets (13, 52, 91) and (19, 76, 133) is that the second number is 4 times the first number, and the third number is 7 times the first number. Among the given options, only the set (17, 68, 119) follows this relationship, where \(17 \times 4 = 68\) and \(17 \times 7 = 119\).
Revision Table: Number Set Logic
| Concept | Explanation | Example |
|---|---|---|
| Number Set Relation | Finding a mathematical rule connecting numbers within a given set or multiple sets. | (2, 4, 6) follows \(x, x+2, x+4\) or \(x, 2x, 3x/2\) (depends on context) |
| Pattern Identification | Spotting the consistent rule or sequence across similar examples. | In (13, 52, 91) and (19, 76, 133), finding the \(\times 4\) and \(\times 7\) relation. |
| Testing Options | Applying the identified pattern to each choice to find the matching one. | Checking if (17, 68, 119) fits the \((x, x \times 4, x \times 7)\) pattern. |
Additional Information: Solving Number Analogy Questions
Number analogy questions, like the one discussed, are common in aptitude tests. They require logical reasoning and the ability to spot mathematical patterns quickly. Here are some common patterns to look for:
- Arithmetic Progression: Numbers increasing or decreasing by a constant difference (e.g., 2, 5, 8 - difference is 3).
- Geometric Progression: Numbers increasing or decreasing by a constant ratio (e.g., 3, 6, 12 - ratio is 2).
- Multiplication/Division: Numbers related by simple multiplication or division from the first term (like in our example).
- Addition/Subtraction: Numbers related by simple addition or subtraction from the first term.
- Squares/Cubes: Numbers might be squares or cubes of related integers.
- Combinations: Patterns might involve a combination of operations (e.g., multiply by 2 and add 1).
- Difference of Differences: Sometimes the pattern is in the difference between consecutive numbers.
Always perform operations on the whole numbers as instructed, and systematically check each possible relationship you identify with all the given examples before testing the options. This ensures the pattern is consistent.
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)
(52, 34, 43)
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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)
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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.)
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Select the set in which the number 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.)
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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 set in which the number 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.)
(17, 87, 104)
(20, 102, 122)
Select the set in which the number 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.)
(9, 7, 189)
(4, 13, 156)
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.)
(4, 60, 5)
(5, 90, 6)
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.)
(20, 16, 8)
(10, 13, 12)
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.)
(12, 9, 4)
(18, 9, 6)
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 : ?
