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)
(13, 67, 80)
Understanding Number Set Analogy Questions
Number set analogy questions ask you to find the relationship or pattern between the numbers in a given set (or sets) and then identify an option set that follows the same relationship. Operations must be performed on the whole numbers as they are, without breaking them into individual digits.
Analyzing the Given Number Sets
We are given two sets of numbers:
- (17, 87, 104)
- (20, 102, 122)
Let's look for a pattern or relationship between the three numbers in each set. Let the numbers in a set be \(a\), \(b\), and \(c\).
Analyzing the First Set: (17, 87, 104)
Let \(a = 17\), \(b = 87\), and \(c = 104\).
Let's check common arithmetic relationships:
- Is \(a + b = c\)? \(17 + 87 = 104\). Yes, this holds true.
- How is \(b\) related to \(a\)? Let's try multiplication and addition/subtraction. \(17 \times 5 = 85\). \(87 - 85 = 2\). So, \(b = 5 \times a + 2\). Let's check: \(5 \times 17 + 2 = 85 + 2 = 87\). Yes, this also holds true.
Analyzing the Second Set: (20, 102, 122)
Let \(a = 20\), \(b = 102\), and \(c = 122\).
Let's check the same relationships we found in the first set:
- Is \(a + b = c\)? \(20 + 102 = 122\). Yes, this holds true.
- Is \(b = 5 \times a + 2\)? \(5 \times 20 + 2 = 100 + 2 = 102\). Yes, this also holds true.
Identifying the Number Relationship Pattern
From the analysis of both given sets, we can conclude that the pattern or relationship between the numbers \(a\), \(b\), and \(c\) in a set is:
- \(c = a + b\)
- \(b = 5 \times a + 2\)
Both conditions must be met for a set to follow the same pattern.
Evaluating the Options
Now, let's check each option to see which set of numbers follows these two relationships.
Option 1: (11, 57, 70)
Let \(a = 11\), \(b = 57\), \(c = 70\).
- Check 1: \(a + b = c\)? \(11 + 57 = 68\). Is \(68 = 70\)? No.
This option does not follow the first relationship, so it does not match the pattern.
Option 2: (15, 77, 90)
Let \(a = 15\), \(b = 77\), \(c = 90\).
- Check 1: \(a + b = c\)? \(15 + 77 = 92\). Is \(92 = 90\)? No.
This option does not follow the first relationship, so it does not match the pattern.
Option 3: (13, 67, 80)
Let \(a = 13\), \(b = 67\), \(c = 80\).
- Check 1: \(a + b = c\)? \(13 + 67 = 80\). Is \(80 = 80\)? Yes.
- Check 2: \(b = 5 \times a + 2\)? \(5 \times 13 + 2 = 65 + 2 = 67\). Is \(67 = 67\)? Yes.
Both relationships hold true for this option. This set follows the same pattern as the given sets.
Option 4: (19, 97, 117)
Let \(a = 19\), \(b = 97\), \(c = 117\).
- Check 1: \(a + b = c\)? \(19 + 97 = 116\). Is \(116 = 117\)? No.
This option does not follow the first relationship, so it does not match the pattern.
Conclusion on Number Set Pattern
Based on the evaluation, only Option 3, the set (13, 67, 80), follows the same number relationships \(c = a + b\) and \(b = 5 \times a + 2\) as the given sets (17, 87, 104) and (20, 102, 122).
| Set | a | b | c | \(a+b=c\) | \(5a+2=b\) | Follows Pattern? |
|---|---|---|---|---|---|---|
| (17, 87, 104) | 17 | 87 | 104 | \(17+87=104\) (Yes) | \(5(17)+2 = 85+2 = 87\) (Yes) | Given Set (Pattern Source) |
| (20, 102, 122) | 20 | 102 | 122 | \(20+102=122\) (Yes) | \(5(20)+2 = 100+2 = 102\) (Yes) | Given Set (Pattern Source) |
| (11, 57, 70) | 11 | 57 | 70 | \(11+57=68 \neq 70\) (No) | \(5(11)+2 = 55+2 = 57\) (Yes) | No |
| (15, 77, 90) | 15 | 77 | 90 | \(15+77=92 \neq 90\) (No) | \(5(15)+2 = 75+2 = 77\) (Yes) | No |
| (13, 67, 80) | 13 | 67 | 80 | \(13+67=80\) (Yes) | \(5(13)+2 = 65+2 = 67\) (Yes) | Yes |
| (19, 97, 117) | 19 | 97 | 117 | \(19+97=116 \neq 117\) (No) | \(5(19)+2 = 95+2 = 97\) (Yes) | No |
Revision Table: Key Concepts
| Concept | Description | Application in this Problem |
|---|---|---|
| Number Analogy | Finding a relationship between numbers in one set and applying it to others. | Identifying patterns in (17, 87, 104) and (20, 102, 122). |
| Pattern Recognition | Observing sequences or structures to find underlying rules. | Discovering \(c = a+b\) and \(b = 5a+2\). |
| Logical Reasoning | Using given information and rules to reach a conclusion. | Testing each option against the identified number pattern rules. |
Additional Information: Solving Number Pattern Questions
To effectively solve number pattern and analogy questions, consider these strategies:
- Look for simple relationships first: Check for addition, subtraction, multiplication, or division between numbers.
- Consider relationships between different pairs: See how the first number relates to the second, the second to the third, or the first to the third.
- Look for multi-step relationships: The pattern might involve a combination of operations, like multiplication followed by addition or subtraction (\(b = m \times a + k\)).
- Check differences or ratios: Look at the differences between consecutive numbers or their ratios.
- Square or cube relationships: Sometimes numbers are related by squares or cubes.
- Test proposed patterns rigorously: Once you think you've found a pattern, test it on all the given examples before applying it to the options.
- Work systematically through options: Apply the identified pattern to each option one by one until you find a match.
Practicing different types of number pattern problems helps improve your ability to spot these relationships quickly.
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)
(61, 33, 47)
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)
(221, 144, 73)
(222, 153, 75)
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)
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.)
(111, 117, 123)
(169, 200, 231)
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.)
(7, 9, 257)
(10, 3, 170)
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)
(137, 95, 67)
(246, 204, 176)
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 : ?
