Select the option in which the numbers are related in the same way as are the numbers of the following set. (4, 7, 359)
(6, 8, 548)
Finding the Number Relation Pattern
The question asks us to identify the relationship between the numbers in the set (4, 7, 359) and find which of the given options follows the same relationship or pattern. We need to analyze the numbers 4, 7, and 359 to discover how they are connected.
Analyzing the Given Set (4, 7, 359)
Let's denote the first number as $A$, the second number as $B$, and the third number as $C$. In the set (4, 7, 359), we have $A=4$, $B=7$, and $C=359$. We need to find a rule or formula that connects $A$, $B$, and $C$.
Let's try some common mathematical operations involving $A$ and $B$ to see if we can arrive at $C$.
- Addition: $A + B = 4 + 7 = 11$ (Not 359)
- Multiplication: $A \times B = 4 \times 7 = 28$ (Not 359)
- Powers: Let's consider squares and cubes of $A$ and $B$.
- $A^2 = 4^2 = 16$
- $B^2 = 7^2 = 49$
- $A^3 = 4^3 = 64$
- $B^3 = 7^3 = 343$
Now let's try combining these powers:
- $A^2 + B^2 = 16 + 49 = 65$ (Not 359)
- $A^3 + B^3 = 64 + 343 = 407$ (Not 359)
- $A^2 + B^3 = 16 + 343 = 359$ (This matches!)
It appears the pattern or relation in the given set (4, 7, 359) is: The third number is the sum of the square of the first number and the cube of the second number.
Pattern: $C = A^2 + B^3$
Testing the Pattern on the Options
Now we will apply this pattern ($A^2 + B^3 = C$) to each of the given options to see which one follows the same rule.
| Option | Set (A, B, C) | Calculation ($A^2 + B^3$) | Result | Matches C? |
|---|---|---|---|---|
| 1 | (6, 8, 548) | $6^2 + 8^3 = 36 + 512$ | 548 | Yes |
| 2 | (3, 2, 71) | $3^2 + 2^3 = 9 + 8$ | 17 | No (Expected 71) |
| 3 | (10, 3, 172) | $10^2 + 3^3 = 100 + 27$ | 127 | No (Expected 172) |
| 4 | (5, 4, 98) | $5^2 + 4^3 = 25 + 64$ | 89 | No (Expected 98) |
From the analysis above, only Option 1, (6, 8, 548), satisfies the identified pattern $A^2 + B^3 = C$, because $6^2 + 8^3 = 36 + 512 = 548$, which is equal to the third number in the set.
Conclusion
The numbers in the set (4, 7, 359) are related by the formula $A^2 + B^3 = C$. The option that shows the same relationship is (6, 8, 548).
Revision Table: Number Relation
| Concept | Description | Example (from question) |
|---|---|---|
| Number Analogy/Relation | Finding the mathematical rule connecting numbers in a set. | Discovering $(4, 7, 359)$ follows $A^2 + B^3 = C$. |
| First Number (A) | The first element in the set. | 4 in (4, 7, 359) |
| Second Number (B) | The second element in the set. | 7 in (4, 7, 359) |
| Third Number (C) | The third element in the set, result of the relation. | 359 in (4, 7, 359) |
Additional Information: Number Patterns in Reasoning
Number patterns and analogies are common in reasoning questions. These questions test your ability to observe, identify rules, and apply them. The rules can involve various mathematical operations:
- Basic operations (addition, subtraction, multiplication, division)
- Powers and roots (squares, cubes, square roots, cube roots)
- Combinations of operations
- Arithmetic or geometric progressions
- Digit manipulation (sum of digits, product of digits)
To solve such problems, it's helpful to systematically try different simple rules first before moving to more complex combinations of operations or powers. Calculating squares and cubes of small numbers can be very useful.
Similar Questions
Select the options in which the numbers are related in the same way as are the numbers of the following set.
(541, 14, 737)
Select the set in which the numbers are related in the same way as are the numbers of the following set.
(5, 2, 23)
(6, 2, 34)
(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)
Study the given pattern carefully and select the number that can replace the question mark (?) in it.
(6, 8, 11)
(2, 1, 2)
(6, 7, ?)
(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)
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)
(3, 16, 6)
(4, 22, 6)
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.
14 : 400 :: 37 : ? :: 42 : 2304
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)
(76, 4, 19)
(98, 2, 49)
A series is given, with one term missing. Choose the correct alternative from the given ones that will complete the series.
10, 18, 28, ?
The age of the father 4 years ago was 8 times the age of his son. At present, the father’s age is 4 times that of his son. Find the present age of son.
Select the option that is related to the third number in the same way as the second number is related to the first number.
3824 : 4935 : : 5716 : ?
Select the option in which the numbers are related in the same way as are the numbers of the following set.
(7, 52, 346)
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 : ?In the following question, select the related number from the given alternatives.
52 : 57 ∷ 46 : ?Select the option in which the numbers are related in the same way as are the numbers of the following set.
(4, 25, 105)
Select the option that is related to the third term in the same way as the second term is related to the first term.
267 : 5 :: 549 : ?
