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 : ?
6827
Understanding Number Analogy Patterns
Number analogy questions test your ability to find the relationship between two numbers and apply that same relationship to a third number to find a fourth one. The given analogy is 3824 : 4935 : : 5716 : ?
We need to determine the relationship between the first number (3824) and the second number (4935).
Analyzing the Relationship: 3824 to 4935
Let's look at the digits of the first number (3824) and compare them to the corresponding digits of the second number (4935).
- The first digit of 3824 is 3. The first digit of 4935 is 4. ($3 + 1 = 4$)
- The second digit of 3824 is 8. The second digit of 4935 is 9. ($8 + 1 = 9$)
- The third digit of 3824 is 2. The third digit of 4935 is 3. ($2 + 1 = 3$)
- The fourth digit of 3824 is 4. The fourth digit of 4935 is 5. ($4 + 1 = 5$)
The pattern observed is that each digit of the first number is increased by 1 to get the corresponding digit of the second number.
This can be represented as: If the first number is $d_1d_2d_3d_4$, the second number is $(d_1+1)(d_2+1)(d_3+1)(d_4+1)$.
Applying the Pattern to 5716
Now, we apply the same pattern to the third number, 5716, to find the missing fourth number.
- First digit: 5. Add 1: $5 + 1 = 6$.
- Second digit: 7. Add 1: $7 + 1 = 8$.
- Third digit: 1. Add 1: $1 + 1 = 2$.
- Fourth digit: 6. Add 1: $6 + 1 = 7$.
Combining the new digits, we get 6827.
Conclusion: The Missing Number
Following the established pattern, the number that is related to 5716 in the same way as 4935 is related to 3824 is 6827.
Revision Table: Number Analogy
| First Pair | Relationship | Second Pair |
|---|---|---|
| 3824 | Each digit + 1 | 5716 |
| 4935 | 6827 |
Additional Information: Solving Analogy Questions
Number analogy problems can have various types of relationships. Some common patterns include:
- Adding or subtracting a constant value to the entire number.
- Multiplying or dividing the entire number by a constant.
- Performing operations (addition, subtraction, multiplication, division) on individual digits.
- Using mathematical operations involving squares, cubes, or prime numbers.
- Reversing the digits or rearranging them.
- Combinations of these patterns.
To solve analogy questions effectively, practice is key. Always start by carefully observing the relationship between the first pair of numbers. Look for simple patterns first, and then explore more complex ones if necessary.
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