Select the option that is related to the third number in the same way as the second number is related to the first number and the sixth number is related to the fifth number. 97 : 2 :: 63 : ? :: 74 : 3
3
Understanding Number Analogies and Patterns
Number analogy questions test your ability to find the relationship between a given pair of numbers and apply that same relationship to another pair. We are given three pairs, two complete and one with a missing number. Our task is to identify the pattern in the complete pairs and use it to find the missing number.
Analyzing the Provided Number Pairs
The given pairs are:
- First Pair: 97 : 2
- Second Pair: 63 : ?
- Third Pair: 74 : 3
Let's examine the relationship between the first and second numbers in the complete pairs (97 : 2 and 74 : 3).
Examining the First Pair: 97 : 2
Consider the first number, 97. It's a two-digit number with digits 9 and 7. Let's think about how we can get 2 from 97 or its digits.
- If we subtract the second number from the first: \(97 - 2 = 95\) (Doesn't seem helpful).
- Let's look at the digits 9 and 7.
- Sum of digits: \(9 + 7 = 16\). This is not 2.
- Product of digits: \(9 \times 7 = 63\). This is not 2.
- Difference of digits: \(|9 - 7| = |2| = 2\). This matches the second number in the pair.
The absolute difference between the digits of the first number seems like a potential pattern.
Examining the Third Pair: 74 : 3
Now let's check if this pattern holds for the third pair, 74 : 3. The first number is 74, with digits 7 and 4.
Using the potential pattern (absolute difference of digits):
- Difference of digits: \(|7 - 4| = |3| = 3\). This matches the second number in this pair.
The pattern holds true for both complete pairs.
Identifying the Rule
The pattern or rule connecting the numbers in each pair is: the second number is the absolute difference between the individual digits of the first number.
For a two-digit number represented as \(10a + b\), where \(a\) is the tens digit and \(b\) is the units digit, the related number is \(|a - b|\).
Applying the Pattern to Find the Missing Number
We now apply this established rule to the second pair, 63 : ?.
The first number is 63. Its digits are 6 and 3.
Following the rule, the missing number is the absolute difference between the digits 6 and 3.
\(|6 - 3| = |3| = 3\)
So, the missing number is 3.
Summary of the Relationship
The analogy follows the pattern where the second number is the absolute difference between the digits of the first number.
| First Number | Digits | Calculation (Absolute Difference) | Second Number |
|---|---|---|---|
| 97 | 9, 7 | \(|9 - 7| = 2\) | 2 |
| 63 | 6, 3 | \(|6 - 3| = 3\) | 3 (The missing number) |
| 74 | 7, 4 | \(|7 - 4| = 3\) | 3 |
Revision Table: Important Concepts for Number Analogies
| Concept | Explanation | Relevance Here |
|---|---|---|
| Pattern Recognition | The ability to observe and identify the underlying rule or sequence. | Crucial for finding the relationship between number pairs. |
| Digit Operations | Performing mathematical operations on the individual digits of a number, not just the number as a whole. | The solution depends on the difference between digits (9 and 7, 7 and 4, 6 and 3). |
| Consistency Check | Verifying if the identified pattern applies consistently across all provided complete examples. | Confirmed the digit difference rule worked for both 97:2 and 74:3. |
Additional Information: Strategies for Solving Analogy Problems
Solving number analogy and other reasoning problems often benefits from a systematic approach:
- Look for simple arithmetic relations (addition, subtraction, multiplication, division).
- Consider squares, cubes, or roots of the numbers.
- Examine the digits: sum, product, difference, or even order of digits.
- Think about number properties: prime, composite, odd, even.
- If the numbers are large, consider relationships between the numbers themselves, or breaking them down into parts.
- Always test your potential pattern on all given examples to ensure it's consistent.
Practice with various types of patterns will improve your speed and accuracy in solving these problems.
Important Questions from Similarity
'Alone' is related to 'Unaccompanied' in the same way as 'Amount' is related to ______.
Select the option 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/deleting/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, 16, 64)
(7, 49, 343)
Select the set in which the numbers are related in the same way as are the numbers of the following sets.
(15, 135, 6)(12, 84, 5)
Select the option in which the numbers are related in the same way as are the numbers in the given set.
(146, 102, 58)
In the given word pairs, the first word is related to the second word following a certain logic. Study the given pairs carefully, and from the given options, select the pair that follows the same logic.
Dry ∶ Wet
