Select the number – pair in which the two numbers are related in the same way as are the two numbers of the following number – pair 28 : 63
16 : 36
Finding the Number Pair Analogy
The question asks us to identify the number pair that shares the same relationship as the pair 28 : 63. To solve this, we first need to analyze the relationship between 28 and 63.
Analyzing the Given Number Pair: 28 : 63
Let's find the greatest common divisor (GCD) of 28 and 63.
- Factors of 28 are 1, 2, 4, 7, 14, 28.
- Factors of 63 are 1, 3, 7, 9, 21, 63.
The greatest common divisor of 28 and 63 is 7.
Now, let's divide both numbers in the pair by their GCD:
$$ \frac{28}{7} = 4 $$
$$ \frac{63}{7} = 9 $$
The ratio of the two numbers in the pair 28 : 63 is 4 : 9. So, the relationship is that the two numbers are in the ratio 4:9, or one number is (4/9) times the other, or both numbers are multiples of some number, with the base factors being 4 and 9.
We need to find an option pair where the two numbers have the same ratio of 4 : 9.
Evaluating the Options
Let's check each option pair to see if their ratio is 4 : 9.
Option 1: 48 : 98
Find the GCD of 48 and 98.
- Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
- Factors of 98: 1, 2, 7, 14, 49, 98
GCD(48, 98) = 2.
Divide both numbers by their GCD:
$$ \frac{48}{2} = 24 $$
$$ \frac{98}{2} = 49 $$
The ratio is 24 : 49. This is not 4 : 9.
Option 2: 16 : 36
Find the GCD of 16 and 36.
- Factors of 16: 1, 2, 4, 8, 16
- Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
GCD(16, 36) = 4.
Divide both numbers by their GCD:
$$ \frac{16}{4} = 4 $$
$$ \frac{36}{4} = 9 $$
The ratio is 4 : 9. This matches the ratio of the original pair 28 : 63.
Option 3: 36 : 78
Find the GCD of 36 and 78.
- Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
- Factors of 78: 1, 2, 3, 6, 13, 26, 39, 78
GCD(36, 78) = 6.
Divide both numbers by their GCD:
$$ \frac{36}{6} = 6 $$
$$ \frac{78}{6} = 13 $$
The ratio is 6 : 13. This is not 4 : 9.
Option 4: 12 : 28
Find the GCD of 12 and 28.
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 28: 1, 2, 4, 7, 14, 28
GCD(12, 28) = 4.
Divide both numbers by their GCD:
$$ \frac{12}{4} = 3 $$
$$ \frac{28}{4} = 7 $$
The ratio is 3 : 7. This is not 4 : 9.
Conclusion
The only number pair that has the same 4 : 9 ratio as 28 : 63 is 16 : 36.
| Number Pair | GCD | Ratio (Simplified) | Matches 28:63? |
|---|---|---|---|
| 28 : 63 | 7 | 4 : 9 | Base Pair |
| 48 : 98 | 2 | 24 : 49 | No |
| 16 : 36 | 4 | 4 : 9 | Yes |
| 36 : 78 | 6 | 6 : 13 | No |
| 12 : 28 | 4 | 3 : 7 | No |
Revision Table: Number Analogy Basics
| Concept | Description | Example |
|---|---|---|
| Analogy | A comparison between two things based on their similar structure or relationship. | Tree : Forest :: Cloud : Sky |
| Number Analogy | Finding a relationship between two numbers and applying it to other pairs. | 4 : 16 (square relationship) |
| Ratio | A comparison of two quantities by division. | a : b or a/b |
| Greatest Common Divisor (GCD) | The largest positive integer that divides two or more integers without a remainder. Used to simplify ratios. | GCD(12, 18) = 6 |
Additional Information: Solving Number Analogies
Solving number analogy questions often involves identifying the mathematical relationship between the numbers in the given pair. Common relationships include:
- Arithmetic operations (addition, subtraction, multiplication, division)
- Powers or roots (squares, cubes, square roots, cube roots)
- Sequences (e.g., consecutive numbers, prime numbers, odd/even numbers)
- Specific factors or multiples
- Ratios
- Combinations of the above
A good strategy is to:
- Look for obvious relationships like addition, subtraction, multiplication, or division.
- Consider powers or roots.
- Calculate the ratio of the numbers and simplify it using GCD. This often reveals the core relationship, as seen in the 28 : 63 example.
- Check for sequential relationships or properties of the numbers (prime, composite, even, odd).
- Apply the identified relationship to each option pair.
- Select the option that fits the established rule.
Practicing different types of number analogy problems helps in quickly recognizing common patterns and relationships.
Similar Questions
What comes next?
AJ, BL, CN, ?
In the word "FUNDAMENTAL", if we assign even numbers to vowels (A=2, E=4, I=6, O=8, U=10), what is the sum of all vowel values?
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YL 93, XK 88, WJ 83, VI 78, ?
Select the set in which the numbers are related in the same way as are the numbers of the following sets.
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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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(6, 8, 10)
Select the option that is related to the fifth term in the same way as the second term is related to the first term and the fourth term is related to the third term.
132 : 10 :: 42 : 5 :: 272 : ?
Study the given pattern carefully and select the number that can replace the question mark (?) in it.
(6, 2, 34)
(1, 5, 13)
(9, 1, ?)
(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 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)
(2, 114, 19)
(12, 216, 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.
6 : 646 :: 5 : ? :: 4 : 190
Important Questions from Letter and Number Based
Select the option that is related to the third number in the same way as the second number is related to the first number.
22 : 441 :: 13 : ?Select the option that is related to the third number in the same way as the second number is related to the first number.
31 : 90 :: 43 : ?
Select the option which is related to the third number in the same way as the second number is related to the first number.
7 : 56 :: 13 : ?
Select the option that is related to the third number in the same way as the second number is related to the first number.
77 : 11 :: 259 : ?
Select the option that is related to the third number in the same way as the second number is related to the first number.
15 : 270 :: 13 : ?
