Solving the Number Analogy: 18:4::36:16::27:?

This question asks us to find the missing number in an analogy based on the relationship between the first and second numbers, and the third and fourth numbers. We need to identify the pattern connecting each pair and apply it to the third pair to find the missing value.

Analyzing the First Pair: 18 ∶ 4

Let's look at the first pair of numbers, 18 and 4. We need to figure out how 4 is related to 18. Let's explore possible mathematical operations or relationships.

• Addition/Subtraction: $18 - 14 = 4$.
• Multiplication/Division: $18 \div 4$ is not a simple integer.
• Squaring/Square Roots: $\sqrt{18}$ is not an integer. $4^2 = 16$, $18^2$ is large.
• Relationship involving digits: $1+8 = 9$. $\sqrt{9} = 3$. Not 4.

Let's consider if the second number is derived from an operation on the first number. What if the first number is related to the square root of something? The second number, 4, is a perfect square ($2^2$). Could the pattern involve squaring a result obtained from the first number?

Let's try dividing the first number by something that gives a number that, when squared, gives the second number. If the second number is $2^2$, perhaps we get 2 from 18? $18 \div 9 = 2$. Let's test if squaring this result gives the second number: $2^2 = 4$. This seems like a potential pattern: divide the first number by 9 and square the result.

Confirming the Pattern with the Second Pair: 36 ∶ 16

Now let's test this potential pattern with the second pair of numbers, 36 and 16. According to our hypothesis, we should divide the first number (36) by 9 and then square the result. The second number in this pair is 16, which is $4^2$. Let's see if our pattern holds.

Divide the first number by 9: $\frac{36}{9} = 4$.

Square the result: $4^2 = 16$.

This matches the second number in the pair (16). The pattern seems to be consistent: $(\frac{\text{First Number}}{9})^2 = \text{Second Number}$.

Applying the Pattern to the Third Pair: 27 ∶ ?

Now that we have identified and confirmed the pattern, we can apply it to the third pair to find the missing number. The first number in this pair is 27. We need to find the number that results from applying the same rule.

Divide the first number (27) by 9: $\frac{27}{9} = 3$.

Square the result: $3^2 = 9$.

So, the missing number is 9.

Result and Conclusion

Based on the pattern observed and confirmed in the first two pairs, the relationship between 27 and the missing number is that the missing number is the square of 27 divided by 9.

Calculation: $(\frac{27}{9})^2 = 3^2 = 9$.

The missing number is 9. Looking at the options provided, Option 2 is 9.

Revision Table - Number Analogy Pattern

Additional Information - Number Analogy Solving Tips

Number analogy questions test your ability to find logical relationships between numbers. Here are some common patterns to look for:

• Arithmetic Operations: Addition, subtraction, multiplication, division.
• Squares and Cubes: The numbers might be squares, cubes, or related to them (e.g., $n^2+1$, $n^3-1$).
• Prime Numbers: The sequence might involve prime numbers.
• Digit Operations: Relationships might involve the sum or product of digits.
• Sequences: The numbers might follow an arithmetic or geometric progression, or a more complex series.
• Combination of Patterns: Sometimes, a pattern might involve multiple steps or a combination of the above.

Solving these questions often involves trial and error and recognizing common mathematical properties of numbers.