Understanding Number Analogy to Find the Related Number

In number analogy questions like 5 ∶ 25 ∷ 10 ∶ ?, we are given a pair of numbers that share a specific relationship. Our task is to identify this relationship and apply it to the first number of the second pair to find the missing related number.

Analyzing the Relationship in the First Pair: 5 : 25

Let's examine the relationship between 5 and 25. How can we get 25 from 5?

We can consider a few possibilities:

• Squaring the number: If we square the first number, we get $5^2 = 5 \times 5 = 25$. This matches the given second number in the pair.
• Multiplying by a constant: If we multiply the first number by a constant, say $k$, to get the second number, we have $5 \times k = 25$. Solving for $k$, we get $k = \frac{25}{5} = 5$. So, multiplying by 5 gives 25.

Both $x \to x^2$ and $x \to x \times 5$ are possible relationships based on the first pair (5, 25).

Applying the Relationship to Find the Related Number in the Second Pair: 10 : ?

Now, we apply the same relationships to the first number of the second pair, which is 10, to find the missing related number.

• Using the squaring relationship ($x \to x^2$): $10^2 = 10 \times 10 = 100$.
• Using the multiplication relationship ($x \to x \times 5$): $10 \times 5 = 50$.

Selecting the Correct Related Number from Options

We need to check which of the results (100 or 50) is available in the given options. The options are:

• 96
• 50
• 42
• 121

Upon checking the options, we see that 50 is one of the choices, while 100 is not. This indicates that the relationship used in this analogy is likely multiplication by 5.

Therefore, the related number for 10 is $10 \times 5 = 50$.

Conclusion

The analogy follows the pattern where the second number is obtained by multiplying the first number by 5.

$5 \times 5 = 25$

$10 \times 5 = 50$

Thus, the missing related number is 50.