Solving the Number Analogy 8:64 :: 10:?

This question asks us to find the missing number in the analogy $8:64::10:?$. An analogy presents a relationship between two pairs of numbers. Our goal is to identify the pattern in the first pair ($8$ and $64$) and apply it to the second pair ($10$ and the unknown number).

Identifying the Pattern

Let's examine the relationship between the first number, 8, and the second number, 64.

• We can see that 64 is the result of multiplying 8 by itself.
• Mathematically, this can be represented as $8 \times 8 = 64$.
• Alternatively, we can express this using exponents: $8^2 = 64$.

This suggests the pattern is to square the first number to get the second number.

Applying the Pattern

Now, we apply the same pattern to the second pair of the analogy, which starts with the number 10.

Using the squaring pattern identified:

• The first number is 10.
• We need to calculate $10^2$.
• $10^2 = 10 \times 10 = 100$.

Therefore, the missing number in the analogy is 100.

Comparing with Options

The options provided are 80, 120, 100, and 90. Our calculated result, 100, matches one of the options.

• Option 1: 80 (Incorrect)
• Option 2: 120 (Incorrect)
• Option 3: 100 (Correct)
• Option 4: 90 (Incorrect)

The correct number to complete the analogy $8:64::10:?$ is 100.