Select the option that is related to the fifth number in the same way as the second number is related to the first number and the fourth number is related to the third number.

625 : 5 :: 2560 : 8 :: 5000 : ?

The correct answer is 10.

To solve this, we need to find the hidden relationship between each pair of numbers and confirm it holds across all three pairs.

Step 1: Analyze the first pair — 625 : 5

Let's ask: how is 625 built from 5?

Notice that:

5^3=125

125\times 5=625

So: 5^3\times 5=5^4=625 ✓

The rule is: First number = (Second number)³ × 5

Step 2: Verify with the second pair — 2560 : 8

Apply the same rule: 8^3\times 5

8^3=512

512\times 5=2560 ✓

The rule holds perfectly for the second pair as well.

Step 3: Apply the rule to find the missing number — 5000 : ?

Let the unknown number be x. Then:

x^3\times 5=5000

x^3=\frac{5000}{5}=1000

x=\sqrt[3]{1000}=10

Step 4: Verify

{10}^3\times 5=1000\times 5=5000 ✓

The consistent rule across all three pairs is: First Number = (Second Number)³ × 5. Applying this to the third pair confirms that the missing fifth number is 10.