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.
864 : 12::1372:14::2048 : ?

Correct option is A

Logic: Square of the 2nd number × Half of the 2nd number = 1st number

Now, let's apply this logic to the given pairs:

First pair: 864 : 12

• Square of 12 = $$12^2$$​=144
• Half of 12 =$$\frac{12}{2} = 6$$​​
• Multiply these values: 144×6=864This satisfies the relationship.

Second pair: 1372 : 14

• Square of 14 = $$14^2$$​=196
• Half of 14 =$$\frac{14}{2} = 7$$​​
• Multiply these values: 196×7=1372 This also satisfies the relationship.

Third pair: 2048 : ?

Let the missing number be x. According to the logic:

• Square of x = $$x^2$$​​
• Half of x = $$\frac{x}{2}$$​​

The equation becomes:$$x^2 × \frac{x}{2} = 2048$$​​

$$\frac{x^3}{2} = 2048$$​​

$$x^3 = 4096$$​​

$$\sqrt[3]{4096} = 16$$​​

So, the missing number is 16.