Ace the Officer Aptitude Rating (OAR) 2026 – Unleash Your Inner Officer!

To determine the value of \( y \) when \( x = 8 \), given that \( x^2 \) varies directly with \( y \), we start by expressing the relationship mathematically. The statement that \( x^2 \) varies directly with \( y \) implies that there exists a constant \( k \) such that:

\[ y = k \cdot x^2 \]

From the information provided, when \( x = 2 \), \( y = 10 \). We can substitute these values into the equation to find the constant \( k \):

\[ 10 = k \cdot (2^2) \]

\[ 10 = k \cdot 4 \]

\[ k = \frac{10}{4} = 2.5 \]

Now that we have determined \( k \), we can use it to find \( y \) when \( x = 8 \):

\[ y = k \cdot x^2 \]

\[ y = 2.5 \cdot (8^2) \]

\[ y = 2.5 \cdot 64 \]

\[ y = 160 \]

Thus, when \( x = 8 \), the