Question

\(x^2 - 1 = y\)
\(x = 3\)
Column A: \(y^2\)
Column B: 80

• A. The quantity in Column A is greater.
• B. The quantity in Column B is greater.
• C. The two quantities are equal.
• D. The relationship cannot be determined from the information given.

Hint:

In quantitative comparison questions, always calculate the value in Column A first before making a comparison. Be careful with the order of operations (PEMDAS/BODMAS) when evaluating expressions.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This question asks us to compare two quantities. We first need to calculate the value of the expression in Column A using the given information and then compare it to the value in Column B.
Step 2: Key Formula or Approach:
The approach is to substitute the given value of \(x\) into the equation for \(y\), solve for \(y\), and then calculate \(y^2\).
Step 3: Detailed Explanation:
We are given the equation \(y = x^2 - 1\) and the value \(x = 3\).
First, substitute \(x = 3\) into the equation to find the value of \(y\):
\[ y = (3)^2 - 1 \]
\[ y = 9 - 1 \]
\[ y = 8 \]
Now, we need to find the value for Column A, which is \(y^2\).
\[ y^2 = (8)^2 = 64 \]
So, the quantity in Column A is 64.
The quantity in Column B is 80.
Step 4: Final Answer:
Comparing the two quantities, we have \(64<80\). Therefore, the quantity in Column B is greater.