Question

Given:
\(y = x^2 - 10\)
\(y = 15\)

Quantity A: \(y/3\)
Quantity B: x

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

Hint:

Always remember that taking the square root of both sides of an equation like \(x^2 = c\) (where c>0) yields two solutions: \(x = \sqrt{c}\) and \(x = -\sqrt{c}\). Forgetting the negative root is a common mistake in quantitative comparison problems.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
We need to compare two quantities. First, we must use the given system of equations to find the possible values for x and y. Then we can evaluate and compare Quantity A and Quantity B.
Step 2: Key Formula or Approach:
1. Find the value of y. 2. Substitute the value of y into the first equation to find the possible values for x. 3. Calculate Quantity A. 4. Compare Quantity A with the possible values of Quantity B (x).
Step 3: Detailed Explanation:
We are given directly that \(y = 15\).
Now we can calculate Quantity A: \[ \text{Quantity A} = \frac{y}{3} = \frac{15}{3} = 5 \] Next, we find the value(s) of x by substituting \(y = 15\) into the first equation: \[ 15 = x^2 - 10 \] Add 10 to both sides: \[ 25 = x^2 \] Take the square root of both sides. Remember that the square root can be positive or negative. \[ x = \pm\sqrt{25} \] \[ x = 5 \quad \text{or} \quad x = -5 \] So, Quantity B (x) can be either 5 or -5.

Comparison:
Case 1: If \(x = 5\).
Quantity A = 5 and Quantity B = 5. In this case, the quantities are equal.
Case 2: If \(x = -5\).
Quantity A = 5 and Quantity B = -5. In this case, Quantity A is greater.
Since the relationship between the two quantities changes depending on the value of x, we cannot determine a single consistent relationship.
Step 4: Final Answer:
The relationship cannot be determined from the information given.