Question:
Given the equations:
\(x^2 + 5x - 24 = 0\)
\(y^2 - 9y + 20 = 0\)
Quantity A: x
Quantity B: y
Given the equations:
\(x^2 + 5x - 24 = 0\)
\(y^2 - 9y + 20 = 0\)
Quantity A: x
Quantity B: y
\(x^2 + 5x - 24 = 0\)
\(y^2 - 9y + 20 = 0\)
Quantity A: x
Quantity B: y
Show Hint
In quantitative comparison questions involving variables with multiple possible values, check the extreme values. Compare the maximum possible value of one quantity with the minimum possible value of the other. If a consistent relationship holds (e.g., max(A)<min(B)), you have your answer. If not, the relationship cannot be determined.
Updated On: Oct 3, 2025
- Quantity A is greater.
- Quantity B is greater.
- The two quantities are equal.
- The relationship cannot be determined from the information given.
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept:
We are asked to compare the possible values of x and y, which are the solutions (roots) of two separate quadratic equations. We must solve each equation to find the possible values for x and y.
Step 2: Key Formula or Approach:
We will solve each quadratic equation by factoring. For an equation of the form \(ax^2 + bx + c = 0\), we look for two numbers that multiply to \(c\) and add to \(b\).
Step 3: Detailed Explanation:
Solving for x:
The equation for x is \(x^2 + 5x - 24 = 0\).
We need two numbers that multiply to -24 and add to +5. These numbers are +8 and -3.
So, we can factor the equation as: \[ (x + 8)(x - 3) = 0 \] This gives two possible values for x: \[ x = -8 \quad \text{or} \quad x = 3 \]
Solving for y:
The equation for y is \(y^2 - 9y + 20 = 0\).
We need two numbers that multiply to +20 and add to -9. These numbers are -4 and -5.
So, we can factor the equation as: \[ (y - 4)(y - 5) = 0 \] This gives two possible values for y: \[ y = 4 \quad \text{or} \quad y = 5 \]
Comparing Quantity A and Quantity B:
The possible values for Quantity A (x) are \{-8, 3\}.
The possible values for Quantity B (y) are \{4, 5\}.
Let's compare the largest possible value of x with the smallest possible value of y.
The largest value for x is 3.
The smallest value for y is 4.
Since \(3<4\), any possible value of y will be greater than any possible value of x.
Step 4: Final Answer:
Quantity B is always greater than Quantity A.
We are asked to compare the possible values of x and y, which are the solutions (roots) of two separate quadratic equations. We must solve each equation to find the possible values for x and y.
Step 2: Key Formula or Approach:
We will solve each quadratic equation by factoring. For an equation of the form \(ax^2 + bx + c = 0\), we look for two numbers that multiply to \(c\) and add to \(b\).
Step 3: Detailed Explanation:
Solving for x:
The equation for x is \(x^2 + 5x - 24 = 0\).
We need two numbers that multiply to -24 and add to +5. These numbers are +8 and -3.
So, we can factor the equation as: \[ (x + 8)(x - 3) = 0 \] This gives two possible values for x: \[ x = -8 \quad \text{or} \quad x = 3 \]
Solving for y:
The equation for y is \(y^2 - 9y + 20 = 0\).
We need two numbers that multiply to +20 and add to -9. These numbers are -4 and -5.
So, we can factor the equation as: \[ (y - 4)(y - 5) = 0 \] This gives two possible values for y: \[ y = 4 \quad \text{or} \quad y = 5 \]
Comparing Quantity A and Quantity B:
The possible values for Quantity A (x) are \{-8, 3\}.
The possible values for Quantity B (y) are \{4, 5\}.
Let's compare the largest possible value of x with the smallest possible value of y.
The largest value for x is 3.
The smallest value for y is 4.
Since \(3<4\), any possible value of y will be greater than any possible value of x.
Step 4: Final Answer:
Quantity B is always greater than Quantity A.
Was this answer helpful?
0
0
Top GRE Quantitative Aptitude Questions
One pen costs \(\$\)0.25 and one marker costs \(\$\)0.35. At those prices, what is the total cost of 18 pens and 100 markers?
- Working alone at its constant rate, machine A produces kkk liters of a chemical in 10 minutes. Working alone at its constant rate, machine B produces kkk liters of the chemical in 15 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce kkk liters of the chemical?
- If the dollar amount of sales at Store P was $800,000 for 2006, what was the dollar amount of sales at that store for 2008?
- At Store T, the dollar amount of sales for 2007 was what percent of the dollar amount of sales for 2008? Give your answer to the nearest 0.1%.
- If the ratio of A to B is 3:4 and the ratio of B to C is 5:6, what is the ratio of A to C?
View More Questions
Top GRE Quadratic Equation Questions
- The product of two consecutive positive integers is 272. What is the larger of the two integers?
- Given the equation \(x^2 - 5x = 6 - y^2 + 3y = 9y + 9\).
Quantity A: \(x\)
Quantity B: \(y\) - One of the roots of the equation x² + kx - 12 = 0 is 3, and k is a constant.
Quantity A: The value of k
Quantity B: -1
Top GRE Questions
One pen costs \(\$\)0.25 and one marker costs \(\$\)0.35. At those prices, what is the total cost of 18 pens and 100 markers?
- Working alone at its constant rate, machine A produces kkk liters of a chemical in 10 minutes. Working alone at its constant rate, machine B produces kkk liters of the chemical in 15 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce kkk liters of the chemical?
- If the dollar amount of sales at Store P was $800,000 for 2006, what was the dollar amount of sales at that store for 2008?
- At Store T, the dollar amount of sales for 2007 was what percent of the dollar amount of sales for 2008? Give your answer to the nearest 0.1%.
- If the ratio of A to B is 3:4 and the ratio of B to C is 5:6, what is the ratio of A to C?
View More Questions