Carcass wrote:
x and y are positive integers and \(x > y\).
Quantity A |
Quantity B |
\(x^2-y^2\) |
\(x+y\) |
There are two methods for solving this Quantitative Comparison - Plugging in Values or Algebraically. Let's first try plugging in.
If we were to select the easy values of x = 2 and y = 1, then Quantity A = 2² - 1² = 3 and Quantity B = 2 + 1 = 3.
In this scenario the quantities would be equal, so eliminate Choice A and Choice B since neither quantity is greater than the other.
Now, plug in a different value for only one of the variables such as x = 3 and y = 1.
Then, Quantity A = 3² - 1² = 8 and Quantity B = 3 + 1 = 4.
In this scenario Quantity A is greater, so eliminate Choice C and select Choice D since the relationship between the quantities is inconsistent.
Now, let's consider the algebraic approach.
The quadratic equation x² - y² in Quantity A can be factored to (x + y)(x - y).
Since x - y can = 1, it should be apparent that (x + y)(1) could be equal to x + y in Quantity B, but doesn't have to be equal, so you could also select Choice D immediately based on this deduction.