If x + y = 36, what is the value of xy?

Target question: What is the value of xy?

Given: x + y = 36

Statement 1: y − x = 14
So, we have the system:
y − x = 14
y + x = 36

Do we need to solve this system to determine the values of x and y and then find the product xy?
No.
All we need to do is confirm that the two equations are not equivalent.

Here's what I mean:
If the equation in statement 1 were 2x + 2y = 72, then this equation is equivalent to the given equation, y + x = 36. Notice that, if we take y + x = 36 and multiply both sides by 2, we get: 2x + 2y = 72. As such, the equations y + x = 36 and 2x + 2y = 72 are equivalent.
In cases where the two equations are equivalent, we have an infinite number of solutions, which means we can't solve that particular system.

Since the two equations in our system are not equivalent, we can be certain that there will be only one solution.
As such, we COULD solve the system for x and y, which means we COULD find the value of xy with certainty.
Since we COULD answer the target question with certainty, statement 1 is SUFFICIENT

Aside: there are cases when two non-equivalent equations can also have ZERO solutions, but this scenario would not appear in a Data Sufficiency question. For more on this, please see the second video below.

Statement 2: y = 2x + 3
So, we have the system:
y = 2x + 3
y + x = 36
Since the two equations in this system are not equivalent, we can be certain that there will be only one solution.
As such, we COULD solve the system for x and y, which means we COULD find the value of xy with certainty.
Since we COULD answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

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