Problem Solving

If x > y, x < 6, and y > -3, what is the largest prime number that could be equal to x + y?

A. 11
B. 13
C. 7
D. 5
E. 2

The OA is A.

It is difficult. Can any experts help me?

Vincen wrote:If x > y, x < 6, and y > -3, what is the largest prime number that could be equal to x + y?

A. 11
B. 13
C. 7
D. 5
E. 2

We can PLUG IN THE ANSWERS, which represent the largest prime number that could be equal to x+y.
Since the question stem asks for the largest possible prime number, start with the greatest answer choice.

B: x+y=13, implying that x=13-y
Substituting x=13-y into x<6, we get:
13-y < 6
7 < y
y>7.
Not viable, since x<6, and the prompt requires that x>y.

A: x+y=11, implying that x=11-y
Substituting x=11-y into x<6, we get:
11-y < 6
5 < y
y>5.
This works:
If y=5.1 and x=5.9, then all of the constraints are satisified:
y>-3
x<6
x>y
x+y = 11.

The correct answer is A.