GRE
GRE Quantitative Reasoning Section

Comparison of Integer Sums and Products

Hard Arithmetic Integers

Consider two integers, $x$ and $y$. The product of these integers is represented by the equation:

$$xy = 72$$

Additionally, the following condition holds: the sum of the integers $x$ and $y$ can be expressed as:

$$x + y = k$$

where $k$ is some integer value. Determine the relationship between Quantity A and Quantity B defined as follows:

Quantity A: The maximum value of $k$ that can be achieved for the integers $x$ and $y$ given that their product is 72.

Quantity B: The minimum value of $k$ that can be achieved for the integers $x$ and $y$ given that their product is 72.

Hint

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