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Last Updated on May 4, 2023
GMAT OFFICIAL GUIDE PS
Solution:
To solve this problem it’s easier to refer to a diagram of what is provided in the problem stem. In creating the diagram we can also fill in any variables we need to solve the problem.
Notice that we labeled the width of the border as x. We are given that the area of the border is 144 square inches. Knowing this, we can set up the following equation:
Area of Entire Shape – Area of Picture = Area of Border
(8 + 2x)(10 + 2x) – (8) (10) = 144
80 + 16x + 20x + 4x^2 – 80 = 144
4x^2 + 36x – 144 = 0
x^2 + 9x – 36 = 0
(x + 12)(x – 3) = 0
x = -12 or x = 3
Since we cannot have a negative length, x = 3. Thus, the width of the border is 3 inches.
Answer: A
