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Last Updated on May 4, 2023
GMAT OFFICIAL GUIDE PS
Solution:
This is an interesting question because our initial instincts tell us to square x -1 by the FOIL method. However, an easier method is to instead take the square root of both sides of the equation.
(x – 1)^2 = 400
√(x – 1)^2 = √400
This gives us:
|x – 1| = 20
Because there is an expression inside the absolute value sign, we must consider that the entire expression, and not just the variable, can be either positive or negative. We’ll need to solve the equation twice.
Solve for x-1 as positive:
|x – 1| = 20
x – 1 = 20
x = 21
Solve for x-1 as negative:
|x – 1| = 20
-(x – 1) = 20
-x + 1 = 20
-x =19
x = -19
Thus, x – 5 can equal either 21 – 5 = 16 or -19 – 5 = -24.
Answer: C
