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05 Jan 2022, 03:15
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94% (00:39) correct
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Which of the following represents the solution set to the equation \(|x – 7| = 12\)?
A. {5, 19}
B. {-5, 19}
C. {5, -5}
D. {19, -19}
E. {5, -19}
A. {5, 19}
B. {-5, 19}
C. {5, -5}
D. {19, -19}
E. {5, -19}
05 Jan 2022, 07:08
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Bunuel
Which of the following represents the solution set to the equation \(|x – 7| = 12\)?
A. {5, 19}
B. {-5, 19}
C. {5, -5}
D. {19, -19}
E. {5, -19}
A. {5, 19}
B. {-5, 19}
C. {5, -5}
D. {19, -19}
E. {5, -19}
STRATEGY: As with all GMAT Problem Solving questions, we should immediately ask ourselves, Can I use the answer choices to my advantage?
In this case, we can easily test the answer choices.
Now we should give ourselves about 20 seconds to identify a faster approach.
In this case, we can also solve the equation.
Since there aren't many values (among the answer choices) to test, I'm going to test the given values.
Is x = 5 a solution?
Plug into the equation to get: |5 – 7| = 12
Simplify: |-2| = 12
Doesn't work.
Since x = 5 is NOT a solution, we can eliminate answer choices A, C and E, since they state that x = 5 IS a solution.
Is x = -5 a solution?
Plug into the equation to get: |(-5) – 7| = 12
Simplify: |-12| = 12
WORKS!
Since x = -5 IS a solution, we can eliminate answer choice D, since it states that x = -5 is NOT a solution.
By the process of elimination, the correct answer is B
-------------------------------------------
ALTERNATE SOLUTION
If |x| = k, then x = k or x = -k
So, we get: x – 7 = 12 or x – 7 = -12
If x – 7 = 12, then we can solve the equation to get x = 19
If x – 7 = -12, then we can solve the equation to get x = -5
Answer: B
General Discussion
21 May 2022, 10:36
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We need to find all the solutions for |x – 7| = 12
So, Answer will be B
Hope it helps!
Watch the following video to learn the Basics of Absolute Values
| As we have |x-7| in the equation so we will have two cases | |
| -Case 1: x-7 ≥ 0 or x ≥ 7 => |x-7| = x-7 => x-7 = 12 => x = 19 But condition was x ≥ 7 which is true for x = 19 => x = 19 is a SOLUTION | -Case 2: x-7 < 0 or x < 7 => |x-7| = -(x-7) = 7 - x => 7 - x = 12 => x = 7 - 12 = -5 But condition was x < 7 which is true for x = -5 => x = -15 is a SOLUTION |
So, Answer will be B
Hope it helps!
Watch the following video to learn the Basics of Absolute Values
