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If x is an integer, then how many values of x will satisfy the equation

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by BTGModeratorVI » Thu Aug 27, 2020 12:09 pm

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Answers

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If x is an integer, then how many values of x will satisfy the equation ||x - 2| + 7| = 6?

A) 0
B) 1
C) 2
D) 3
E) 4

Answer: A
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Re: If x is an integer, then how many values of x will satisfy the equation

by Brent@GMATPrepNow » Thu Aug 27, 2020 4:34 pm
BTGModeratorVI wrote: ↑
Thu Aug 27, 2020 12:09 pm
 If x is an integer, then how many values of x will satisfy the equation ||x - 2| + 7| = 6?

A) 0
B) 1
C) 2
D) 3
E) 4

Answer: A
Source: e-GMAT
Given: ||x - 2| + 7| = 6
This means EITHER |x - 2| + 7 = 6 OR |x - 2| + 7 = -6
Let's examine each possibility....

Take: |x - 2| + 7 = 6
Subtract 7 from both sides to get: |x - 2| = -1
Since the absolute value of any expression will ALWAYS be greater than or equal to 0, we can see that the equation |x - 2| = -1 has no solution.

Take: |x - 2| + 7 = -6
Subtract 7 from both sides to get: |x - 2| = -13
Since the absolute value of any expression will ALWAYS be greater than or equal to 0, we can see that the equation |x - 2| = -13 has no solution.

Since there are no values of X that will satisfy the original equation, correct answer is A

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Brent
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Re: If x is an integer, then how many values of x will satisfy the equation

by Scott@TargetTestPrep » Mon Aug 31, 2020 10:32 am
BTGModeratorVI wrote: ↑
Thu Aug 27, 2020 12:09 pm
 If x is an integer, then how many values of x will satisfy the equation ||x - 2| + 7| = 6?

A) 0
B) 1
C) 2
D) 3
E) 4

Answer: A
Solution:

We could have |x - 2| + 7 = 6 or |x - 2| + 7 = -6 (since |6| = |-6| = 6).

If |x - 2| + 7 = 6, then |x - 2| = -1. However, an absolute value can’t be negative, so there are no solutions to this equation.

If |x - 2| + 7 = -6, then |x - 2| = -13. Again, an absolute value can’t be negative, so there are no solutions to this equation either.

Answer: A

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