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minustark
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How many solutions does the equation |x−A|=B have? 24 Sep 2019, 18:22
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50% (01:03) correct 50% (01:12) wrong based on 64 sessions

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How many solutions does the equation |x−A|=B have?

Statement 1: A=8

Statement 2: B=−8
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B
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How many solutions does the equation |x−A|=B have? 24 Sep 2019, 21:23
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For b=-8, there will be zero solutions as modulus can not be negative.

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How many solutions does the equation |x−A|=B have? 24 Sep 2019, 23:26
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Interesting question. What is the question source?
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How many solutions does the equation |x−A|=B have? 25 Sep 2019, 11:34
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minustark
How many solutions does the equation |x−A|=B have?

Statement 1: A=8

Statement 2: B=−8
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|x−A|=B

(1) A = 8
Many solutions are possible.
Insufficient

(2) B = -8
modulus can never be negative
—> 0 solutions
Sufficient

IMO B

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How many solutions does the equation |x−A|=B have? 25 Sep 2019, 12:18
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minustark
How many solutions does the equation |x−A|=B have?

Statement 1: A=8

Statement 2: B=−8
Show more

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

Since we have \(|x-A| ≥ 0\), \(|x-A| = -8\) does not have a solution.
Then we have an answer 'no', which is a unique answer.
Since 'no' is also a unique answer by CMT (Common Mistake Type) 1, Condition 1) is sufficient.

Condition 1)
If we have \(A = 8\), \(B = 8\), then we have \(x = 0\) or \(x = 16\) and we have two solutions.
If we have \(A = 8\), \(B = -8\), then we don't have a solution.
Since condition 1) does not yield a unique answer, it is not sufficient.

Therefore, B is the answer.
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How many solutions does the equation |x−A|=B have? 27 Sep 2019, 01:54
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But isn't the question asking for the number of solutions rather than for an unique solution?

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minustark
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How many solutions does the equation |x−A|=B have? 20 Oct 2019, 18:42
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philipssonicare
Interesting question. What is the question source?
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It's from Beat the gmat course.
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How many solutions does the equation |x−A|=B have? 28 Apr 2022, 23:18
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Whether "No solution" is a "Definite Solution"? Nope.
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