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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Is √(x+1)^2=x+1 ? tagged by: Max@Math Revolution ##### This topic has 2 expert replies and 0 member replies ### GMAT/MBA Expert ## Is √(x+1)^2=x+1 ? ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [Math Revolution GMAT math practice question] Is $$\sqrt{\left(x+1\right)^2}=x+1$$ ? 1) x(x-2) = 0 2) x(x+2) = 0 _________________ Math Revolution Finish GMAT Quant Section with 10 minutes to spare. The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. Only$149 for 3 month Online Course
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Max@Math Revolution wrote:
[Math Revolution GMAT math practice question]

Is $$\sqrt{\left(x+1\right)^2}=x+1$$ ?

1) x(x-2) = 0
2) x(x+2) = 0
√(a²) = |a|.
Question stem, rephrased:
Is |x+1| = x+1?
The answer will be YES if x+1 is NONNEGATIVE:
x+1≥0
x≥-1.
Question stem, rephrased again:
Is x≥-1?

Statement 1:
x=0 or x=2.
Since x≥-1 in both cases, the answer to the question stem is YES.
SUFFICIENT.

Statement 2:
x=0 or x=-2.
If x=0, the answer to the question stem is YES, but if x=-2, the answer to the questions stem is NO.
INSUFFICIENT.

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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.

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

The question is equivalent to asking if x ≥ -1 as shown below:
$$\sqrt{\left(x+1\right)^2}=x+1$$
=> |x+1| = x+1
=> x ≥ -1

Since we have 1 variable (x) and 0 equations, D is most likely to be the answer. So, we should consider each condition on its own first.

Condition 1)
x(x-2) = 0
=> x = 0 or x = 2
If x = 0, then x ≥ -1 and the answer is ‘yes’.
If x = 2, then x ≥ -1 and the answer is ‘yes’.
Since it gives a unique answer, condition 1) is sufficient.

Condition 2)
x(x+2) = 0
=> x = 0 or x = -2
If x = 0, then x ≥ -1 and the answer is ‘yes’.
If x = -2, then x < -1 and the answer is ‘no’.
Since it does not give a unique answer, condition 2) is not sufficient.

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.

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