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# x=?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8007
GMAT 1: 760 Q51 V42
GPA: 3.82

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29 Mar 2018, 01:09
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Difficulty:

55% (hard)

Question Stats:

59% (01:55) correct 41% (01:57) wrong based on 73 sessions

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[GMAT math practice question]

$$x=?$$

$$1)\sqrt{x^2-1}+\sqrt{y^2-1}=0$$
$$2)(x^2-1)^2+(y^2-1)^2=0$$

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MathRevolution: 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 $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Intern Joined: 28 Feb 2018 Posts: 8 Re: x=? [#permalink] ### Show Tags 29 Mar 2018, 01:28 from 1) x2+y2=0 solve 2) and replace value from1) in 2) so x=0 Director Joined: 21 May 2013 Posts: 636 Re: x=? [#permalink] ### Show Tags 29 Mar 2018, 02:16 Priyanka8793 wrote: from 1) x2+y2=0 solve 2) and replace value from1) in 2) so x=0 x can be both 1 or -1 in both the statements. So, both statements combined are not sufficient. Answer E Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8007 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: x=? [#permalink] ### Show Tags 01 Apr 2018, 18:42 => 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. Since we have 2 variables (x and y) and 0 equations, C is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first. Conditions 1) & 2) together: $$\sqrt{x^2-1}+\sqrt{y^2-1}=0$$ => $$x^2 = 1$$ and $$y^2 = 1$$ => $$x = ±1$$ and $$y = ±1$$ $$(x^2-1)^2+(y^2-1)^2=0$$ =>$$x^2 = 1$$and $$y^2 = 1$$ => $$x = ±1$$ and $$y = ±1$$ The two conditions yield $$x = ±1$$ and $$y = ±1$$. As this does not give us a unique value of x, both conditions together are not sufficient. Therefore, E is the answer. Answer: E Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E. _________________ MathRevolution: 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$79 for 1 month Online Course"
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Re: x=?   [#permalink] 01 Apr 2018, 18:42
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