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# What is the value of x? 1) x^-2x=1 2) x^x=1

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6028
GMAT 1: 760 Q51 V42
GPA: 3.82
What is the value of x? 1) x^-2x=1 2) x^x=1  [#permalink]

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20 Oct 2017, 01:09
00:00

Difficulty:

45% (medium)

Question Stats:

56% (00:35) correct 44% (00:44) wrong based on 81 sessions

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[GMAT math practice question]

What is the value of x?

1) $$x^{-2x}=1$$
2) $$x^x=1$$

_________________

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 $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Expert Joined: 02 Aug 2009 Posts: 6554 What is the value of x? 1) x^-2x=1 2) x^x=1 [#permalink] ### Show Tags 20 Oct 2017, 01:30 1 MathRevolution wrote: [GMAT math practice question] What is the value of x? 1) $$x^{-2x}=1$$ 2) $$x^x=1$$ Hi... 1) $$x^{-2x}=1$$ x can have two values.. 1.....$$1^{-2*1}=1^{-2}=\frac{1}{1^2}=1$$ -1.....$$-1^{-2*-1}=-1^{2}=1$$ different answers possible Insuff 2) $$x^x=1$$ Only possibility is x as 1 suff B _________________ 1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html GMAT online Tutor Director Status: Preparing for GMAT Joined: 25 Nov 2015 Posts: 746 Location: India GPA: 3.64 Re: What is the value of x? 1) x^-2x=1 2) x^x=1 [#permalink] ### Show Tags 20 Oct 2017, 10:25 S1- $$x^{-2x}$$=1 $$\frac{1}{x^{2x}}$$ = 1 $$x^{2x}$$=1 $$|x^x|$$=1 $$x^x$$ = 1 or -1 Insufficient. S2 - $$x^x$$=1 Only possible value is x=1. Answer B Please give kudos, if u liked my post! _________________ Please give kudos, if you like my post When the going gets tough, the tough gets going... Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6028 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: What is the value of x? 1) x^-2x=1 2) x^x=1 [#permalink] ### Show Tags 22 Oct 2017, 21:17 => Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember that equal number of variables and independent equations ensures a solution. We have 1 variable and 0 equation. D is most likely to be the answer. Condition 1) Both x =1 and x = -1 satisfy condition 1). Since the solution are not unique, this condition is not sufficient. Condition 2) Only x = 1 satisfies condition 2). This is sufficient. Note. 00 = 1 is not in the scope of GMAT exam. Therefore, B is the answer. For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both con 1) and con 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. D is most likely to be the answer using con 1) and con 2) separately according to DS definition. Obviously, there may be cases where the answer is A, B, C or E. Answer: B _________________ 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$99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
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Re: What is the value of x? 1) x^-2x=1 2) x^x=1 &nbs [#permalink] 22 Oct 2017, 21:17
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