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If x is not equal to 0 or 1, what is the value of x2? [#permalink]
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19 May 2015, 06:37
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If x is not equal to 0 or 1, what is the value of x2? (1) \(\frac{(x+1)}{(xx^3)}>0\) (2) \(x^4 = 16\) This is Question 1 for the eGMAT Question Series on Absolute Value.Provide your solution below. Kudos for participation. Happy Solving! Best Regards The eGMAT Team
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Re: If x is not equal to 0 or 1, what is the value of x2? [#permalink]
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19 May 2015, 09:19
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EgmatQuantExpert wrote: If x is not equal to 0 or 1, what is the value of x2? (1) \(\frac{(x+1)}{(xx^3)}>0\) (2) \(x^4 = 16\) This is Question 1 for the eGMAT Question Series on Absolute Value.Provide your solution below. Kudos for participation. The Official Answer and Explanation will be posted on 20th May. Till then, Happy Solving! Best Regards The eGMAT Team Statement 1Does't give you a final value of x2. I tried to rearange the inequality but you can not multiply by \(xx^3\) because the term can be positive or negative (you don't know). Therefore the whole Statement 1 just tells you that some Division with X is > 0 and is therefore insufficient because it doesn't provide a VALUE for x2. Statement 2x can be 2 or 2. Which is insufficient. If you combine Statement 1 and 2 you know that in order to be true, Statement 1 needs a positive denominator which is just possible if X equals 2 (x^3 would then be 8 and the denominator would be 8*2 = 16. Answer Choice C
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Re: If x is not equal to 0 or 1, what is the value of x2? [#permalink]
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19 May 2015, 09:23
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Statement 1 says x is negative. Statement 2 gives 2 and 2 as values. Combining the two we get x as 2 So Answer must be C
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Re: If x is not equal to 0 or 1, what is the value of x2? [#permalink]
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19 May 2015, 09:29
EgmatQuantExpert wrote: If x is not equal to 0 or 1, what is the value of x2? (1) \(\frac{(x+1)}{(xx^3)}>0\) (2) \(x^4 = 16\) This is Question 1 for the eGMAT Question Series on Absolute Value.Provide your solution below. Kudos for participation. The Official Answer and Explanation will be posted on 20th May. Till then, Happy Solving! Best Regards The eGMAT Team hi, (1) \(\frac{(x+1)}{(xx^3)}>0\)... we know that for fraction to be greater than 0 both deno and numerator should be of same sign.... numeratos has to be +ive as it is mod.. so xx^3 should be positive so x is a negative integer.. no other info ... insuff (2) \(x^4 = 16\) x can be 2 or 2... insuff combined we get x as 2 .. suff ans C
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Re: If x is not equal to 0 or 1, what is the value of x2? [#permalink]
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20 May 2015, 02:21
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Stmt 1fraction is > 0 then Numerator & Denominator need to be same sign. Numerator x2 > 0 Denominator \(xx^3 > 0\) for this ( \(x^3 < 0\)) , implies x < 0 insufficient.Stmt 2x can be 2 or 2. insufficient.combine 1 and 2 we get the answer, from 1 we know x < 0, and from 2 we know (x = 2 or 2) Ans : C
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Re: If x is not equal to 0 or 1, what is the value of x2? [#permalink]
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22 May 2015, 02:58
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EgmatQuantExpert wrote: If x is not equal to 0 or 1, what is the value of x2? (1) \(\frac{(x+1)}{(xx^3)}>0\) (2) \(x^4 = 16\) This is Question 1 for the eGMAT Question Series on Absolute Value. Official ExplanationIn order to find the value of x2, we first need to know the value of x. From question statement, we know that x is not equal to 0 or 1. Let's see if St. 1 and/or 2 can get us a unique value of x. Analyzing St. 1 Independently
\(\frac{(x+1)}{(xx^3 )}>0\)Multiplying both sides by a positive number doesn’t impact the sign of inequality. So, multiplying both sides by \(\frac{(x)}{(x+1)}\), we get: \(\frac{(1)}{x^3} >0\) (Note that we could multiply both sides by this number because we were told that x ≠ 1. Therefore, x + 1 ≠ 0 (division by 0 is not defined))Now, multiplying both sides by 1 will reverse the sign of inequality. We get: \(\frac{1}{x^3}<0\) \(x^3\) will have the same +/ sign as x This means, \(1/x\) is negative. This means, x is negative. This information is not sufficient to find the value of x. Analyzing St. 2 independently \(x^4 = 16\)That is, \(x^4  2^4 = 0\) \((x^2 + 2^2)(x+2)(x2) = 0\) This gives us, x = 2 or 2 Since we don’t get a unique value of x, not sufficient. Combining St. 1 and St. 2From St. 1, x is negative From St. 2, x = 2 or 2 Combining both, x = 2 Sufficient.
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Re: If x is not equal to 0 or 1, what is the value of x2? [#permalink]
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11 Jul 2016, 08:05
from the 1 statement we come to know that x is negative as we have denominator as negative.So the expression to be grater than 0 x^3 should be negative.then only it will br=e greater than zero.We do not get any definite value except x is negative.So NS
From2 statement we get that x could be 2 or 2 and both give different answers when put inside the expression.So NS
Combined we get x is negative which is only 2.And we get definite value.So answer is C.
Let me know if i am wrong.



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Re: If x is not equal to 0 or 1, what is the value of x2? [#permalink]
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17 Aug 2017, 18:28
I know this is unnecessary, but can anyone confirm that the below is correct if it was necessary to do so. Trying to make sure I understand the 3 step approach to absolute modulus.
For statement 1:
Since l x+1 l is always positive, then l x+ 1 l >0
critical point is 1,
a) so if x>1, then x+1 is positive, so x+1>0, and x>1, b) if x<1, then X+1 is negative, so (x+1)>0, and x<1,
so x>1 or x<1 right?
Denominator needs to have the same sign as the numerator, so x must be negative for denominator to be positive. so x>1, but doesn't solve what lx2l is.
2) x^4=16, x= 2 or 2, insuff.
c: x>1, so x=2. Suff.
Did I handle the splitting up the modulus correctly in statement 1? Thank you! Kudos to whoever answers.



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Re: If x is not equal to 0 or 1, what is the value of x2? [#permalink]
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26 Feb 2018, 04:25
EgmatQuantExpert wrote: If x is not equal to 0 or 1, what is the value of x2?
(1) \(\frac{(x+1)}{(xx^3)}>0\)
(2) \(x^4 = 16\)
X is NOT equal to 1 or 0. x2 = ??? Strategically I will start with statement 2 to have sense of numbers. Statement 2\(x^4 = 16\) x =2.....22= 0 or x =2...22= 4 Hence it gives Two different values Insufficient Statement 1 From what we have let's test the answers we got: Let x =2.........\(\frac{(x+1)}{(xx^3)}>0\)..When x is positive, then this will make Statement 1 invalid........ Discard any positive number. Let x =2.........\(\frac{(x+1)}{(xx^3)}>0\) ..Any negative number will make make Statement 1 valid... But No certain value. Insufficient Combine 1 & 2 From 1: We know that we need a negative number to make make it valid From 2: We got 2 Hence we reach certain value Answer: C




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