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If x < 0, which of the following must be true? [#permalink]
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03 Dec 2014, 07:19
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Re: If x < 0, which of the following must be true? [#permalink]
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03 Dec 2014, 09:28
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We're told that x is negative and that is all. Let's evaluate.
Since x is negative, x^2 is always positive (>0). True. Since x is negative then x2x>0. True as we're essentially adding a negative number to a larger (effectively positive number). For example, if x=.5, then 0.5 + 1>0 or if x = 1, then 1+2>0. However, the third doesn't have to be true. If x is a negative fraction, then x^2 is positive and larger than x^3. If x=1/2, then x^3+x^2 = 1/8 + 1/4>0. However, if x=1, then 1+1=0. Insufficient, not always true.
Choice B



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Re: If x < 0, which of the following must be true? [#permalink]
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03 Dec 2014, 19:35
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I. x^2 > 0 TRUE Irrespective of x sign, it will always be positive because of even power and since x is less than 0 x^2 can't be 0. II. x − 2x > 0 TRUE Since x<0 , x will be positive III. x^3 + x^2 < 0 Can not say x^2(x+1)<0 , since x^2 will always be positive => x+1 < 0 => x < 1. But we know that x<0, so x could be 1/2 etc.
Answer is B.



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Re: If x < 0, which of the following must be true? [#permalink]
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03 Dec 2014, 19:44
Bunuel wrote: Tough and Tricky questions: Must or Could be True Questions. If x < 0, which of the following must be true? I. x^2 > 0 II. x − 2x > 0 III. x^3 + x^2 < 0 A) I only B) I & II C) II & III D) All of the above E) None of the above Kudos for a correct solution.Source: Chili Hot GMAT Given: x is negative. Which of the following must be true? I. \(x^2 > 0\) This is always true for real numbers except if x is 0. Since x is negative, this must be true. II. \(x  2x > 0\) \(x > 0\) \(x < 0\) (multiplied both sides by 1). This is given so it must be true. III. \(x^3 + x^2 < 0\) \(x^2*(x + 1) < 0\) x^2 is positive so for x^2 * (x+1) to be negative, x+1 should be negative i.e. x < 1. We know that x < 0 but it could very well lie between 0 and 1 and hence this needn't be true. It may or may not be. So only (I) and (II) must be true. Answer (B)
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Re: If x < 0, which of the following must be true? [#permalink]
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03 Dec 2014, 19:53
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Answer = B) I & II I. x^2 > 0Square of any number is always positive. Always true II. x  2x > 0x > 0 x < 0 (This is the given condition in the problem, which has to be obviously true) III. x^3 + x^2 < 0\(For x = \frac{1}{2}\) \(\frac{1}{4}  \frac{1}{8} > 0\) (Not necessarily true) Answer = B
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Re: If x < 0, which of the following must be true? [#permalink]
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03 Dec 2014, 23:04
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Given: x < 0, I. x^2 > 0 > squaring is never negative > so always true II. x − 2x > 0 > x>0, since x is given as ve no. so ve of ve no. is always +ve > so always true III. x^3 + x^2 < 0 >x^2(x+1)<0 and given is x<0 so it can be 1, in that case (1)^2(1+1)<0 = 0<0 > so not always true Ans. B) I & II
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Re: If x < 0, which of the following must be true? [#permalink]
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21 Feb 2017, 12:03
Bunuel wrote: Tough and Tricky questions: Must or Could be True Questions. If x < 0, which of the following must be true? I. x^2 > 0 II. x − 2x > 0 III. x^3 + x^2 < 0 A) I only B) I & II C) II & III D) All of the above E) None of the above Kudos for a correct solution.Source: Chili Hot GMAT We can invalid III by putting the fraction value of x. So, the correct choice is B.
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Re: If x < 0, which of the following must be true? [#permalink]
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21 Feb 2017, 21:54
Bunuel wrote: Tough and Tricky questions: Must or Could be True Questions. If x < 0, which of the following must be true? I. x^2 > 0 II. x − 2x > 0 III. x^3 + x^2 < 0 A) I only B) I & II C) II & III D) All of the above E) None of the above Kudos for a correct solution.Source: Chili Hot GMAT Given: x<0I. x^2 > 0 Since x is NonZero so x^2 is bound to be Positive hence CORRECT II. x − 2x > 0 i.e. x > 0 i.e. x <0 hence CORRECT III. x^3 + x^2 < 0 i.e. x^2(x+1) < 0 x^2 is always positive but (x+1) may or may not be negative for values of x less than or greater than 1 hence this is not always True Answer: Option B
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