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# Is (x-1)^3< (x-1)?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8251
GMAT 1: 760 Q51 V42
GPA: 3.82

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13 Mar 2018, 00:55
00:00

Difficulty:

25% (medium)

Question Stats:

71% (01:39) correct 29% (02:06) wrong based on 63 sessions

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[GMAT math practice question]

Is $$(x-1)^3< (x-1)$$?

$$1) x>-1$$
$$2) x<0$$

_________________
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" Math Expert Joined: 02 Aug 2009 Posts: 8305 Re: Is (x-1)^3< (x-1)? [#permalink] ### Show Tags 13 Mar 2018, 08:27 MathRevolution wrote: [GMAT math practice question] Is $$(x-1)^3< (x-1)$$? $$1) x>-1$$ $$2) x<0$$ $$(x-1)^3<x-1.......(x-1)^3-(x-1)<0......(x-1)((x-1)^2-1)<0.....(x-1)(x^2-2x)<0....x(x-1)(x-2)<0$$ A) if x<0, x-1 and x-2 are NEGATIVE B) if x>0, one of x-1ans x-2 is POSITIVE and other NEGATIVE. Or x is between 1 and 2 Let's see the statements.. 1) x>-1.. If x is -0.5 or 1.5 Ans is YES If x is 3 or 4, Ans is NO Insufficient 2)x<0 ANS is always YES as in case (A).. Sufficient B _________________ Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8251 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Is (x-1)^3< (x-1)? [#permalink] ### Show Tags 15 Mar 2018, 02:20 => 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 can be modified as follows: $$(x-1)^3< (x-1)$$ $$=> (x-1)^3- (x-1) < 0$$ $$=> (x-1)((x-1)^2- 1) < 0$$ $$=> (x-1)((x-1)+1)((x-1)-1) < 0$$ $$=> x(x-1)(x-2) < 0$$ $$=> x < 0$$ or $$1 < x < 2$$ So, the question asks whether $$x < 0$$ or $$1 < x < 2$$. Condition 1) Since the set of the question doesn’t include that of condition 1), it is not sufficient. Condition 2) Since the set of the question includes that of condition 2), it is sufficient. Therefore, the answer is B. 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$79 for 1 month Online Course"
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Joined: 08 Dec 2013
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Location: India
Concentration: Nonprofit, Sustainability
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19 Jun 2019, 18:15
1
MathRevolution wrote:
[GMAT math practice question]

Is $$(x-1)^3< (x-1)$$?

$$1) x>-1$$
$$2) x<0$$

So we have to find (x-1) <, > or = 0.

Statement 1.
(x-1) > -2, so we have different equations for (x-1) +ve and -ve. Insufficient.

Statement 2. tells us that x<0 so (x-1) is a negative number always.
cube of a negative number is always less than the number provided the negative number is <-1. So we just have to check it by substitution.
Always check [-1,1] anomaly this is a dangerous zone.

Sufficient, so B.
Re: Is (x-1)^3< (x-1)?   [#permalink] 19 Jun 2019, 18:15
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