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

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Is (x-1)^3< (x-1)?  [#permalink]

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New post 13 Mar 2018, 00:55
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Question Stats:

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[GMAT math practice question]

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

\(1) x>-1\)
\(2) x<0\)

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Re: Is (x-1)^3< (x-1)?  [#permalink]

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New post 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
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Re: Is (x-1)^3< (x-1)?  [#permalink]

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New post 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
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Re: Is (x-1)^3< (x-1)?  [#permalink]

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