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# M60-17

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 5999
GMAT 1: 760 Q51 V42
GPA: 3.82

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Updated on: 27 Jul 2018, 19:39
00:00

Difficulty:

35% (medium)

Question Stats:

67% (00:55) correct 33% (00:19) wrong based on 9 sessions

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Is $$x^2-x>0?$$

1) $$x>0$$

2) $$x^3+x>0$$

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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" Originally posted by MathRevolution on 11 Jun 2018, 06:35. Last edited by MathRevolution on 27 Jul 2018, 19:39, edited 5 times in total. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5999 GMAT 1: 760 Q51 V42 GPA: 3.82 M60-17 [#permalink] ### Show Tags Updated on: 27 Jul 2018, 19:53 Official Solution: 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, and then recheck the question. In inequality questions, the law "Question is King" tells us that if the solution set of the question includes the solution set of the condition, then the condition is sufficient Modifying the question: $$x^2-x>0$$ ⇔ $$x(x-1) > 0$$ ⇔ $$x < 0$$ or $$x > 1$$ by the "LLGG" rule. Condition 1): $$x > 0$$ Since the solution set of the question does not include the solution set of condition 1), condition 1) is not sufficient. Condition 2): $$x^3+x>0$$ ⇔ $$x(x^2+1)>0$$ ⇔ $$x>0$$, since $$x^2+1 > 0$$ is always true. Condition 2) is equivalent to the condition 1), so it is not sufficient. Conditions 1) & 2) We have x >0 only from both conditions together. Since the solution set of the question does not include the solution set of conditions 1) and 2) together, they are not sufficient. Therefore, the answer is E. Answer: E If the original condition includes "1 variable", or "2 variables and 1 equation", or "3 variables and 2 equations" etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E. _________________ 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"
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Originally posted by MathRevolution on 11 Jun 2018, 06:35.
Last edited by MathRevolution on 27 Jul 2018, 19:53, edited 2 times in total.
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Joined: 23 Jul 2018
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26 Jul 2018, 18:35
I don't agree with the explanation. I believe this question is mistaking one of the solutions x < 0, for the first condition x >0. 1/2 would satisfy condition one but result in NO, but 2 would result in yes.
Math Expert
Joined: 02 Aug 2009
Posts: 6501

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26 Jul 2018, 19:19
3
Is $$x^2-x>0?$$
$$x^2-x>0..........X(x-1)>0$$..
Two cases..
a) if x>0, then x-1>0....X>1
b) if x<0....x-1<0....X<1
Hence question is asking
Is x<0 and x>1 or is it false that $$0\leq{X}\leq{1}$$
1) $$x>0$$
0<X<1....no
X>1....yes
Insufficient

2) $$x^3+x>0$$
X(x^2+1)>0.
X^2+1>0, so X>0..
Again 0<X<1....no
X>1....yes
Insufficient

Combined..
Same cases remain
Insufficient

E

OA and solution is wrong
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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26 Jul 2018, 20:12
MathRevolution wrote:
Is $$x^2-x>0?$$

1) $$x>0$$

2) $$x^3+x>0$$

To determine whether $$x^2 - x > 0$$

=> $$x * (x - 1) > 0$$

Statement 1

x > 0

x can be 9 => x(x-1) = 9*8 = 72 > 0

x can be 0.5 => x(x-1) = 0.5 * -0.5 = -0.25 < 0

Statement 1 is not sufficient

Statement 2

$$x^3 + x > 0$$

x can be 2 => $$x^3 + x > 0$$ = 8 + 2 = 10 > 0

x can be -2 => $$x^3 + x > 0$$ = -8 - 2 = -10 < 0

Statement 2 is not sufficient

Combining statements 1 and 2

x can be 2 => $$x^3 + x > 0$$ = 8 + 2 = 10 > 0

x can be 0.5 => x(x-1) = 0.5 * -0.5 = -0.25 < 0

Statements 1 and 2 together are not sufficient

Hence option E

MathRevolution Can you please look into this ?
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Joined: 01 Feb 2017
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26 Jul 2018, 21:38
The Q is basically asking to conclude that: x is NOT a proper fracton, positive or negative?

None of the two statements can confirm or dismiss this conclusively. Hence, Ans is E.

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Joined: 27 Dec 2017
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27 Jul 2018, 11:25
I don't agree with the explanation.
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Joined: 08 Feb 2018
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30 Jul 2018, 05:35
I think this is a high-quality question and I don't agree with the explanation. In case of first statement, if x lies between 0 and 1, lets say x=1/2, then x2-x<0, while if x>1, then x2-x>0, hence A is not sufficient.
The same goes for B if x lies in the range of 0 to 1
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Joined: 14 Jul 2018
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30 Jul 2018, 11:30
The explaination is incorrect. The correct answer should be Both the conditions are insufficient for x>0 gives us no information whether x>1 or not.
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Joined: 10 Mar 2016
Posts: 6
GMAT 1: 640 Q49 V28

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05 Aug 2018, 13:19
THE ANS SHOULD BE - E
Re: M60-17 &nbs [#permalink] 05 Aug 2018, 13:19
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# M60-17

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