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# Is x>0?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6613
GMAT 1: 760 Q51 V42
GPA: 3.82

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30 Jul 2018, 00:10
00:00

Difficulty:

45% (medium)

Question Stats:

54% (00:44) correct 46% (00:38) wrong based on 79 sessions

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[Math Revolution GMAT math practice question]

Is $$x>0$$?

$$1) x = |x|$$
$$2) x^2 - x = 0$$

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"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" Math Expert Joined: 02 Aug 2009 Posts: 7097 Re: Is x>0? [#permalink] ### Show Tags 30 Jul 2018, 01:16 Is $$x>0$$? $$1) x = |x|$$ This tells us that X is non-negative.. X can 0 or 1 If x=0, NO If x=1, YES Insufficient $$2) x^2 - x = 0$$ x(x-1)=0 Either x is 0 or 1 If x=0, NO If x=1, YES Insufficient Combined If x=0, NO If x=1, YES Insufficient E _________________ 1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html GMAT online Tutor Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6613 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Is x>0? [#permalink] ### Show Tags 01 Aug 2018, 01:03 => 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. Condition 1) $$x = |x|$$ $$=> x ≥ 0$$ In inequality questions, the law “Question is King” tells us that if the solution set of the question does not include the solution set of a condition, then the condition is not sufficient. Condition 1 is not sufficient. Condition 2) $$x^2-x =0$$ $$=> x(x-1) = 0$$ $$=> x = 0$$ or $$x = 1$$ If $$x = 0$$, then the answer is “no”. If $$x = 1$$, then the answer is “yes”. Since we don’t have a unique solution, condition 2) is not sufficient. Conditions 1) & 2) The two conditions give $$x = 0$$ or $$x = 1$$. They are not sufficient, when taken together, by the argument above. 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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01 Aug 2018, 16:19
MathRevolution wrote:
=>

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.

Condition 1)
$$x = |x|$$
$$=> x ≥ 0$$
In inequality questions, the law “Question is King” tells us that if the solution set of the question does not include the solution set of a condition, then the condition is not sufficient.
Condition 1 is not sufficient.

Condition 2)
$$x^2-x =0$$
$$=> x(x-1) = 0$$
$$=> x = 0$$ or $$x = 1$$
If $$x = 0$$, then the answer is “no”.
If $$x = 1$$, then the answer is “yes”.
Since we don’t have a unique solution, condition 2) is not sufficient.

Conditions 1) & 2)
The two conditions give $$x = 0$$ or $$x = 1$$.
They are not sufficient, when taken together, by the argument above.

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.

Could you please explain what do you mean by "In inequality questions, the law “Question is King” tells us that if the solution set of the question does not include the solution set of a condition, then the condition is not sufficient."
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6613
GMAT 1: 760 Q51 V42
GPA: 3.82

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02 Aug 2018, 10:55
ammuseeru wrote:
MathRevolution wrote:
=>

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.

Condition 1)
$$x = |x|$$
$$=> x ≥ 0$$
In inequality questions, the law “Question is King” tells us that if the solution set of the question does not include the solution set of a condition, then the condition is not sufficient.
Condition 1 is not sufficient.

Condition 2)
$$x^2-x =0$$
$$=> x(x-1) = 0$$
$$=> x = 0$$ or $$x = 1$$
If $$x = 0$$, then the answer is “no”.
If $$x = 1$$, then the answer is “yes”.
Since we don’t have a unique solution, condition 2) is not sufficient.

Conditions 1) & 2)
The two conditions give $$x = 0$$ or $$x = 1$$.
They are not sufficient, when taken together, by the argument above.

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.

Could you please explain what do you mean by "In inequality questions, the law “Question is King” tells us that if the solution set of the question does not include the solution set of a condition, then the condition is not sufficient."

"Question is King" is the word made by Math Revolution in order to help memorizing the following property.

If the solution set of a condition is included in that of a question, the condition is sufficient.
Since King should includes everything, the solution set of the question should include that of the condition in order for the condition to be sufficient.
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Re: Is x>0? &nbs [#permalink] 02 Aug 2018, 10:55
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