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[ Math Revolution GMAT math practice question] \(Is x<0?\) \(1) x=x\) \(2) x>x\)
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MathRevolution wrote: [ Math Revolution GMAT math practice question] \(Is x<0?\) \(1) x=x\) \(2) x>x\) S(1)\(x=x\) This transalte into \(x<=0\). So x could also be 0. Insufficient. S(2) \(x>x\) This translate into x<0. Sufficient. Answer: B
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Re: Is x<0?
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14 Sep 2018, 02:07
Hi, This is prettystraight forward question. Modulus function basic understanding is what it requires. Question: Is x < 0 ? Statement I is insufficient: x = x According to the definition of the modulus x = x , whenever x > = 0 x = x, whenever x < = 0. So here, x < 0 and also it could be equal to zero. So not sufficient. Alternatively, u can try plugging in the values in the given statement too, you can see zero and the negative values will work. Statement II is sufficient: x > x If “x” values are positive, then the given statement won’t be true. Its true only for the negative value of x. So sufficient. So the answer is B.
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Re: Is x<0?
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14 Sep 2018, 06:48
MathRevolution wrote: [ Math Revolution GMAT math practice question] \(Is x<0?\) \(1) x=x\) \(2) x>x\) Target question: Is x < 0? Statement 1: x = x Let's TEST some values. There are several values of x that satisfy statement 1. Here are two: Case a: x = 1. Notice that 1 = (1). In this case, the answer to the target question is YES, x IS less than 0Case b: x = 0. Notice that 0 = 0. In this case, the answer to the target question is NO, x is NOT less than 0Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT Statement 2: x > x If x > x, then we can be certain that x does not equal 0. So, let's see what happens if x is POSITIVE, and what happens if x is NEGATIVE If x is positive, then x > x becomes POSITIVE > POSITIVE This doesn't work, because some POSITIVE number is always equal to that same number. For example, 3 = 3 and 12.9 = 12.9 So, if x is POSITIVE, it cannot be the case that x > x In other words, x CANNOT by positiveSo, if x does not equal 0 and x CANNOT by positive, then we can be certain that x is negativeIn other words, the answer to the target question is YES, x IS less than 0Since we can answer the target question with certainty, statement 2 is SUFFICIENT Answer: B Cheers, Brent
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Re: Is x<0?
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14 Sep 2018, 07:43
MathRevolution wrote: [ Math Revolution GMAT math practice question] Is \(x<0?\) \(1) x=x\) \(2) x>x\) \(x\,\,\mathop < \limits^? \,\,0\) \(\left( 1 \right)\,\,\,\left x \right =  x\,\,\,\,\, \Leftrightarrow \,\,\,\,x \leqslant 0\,\,\,\,\left\{ \begin{gathered} \,{\text{Take}}\,\,x = 0\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{NO}}} \right\rangle \hfill \\ \,{\text{Take}}\,\,x =  1\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{YES}}} \right\rangle \hfill \\ \end{gathered} \right.\) \(\left( 2 \right)\,\,\,x < \left x \right\,\,\,\,\,\,\mathop \Leftrightarrow \limits^{\left( * \right)} \,\,\,\,\,x < 0\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{YES}}} \right\rangle \,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,{\text{SUFF}}{\text{.}}\,\,\,\,\) \(\left( * \right)\,\,x \geqslant 0\,\,\,\, \Rightarrow \,\,\,x = \left x \right\) This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio.
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Re: Is x<0?
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16 Sep 2018, 18:30
=> 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. Since we have 1 variable (x) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first. Condition 1) \(x = x\) \(=> x ≤ 0\) 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. Since the solution set “\(x<0\)” of the question doesn’t include the solution set “\(x ≤ 0\)” of the condition 1), condition 1) is not sufficient. Condition 2) \(x>x\) \(=> x < 0\) Since condition 2) is equivalent to the question, condition 2) is sufficient. Therefore, B is the answer. Answer: B 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.
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Re: Is x<0?
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17 Sep 2018, 03:42
Is x < 0?
A. x = x
Two possible cases
1. x=5 5=(5) 5=5, From this we can say that x<0. Now let's try to disprove it.
2. x=0 0=0, 0 is neither positive not negative
Hence A is insufficient.
B. x>x Let's analyse the statement. If the RHS is positive and greater than LHS, it means x is a ve value.
Let x be 2 2>2 2>2
Hence we can conclude that St 2 alone(B) is sufficient to answer the question.
Thank you Arjun










