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Which of the following must be equal to zero for all real nu
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22 Jan 2014, 01:28
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The Official Guide For GMAT® Quantitative Review, 2ND EditionWhich of the following must be equal to zero for all real numbers x ? I. \(\frac{1}{x}\) II. x + (x) III. x^0 (A) I only (B) II only (C) I and II I only (D) II and III only (E) I, II , and III Problem Solving Question: 55 Category: Arithmetic Properties of numbers Page: 69 Difficulty: 600 GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition  Quantitative Questions ProjectEach week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution. We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation. Thank you!
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Re: Which of the following must be equal to zero for all real nu
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22 Jan 2014, 01:28



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Re: Which of the following must be equal to zero for all real nu
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22 Jan 2014, 04:54
I go for B.
i. 1/x: if divided by any real number, the answer will never be zero. If 'x' =0; the answer is 'undefined' ii. x+(x): any real number will yield a result of zero when substituted for x in the expression iii. x^0: this yields 1 as an answer if x is any real number.



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Re: Which of the following must be equal to zero for all real nu
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22 Jan 2014, 20:06
I. 1/x will not be 0 for any real number; The value will be undefined if x is 0; II. The value will be 0 for any real number. (ex.,) 2 + (2) = 22 = 0; III. x^0 = 1 for real numbers;
II only.
Ans is (B)



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Re: Which of the following must be equal to zero for all real nu
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22 Jan 2014, 22:34
Once we eliminate i, we realize from the answer choices that we can ignore ii and look at iii. Once iii is eliminated, we know ii is the answer.



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Re: Which of the following must be equal to zero for all real nu
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22 Jan 2014, 23:29
Bunuel wrote: The Official Guide For GMAT® Quantitative Review, 2ND EditionWhich of the following must be equal to zero for all real numbers x ? I. \(\frac{1}{x}\) II. x + (x) III. x^0 (A) I only (B) II only (C) I and II I only (D) II and III only (E) I, II , and III Lets look at III first  Anything raise to 0 is 1, so x^0 = 1. Now eliminate any answer choice that has III in options. Options C, D, E are eliminated. I 1/x will never be equal to zero for any real number, value will be undefined if x = o Hence option A is eliminated. We are left only with B, so B is the right answer. II x + (x) will be zero for any real number = x. for example x= 2.6. 2.6  2.6 = 0
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Re: Which of the following must be equal to zero for all real nu
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23 Jan 2014, 01:09
Bunuel wrote: Which of the following must be equal to zero for all real numbers x ? I. \(\frac{1}{x}\) II. x + (x) III. x^0 (A) I only (B) II only (C) I and II I only (D) II and III only (E) I, II , and III Problem Solving Question: 55 Category: Arithmetic Properties of numbers Page: 69 Difficulty: 600 I would go with B 1/x can be 1/2,1/4,... (x)+(x) will be 0 for all real numbers x^0 will either yield 1 or be indeterminate for 0^0
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Re: Which of the following must be equal to zero for all real nu
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23 Jan 2014, 06:12
Answer is B 1/0 is undefined so option A is never 0 also 0^0 is undefined or 1 so option C is also never 0 so we are left with option B only Answer B
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Re: Which of the following must be equal to zero for all real nu
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25 Jan 2014, 11:26



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Re: Which of the following must be equal to zero for all real nu
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04 Dec 2014, 02:51
Isn't zero a real number? And if it is, \(0^0\) is 0 isn't it? Or is it undefined in GMAT?



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Re: Which of the following must be equal to zero for all real nu
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04 Dec 2014, 02:56



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Re: Which of the following must be equal to zero for all real nu
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04 Dec 2014, 04:26
Bunuel wrote: 0 is a real number.But you won't need this for the GMAT because the case of 0^0 is not tested on the GMAT Thanks! But it is interesting you say that because if 0 is a real number then I am forced to use 0^0 for statement (3), in which case, this question isn't a GMAT type question. Oh well, I guess I will just chalk this one up to "fringe maths".



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Re: Which of the following must be equal to zero for all real nu
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04 Dec 2014, 04:28



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Re: Which of the following must be equal to zero for all real nu
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14 Jan 2017, 18:10
1, \(\frac{1}{x}\) # 0 2, x + (x) = x  x = always 0 for any number 3, x^0 = 1 but not 0 B
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Re: Which of the following must be equal to zero for all real nu
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05 Jul 2018, 01:34
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Re: Which of the following must be equal to zero for all real nu &nbs
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