Last visit was: 21 Jul 2024, 13:40 It is currently 21 Jul 2024, 13:40
Toolkit
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Which of the following must be equal to zero for all real numbers x ?

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94441
Own Kudos [?]: 642797 [19]
Given Kudos: 86716
Math Expert
Joined: 02 Sep 2009
Posts: 94441
Own Kudos [?]: 642797 [3]
Given Kudos: 86716
Intern
Joined: 10 Apr 2012
Posts: 31
Own Kudos [?]: 47 [1]
Given Kudos: 13
Concentration: Finance
WE:Analyst (Commercial Banking)
Manager
Joined: 21 Mar 2011
Status:GMATting
Posts: 96
Own Kudos [?]: 288 [0]
Given Kudos: 104
Concentration: Strategy, Technology
GMAT 1: 590 Q45 V27
Re: Which of the following must be equal to zero for all real numbers x ? [#permalink]
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) = 2-2 = 0;
III. x^0 = 1 for real numbers;

II only.

Ans is (B)
Intern
Joined: 05 Dec 2013
Posts: 26
Own Kudos [?]: 17 [2]
Given Kudos: 3
Concentration: Technology
GMAT Date: 02-01-2014
GPA: 3.95
WE:Information Technology (Venture Capital)
Re: Which of the following must be equal to zero for all real numbers x ? [#permalink]
2
Kudos
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.
Intern
Joined: 27 Dec 2013
Posts: 29
Own Kudos [?]: 27 [1]
Given Kudos: 29
Concentration: Finance, General Management
Schools: ISB '15
Re: Which of the following must be equal to zero for all real numbers x ? [#permalink]
1
Kudos
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

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
Manager
Joined: 22 Jan 2014
Posts: 130
Own Kudos [?]: 246 [1]
Given Kudos: 212
WE:Project Management (Computer Hardware)
Re: Which of the following must be equal to zero for all real numbers x ? [#permalink]
1
Kudos
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
SVP
Joined: 27 May 2012
Posts: 1697
Own Kudos [?]: 1496 [0]
Given Kudos: 639
Re: Which of the following must be equal to zero for all real numbers x ? [#permalink]

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
Math Expert
Joined: 02 Sep 2009
Posts: 94441
Own Kudos [?]: 642797 [0]
Given Kudos: 86716
Re: Which of the following must be equal to zero for all real numbers x ? [#permalink]
SOLUTION

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

I. $$-\frac{1}{x}\neq{0}$$ for any real number.

II. x + (-x) = x - x = 0.

III. x^0=1, for all nonzero numbers.

Manager
Joined: 30 May 2012
Posts: 168
Own Kudos [?]: 534 [0]
Given Kudos: 151
Location: United States (TX)
Concentration: Finance, Marketing
GPA: 3.3
WE:Information Technology (Consulting)
Re: Which of the following must be equal to zero for all real numbers x ? [#permalink]
Isn't zero a real number? And if it is, $$0^0$$ is 0 isn't it? Or is it undefined in GMAT?
Math Expert
Joined: 02 Sep 2009
Posts: 94441
Own Kudos [?]: 642797 [0]
Given Kudos: 86716
Re: Which of the following must be equal to zero for all real numbers x ? [#permalink]
Blackbox wrote:
Isn't zero a real number? And if it is, $$0^0$$ is 0 isn't it? Or is it undefined in GMAT?

0 is a real number.

0^0, in some sources equals to 1 (not 0), some mathematicians say it's undefined. But you won't need this for the GMAT because the case of 0^0 is not tested on the GMAT.
Manager
Joined: 30 May 2012
Posts: 168
Own Kudos [?]: 534 [0]
Given Kudos: 151
Location: United States (TX)
Concentration: Finance, Marketing
GPA: 3.3
WE:Information Technology (Consulting)
Re: Which of the following must be equal to zero for all real numbers x ? [#permalink]
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".
Math Expert
Joined: 02 Sep 2009
Posts: 94441
Own Kudos [?]: 642797 [1]
Given Kudos: 86716
Re: Which of the following must be equal to zero for all real numbers x ? [#permalink]
1
Kudos
Blackbox wrote:
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".

In any way 0^0 does NOT equal 0.
Manager
Joined: 25 Mar 2013
Posts: 166
Own Kudos [?]: 133 [0]
Given Kudos: 101
Location: United States
Concentration: Entrepreneurship, Marketing
GPA: 3.5
Re: Which of the following must be equal to zero for all real numbers x ? [#permalink]
1, $$\frac{-1}{x}$$ # 0
2, x + (-x) = x - x = always 0 for any number
3, x^0 = 1 but not 0
B
Non-Human User
Joined: 09 Sep 2013
Posts: 34037
Own Kudos [?]: 853 [0]
Given Kudos: 0
Re: Which of the following must be equal to zero for all real numbers x ? [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Re: Which of the following must be equal to zero for all real numbers x ? [#permalink]
Moderator:
Math Expert
94441 posts