GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 Sep 2018, 16:22

### 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

# Which of the following must be equal to zero for all real nu

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49303
Which of the following must be equal to zero for all real nu  [#permalink]

### Show Tags

22 Jan 2014, 02:28
00:00

Difficulty:

5% (low)

Question Stats:

89% (00:27) correct 11% (00:34) wrong based on 894 sessions

### HideShow timer Statistics

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

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 Project

Each 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:
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!

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 49303
Re: Which of the following must be equal to zero for all real nu  [#permalink]

### Show Tags

22 Jan 2014, 02:28
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.

_________________
Intern
Joined: 10 Apr 2012
Posts: 42
Concentration: Finance
Schools: Goizueta '19 (I)
WE: Analyst (Commercial Banking)
Re: Which of the following must be equal to zero for all real nu  [#permalink]

### Show Tags

22 Jan 2014, 05:54
1
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.
Manager
Status: GMATting
Joined: 21 Mar 2011
Posts: 106
Concentration: Strategy, Technology
GMAT 1: 590 Q45 V27
Re: Which of the following must be equal to zero for all real nu  [#permalink]

### Show Tags

22 Jan 2014, 21:06
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) = 2-2 = 0;
III. x^0 = 1 for real numbers;

II only.

Ans is (B)
Intern
Joined: 05 Dec 2013
Posts: 30
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 nu  [#permalink]

### Show Tags

22 Jan 2014, 23:34
1
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: 32
Concentration: Finance, General Management
Schools: ISB '15
Re: Which of the following must be equal to zero for all real nu  [#permalink]

### Show Tags

23 Jan 2014, 00:29
1
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
_________________

Kindly consider for kudos if my post was helpful!

Manager
Joined: 22 Jan 2014
Posts: 175
WE: Project Management (Computer Hardware)
Re: Which of the following must be equal to zero for all real nu  [#permalink]

### Show Tags

23 Jan 2014, 02:09
1
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
_________________

Illegitimi non carborundum.

Director
Joined: 27 May 2012
Posts: 575
Re: Which of the following must be equal to zero for all real nu  [#permalink]

### Show Tags

23 Jan 2014, 07:12

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
_________________

- Stne

Math Expert
Joined: 02 Sep 2009
Posts: 49303
Re: Which of the following must be equal to zero for all real nu  [#permalink]

### Show Tags

25 Jan 2014, 12:26
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: 209
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 nu  [#permalink]

### Show Tags

04 Dec 2014, 03:51
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: 49303
Re: Which of the following must be equal to zero for all real nu  [#permalink]

### Show Tags

04 Dec 2014, 03:56
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: 209
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 nu  [#permalink]

### Show Tags

04 Dec 2014, 05:26
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".
Math Expert
Joined: 02 Sep 2009
Posts: 49303
Re: Which of the following must be equal to zero for all real nu  [#permalink]

### Show Tags

04 Dec 2014, 05:28
1
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.
_________________
Senior Manager
Joined: 25 Mar 2013
Posts: 256
Location: United States
Concentration: Entrepreneurship, Marketing
GPA: 3.5
Re: Which of the following must be equal to zero for all real nu  [#permalink]

### Show Tags

14 Jan 2017, 19:10
1, $$\frac{-1}{x}$$ # 0
2, x + (-x) = x - x = always 0 for any number
3, x^0 = 1 but not 0
B
_________________

I welcome analysis on my posts and kudo +1 if helpful. It helps me to improve my craft.Thank you

Non-Human User
Joined: 09 Sep 2013
Posts: 8153
Re: Which of the following must be equal to zero for all real nu  [#permalink]

### Show Tags

05 Jul 2018, 02:34
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 nu &nbs [#permalink] 05 Jul 2018, 02:34
Display posts from previous: Sort by

# Which of the following must be equal to zero for all real nu

## Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.