NEW HERE? LEARN MORE
closeclose
Last visit was: 07 May 2024, 08:44 It is currently 07 May 2024, 08:44
Decision Tracker
My Rewards
New posts
New comers' posts

Close
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
Your Progress

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

Is the number x positive?

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
rrsnathan
Manager
Manager
Joined: 30 May 2013
Posts: 126
Own Kudos [?]: 360 [72]
Given Kudos: 72
Location: India
Concentration: Entrepreneurship, General Management
Schools: Booth '16 Carroll '16 ESADE '16 Foster '16 HEC Jan'16 Haas EWMBA '16 Tuck '16
GPA: 3.82
Send PM
GMAT ToolKit User
Is the number x positive? [#permalink] New post   18 Sep 2013, 06:15
9
Kudos
63
Bookmarks
00:00
A
B
C
D
E

Difficulty:

85% (hard)

Question Stats:

46% (01:47) correct 54% (01:40) wrong based on 1012 sessions
Hide Show timer Statistics
Is the number x positive?

(1) On the number line, 0 is closer to x – 1 than to x.
(2) On the number line, 0 is closer to x than to x + 1.
ShowHide Answer
Official Answer
A
Most Helpful Reply
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6817
Own Kudos [?]: 30091 [23]
Given Kudos: 799
Location: Canada
Send PM
Is the number x positive? [#permalink] New post   Updated on: 20 Jul 2020, 14:12
13
Kudos
10
Bookmarks
Expert Reply
Top Contributor
rrsnathan wrote:
Is the number x positive?

(1) On the number line, 0 is closer to x – 1 than to x.
(2) On the number line, 0 is closer to x than to x + 1.

Another approach is the sketch the cases on a number line.

First, recognize that x-1 will always be to the left of x.

Second, recognize that there are 3 possible ways to place x-1 and x with relation to zero.


Target question: Is x positive?

Statement 1: On the number line, 0 is closer to x – 1 than to x.
If zero is closer to x-1 than to x, then we can rule out case #2, leaving us with cases #1 and #3 as possible scenarios.
If case #1 is true, we can see that x must be positive
If case #3 is true, we can see that x must be positive
Since both possible cases yield the same answer to the target question, we can answer the target question with certainty.
So, statement 1 is SUFFICIENT

Statement 2: On the number line, 0 is closer to x than to x + 1.
Recognize that x+1 will always be to the right of x.
Also recognize that there are 3 possible ways to place x and x+1 with relation to zero.

If zero is closer to x than to x+1, then we can rule out case #2, leaving us with cases #1 and #3 as possible scenarios.
If case #1 is true, we can see that x is negative
If case #3 is true, we can see that x is positive
Since the two possible cases yield different answers to the target question, we cannot answer the target question with certainty.
So, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent

Originally posted by BrentGMATPrepNow on 02 Oct 2017, 11:13.
Last edited by BrentGMATPrepNow on 20 Jul 2020, 14:12, edited 3 times in total.
avatar
gmatsheeba
Intern
Intern
Joined: 18 Sep 2013
Posts: 49
Own Kudos [?]: 115 [14]
Given Kudos: 8
Location: India
Concentration: General Management, Strategy
GMAT 1: 680 Q46 V36
GPA: 3.95
WE:Information Technology (Computer Software)
Send PM
Is the number x positive? [#permalink] New post   18 Sep 2013, 06:24
11
Kudos
3
Bookmarks
rrsnathan wrote:
Is the number x positive?

(1) On the number line, 0 is closer to x – 1 than to x.
(2) On the number line, 0 is closer to x than to x + 1.


Ans should be A.

1. x=2, x-1 =1 Yes
x=-1, x-1 =-2 Yes

2. x=-3,x+1 =-2 No
x=-1/3, x+1=2/3 Yes

Hence A is sufficient.
General Discussion
avatar
neelzwiz
Intern
Intern
Joined: 05 Apr 2013
Posts: 14
Own Kudos [?]: 22 [0]
Given Kudos: 8
Schools: CBS '17 Johnson '18 LBS '16
GPA: 3.21
Send PM
Re: Is the number x positive? [#permalink] New post   18 Sep 2013, 06:35
Is the number x positive?

(1) On the number line, 0 is closer to x – 1 than to x.
(2) On the number line, 0 is closer to x than to x + 1.

Take choice 1,

let x -1 = -0.6 => x = 0.6. so X +ve.
let x-1 = = 0.2 => x = 1.2. so x +ve

Take choice 2.

let x -1 = - 0.4 => x = 0.4, so X +ve.
let x-1 = -2.4 => x = -1.4, so X -ve.


Hence the ans is A.

Hope this helps.
User avatar
B
mau5
Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 485
Own Kudos [?]: 3097 [13]
Given Kudos: 141
Send PM
Re: Is the number x positive? [#permalink] New post   18 Sep 2013, 06:47
9
Kudos
4
Bookmarks
rrsnathan wrote:
Is the number x positive?

(1) On the number line, 0 is closer to x – 1 than to x.
(2) On the number line, 0 is closer to x than to x + 1.


|x| denotes the distance between 0 and x on the number line.

F.S 1 states that |0-(x-1)|<|0-x| --> |x-1|<|x| --> Square on both sides, and subtract -->\(1*(2x-1)>0 --> x>\frac{1}{2}\). Sufficient.

F.S 2 states that |x|<|x+1| --> Just as above, this gives --> 1*(2x+1)>0 --> \(x>\frac{-1}{2}\). Insufficient.

A.
User avatar
mohnish104
Manager
Manager
Joined: 03 Dec 2012
Posts: 145
Own Kudos [?]: 835 [3]
Given Kudos: 291
Send PM
Re: Is the number x positive? [#permalink] New post   09 Oct 2013, 02:45
3
Kudos
Forgot to substitute the fractional value :(((((
User avatar
S
Blackbox
Manager
Manager
Joined: 30 May 2012
Posts: 168
Own Kudos [?]: 523 [0]
Given Kudos: 151
Location: United States (TX)
Concentration: Finance, Marketing
GPA: 3.3
WE:Information Technology (Consulting)
Send PM
Re: Is the number x positive? [#permalink] New post   03 Nov 2014, 02:04
Bumping up for any other explanation. This is how I approached it -

(1) On the number line, 0 is closer to x – 1 than to x.
(2) On the number line, 0 is closer to x than to x + 1

(1) assume x= -2; => x-1 = -3. (Given answer choice is not true/satisfied, so x can't be negative)
Consider x= 22; => x-1 =21 (Given answer choice is true/satisfied)

So, it is true that x is positive.

(2) same assumption, x=-32 => x+1 = -31(Given answer choice is not true/satisfied, so x can't be negative)
Consider x=1 => x+1 = 2 (Given answer choice is true/satisfied)

So, it is true that x is positive.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93075
Own Kudos [?]: 621904 [2]
Given Kudos: 81782
Send PM
CAT Tests Forum Quiz Mode
Re: Is the number x positive? [#permalink] New post   03 Nov 2014, 02:16
2
Kudos
Expert Reply
Blackbox wrote:
Bumping up for any other explanation. This is how I approached it -

(1) On the number line, 0 is closer to x – 1 than to x.
(2) On the number line, 0 is closer to x than to x + 1

(1) assume x= -2; => x-1 = -3. (Given answer choice is not true/satisfied, so x can't be negative)
Consider x= 22; => x-1 =21 (Given answer choice is true/satisfied)

So, it is true that x is positive.

(2) same assumption, x=-32 => x+1 = -31(Given answer choice is not true/satisfied, so x can't be negative)
Consider x=1 => x+1 = 2 (Given answer choice is true/satisfied)

So, it is true that x is positive.


For (2) consider the values of x from -1/2 (not inclusive) to 0 (inclusive) to get that (2) is NOT in fact sufficient.
User avatar
S
Blackbox
Manager
Manager
Joined: 30 May 2012
Posts: 168
Own Kudos [?]: 523 [0]
Given Kudos: 151
Location: United States (TX)
Concentration: Finance, Marketing
GPA: 3.3
WE:Information Technology (Consulting)
Send PM
Re: Is the number x positive? [#permalink] New post   05 Nov 2014, 00:50
Bunuel wrote:
For (2) consider the values of x from -1/2 (not inclusive) to 0 (inclusive) to get that (2) is NOT in fact sufficient.


I am not sure what you meant by -1/2 (not inclusive) and 0 (inclusive) and I'd appreciate if you can shed some light on it. But yeah, I messed up not considering fractions. So ...

For option 2 - if x were -1/2 then x+1 would be 1/2. Given statement of 0 closer to x than x+1 is busted with two answers (0 is as much closer to -1/2 as it is to 1/2). Hence option 2 has multiple answers.

It goes to show again :roll: how much I suck at picking magic numbers (or numbers at all). I have to keep reminding myself to test for fractions too. Ugh. Is there any other general approach to this problem besides picking numbers?
User avatar
WoundedTiger
Director
Director
Joined: 25 Apr 2012
Posts: 529
Own Kudos [?]: 2289 [0]
Given Kudos: 740
Location: India
GPA: 3.21
WE:Business Development (Other)
Send PM
Reviews Badge
Re: Is the number x positive? [#permalink] New post   05 Nov 2014, 01:04
Blackbox wrote:
Bunuel wrote:
For (2) consider the values of x from -1/2 (not inclusive) to 0 (inclusive) to get that (2) is NOT in fact sufficient.


I am not sure what you meant by -1/2 (not inclusive) and 0 (inclusive) and I'd appreciate if you can shed some light on it. But yeah, I messed up not considering fractions. So ...

For option 2 - if x were -1/2 then x+1 would be 1/2. Given statement of 0 closer to x than x+1 is busted with two answers (0 is as much closer to -1/2 as it is to 1/2). Hence option 2 has multiple answers.

It goes to show again :roll: how much I suck at picking magic numbers (or numbers at all). I have to keep reminding myself to test for fractions too. Ugh. Is there any other general approach to this problem besides picking numbers?


Hello Blackbox...

What Bunuel intends to says consider value of x between \(-1/2<x\leq{0}\)..

For option 2 - if x were -1/2 then x+1 would be 1/2. Given statement of 0 closer to x than x+1 is busted with two answers (0 is as much closer to -1/2 as it is to 1/2). Hence option 2 has multiple answers.


That is why Bunuel says consider a number greater than -1/2..

Consider x=-1/3...so x=-1/3 and x+1 =2/3 : x is closer to 0 then x+1..

Look at mau5 method above...it is easier to understand and follow..
User avatar
P
mvictor
Board of Directors
Joined: 17 Jul 2014
Posts: 2160
Own Kudos [?]: 1180 [3]
Given Kudos: 236
Location: United States (IL)
Concentration: Finance, Economics
Schools: Stanford '20 (WD)
GMAT 1: 650 Q49 V30
GPA: 3.92
WE:General Management (Transportation)
Send PM
GMAT ToolKit User Reviews Badge
Re: Is the number x positive? [#permalink] New post   02 Feb 2016, 19:18
2
Kudos
1
Bookmarks
rrsnathan wrote:
Is the number x positive?

(1) On the number line, 0 is closer to x – 1 than to x.
(2) On the number line, 0 is closer to x than to x + 1.


1. A is positive. otherwise, if x is negative, then negative minus negative makes an even bigger negative, and the new number would be even farther from 0.
2. it can be x=1 and x+1 =2, and 0 is closer to x, or it can be:
x=-0.1 and x+1=0.9. x is closer to x than to x+1. since we have 2 outcomes, B is not sufficient.

A.
avatar
B
samridhi30
Intern
Intern
Joined: 11 Oct 2015
Posts: 4
Own Kudos [?]: [0]
Given Kudos: 48
Location: India
Send PM
Re: Is the number x positive? [#permalink] New post   09 Feb 2017, 12:07
gmatsheeba wrote:
rrsnathan wrote:
Is the number x positive?

(1) On the number line, 0 is closer to x – 1 than to x.
(2) On the number line, 0 is closer to x than to x + 1.


Ans should be A.

1. x=2, x-1 =1 Yes
x=-1, x-1 =-2 Yes

2. x=-3,x+1 =-2 No
x=-1/3, x+1=2/3 Yes

Hence A is sufficient.
Please press KUDOS if my post HELPED !!



What if x=0 in the first case?
User avatar
P
sahilvijay
Senior Manager
Senior Manager
Joined: 29 Jun 2017
Posts: 312
Own Kudos [?]: 800 [1]
Given Kudos: 76
GPA: 4
WE:Engineering (Transportation)
Send PM
GMAT ToolKit User Reviews Badge
Is the number x positive? [#permalink] New post   22 Feb 2018, 11:00
1
Kudos
samridhi30 wrote:
gmatsheeba wrote:
rrsnathan wrote:
Is the number x positive?

(1) On the number line, 0 is closer to x – 1 than to x.
(2) On the number line, 0 is closer to x than to x + 1.


Ans should be A.

1. x=2, x-1 =1 Yes
x=-1, x-1 =-2 Yes

2. x=-3,x+1 =-2 No
x=-1/3, x+1=2/3 Yes

Hence A is sufficient.
Please press KUDOS if my post HELPED !!



What if x=0 in the first case?


===========>>>>>>>>>>>

1) |x-1|<|x|
square both side
1-2|x|<0
|x|>0.5
=> x>0.5 => A or D


2) |x|<|x+1|
square both
0<2|x|+1
|x|> -0.5
but as we know |x| can never be negative , but it can be zero 0
=> |x|>=0
so x=0 and x>0 are solution therfore insufficient



A is winner
avatar
B
farsar
Intern
Intern
Joined: 05 Jan 2019
Posts: 8
Own Kudos [?]: 1 [0]
Given Kudos: 59
Send PM
Re: Is the number x positive? [#permalink] New post   08 Feb 2019, 09:12
GMATPrepNow wrote:
rrsnathan wrote:
Is the number x positive?

(1) On the number line, 0 is closer to x – 1 than to x.
(2) On the number line, 0 is closer to x than to x + 1.

Another approach is the sketch the cases on a number line.

First, recognize that x-1 will always be to the left of x.

Second, recognize that there are 3 possible ways to place x-1 and x with relation to zero.

Target question: Is x positive?

Statement 1: On the number line, 0 is closer to x – 1 than to x.
If zero is closer to x-1 than to x, then we can rule out case #2, leaving us with cases #1 and #3 as possible scenarios.
If case #1 is true, we can see that x must be positive
If case #3 is true, we can see that x must be positive
Since both possible cases yield the same answer to the target question, we can answer the target question with certainty.
So, statement 1 is SUFFICIENT

Statement 2: On the number line, 0 is closer to x than to x + 1.
Recognize that x+1 will always be to the right of x.
Also recognize that there are 3 possible ways to place x and x+1 with relation to zero.
If zero is closer to x than to x+1, then we can rule out case #2, leaving us with cases #1 and #3 as possible scenarios.
If case #1 is true, we can see that x is negative
If case #3 is true, we can see that x is positive
Since the two possible cases yield different answers to the target question, we cannot answer the target question with certainty.
So, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent


Thank you for this answer! Its by far the clearest. I loved this approach.
avatar
B
5JUwiu4
Intern
Intern
Joined: 01 Apr 2019
Posts: 2
Own Kudos [?]: 0 [0]
Given Kudos: 35
Send PM
Re: Is the number x positive? [#permalink] New post   15 Apr 2019, 16:33
GMATPrepNow

Loved the explanation, but I think I'm missing something.

In statement 1 it states " On the number line, 0 is closer to x – 1 than to x."

You explain x could be on the right of zero and x-1 to the left (0 in the middle). If this is true x must be less than 1 to jump to the negative side of the number line. In this case isn't x and x-1 equidistant from 0? So how can 0 be closer to x-1 than to x?

Thanks in advance.
User avatar
P
ruchik
Manager
Manager
Joined: 29 Nov 2018
Posts: 98
Own Kudos [?]: 183 [0]
Given Kudos: 57
Location: India
Concentration: Entrepreneurship, General Management
Schools: Sloan Fellows '22 IMD '22 (D)
GMAT 1: 730 Q50 V40
GPA: 3.99
WE:Engineering (Computer Hardware)
Send PM
Re: Is the number x positive? [#permalink] New post   16 Apr 2019, 02:43
5JUwiu4 wrote:
GMATPrepNow

Loved the explanation, but I think I'm missing something.

In statement 1 it states " On the number line, 0 is closer to x – 1 than to x."

You explain x could be on the right of zero and x-1 to the left (0 in the middle). If this is true x must be less than 1 to jump to the negative side of the number line. In this case isn't x and x-1 equidistant from 0? So how can 0 be closer to x-1 than to x?

Thanks in advance.


Hi,
The way i looked at option 1 was 0 is closer to x-1 than x. Now if x is negative, x-1 is going to be more negative and hence going to be farther away from 0. So if we attack the problem in reverse away it might be easier. Can we find a negative number x, such that x-1 is closer to 0 than x? the answer is no hence the option is sufficient.

hope it helped.

Please give kudos if you like the explanation.
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6817
Own Kudos [?]: 30091 [1]
Given Kudos: 799
Location: Canada
Send PM
Re: Is the number x positive? [#permalink] New post   16 Apr 2019, 07:49
1
Kudos
Expert Reply
Top Contributor
5JUwiu4 wrote:
GMATPrepNow

Loved the explanation, but I think I'm missing something.

In statement 1 it states " On the number line, 0 is closer to x – 1 than to x."

You explain x could be on the right of zero and x-1 to the left (0 in the middle). If this is true x must be less than 1 to jump to the negative side of the number line. In this case isn't x and x-1 equidistant from 0? So how can 0 be closer to x-1 than to x?

Thanks in advance.


We could have x = 0.8, and x-1 = -0.2
In this case, 0 is closer to x-1 than to x.

Cheers,
Brent
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32819
Own Kudos [?]: 827 [0]
Given Kudos: 0
Send PM
Re: Is the number x positive? [#permalink] New post   06 Nov 2022, 11:40
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.
GMAT Club Bot
gmatclubot
Re: Is the number x positive? [#permalink]
06 Nov 2022, 11:40
Moderator:
Bunuel
Math Expert
93075 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions