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

 It is currently 25 Jun 2019, 13:26 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.  Is the number x positive?

Author Message
TAGS:

Hide Tags

Manager  Joined: 30 May 2013
Posts: 152
Location: India
Concentration: Entrepreneurship, General Management
GPA: 3.82
Is the number x positive?  [#permalink]

Show Tags

5
22 00:00

Difficulty:   85% (hard)

Question Stats: 46% (01:44) correct 54% (01:39) wrong based on 472 sessions

HideShow 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.
CEO  V
Joined: 12 Sep 2015
Posts: 3787
Is the number x positive?  [#permalink]

Show Tags

6
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

Cheers,
Brent
_________________

Originally posted by GMATPrepNow on 02 Oct 2017, 11:13.
Last edited by GMATPrepNow on 06 Oct 2018, 10:01, edited 2 times in total.
Manager  Joined: 18 Sep 2013
Posts: 51
Location: India
Concentration: General Management, Strategy
GMAT 1: 680 Q46 V36 GPA: 3.95
WE: Information Technology (Computer Software)
Re: Is the number x positive?  [#permalink]

Show Tags

10
1
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 !!
General Discussion
Intern  Joined: 05 Apr 2013
Posts: 17
GPA: 3.21
Re: Is the number x positive?  [#permalink]

Show Tags

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.
Verbal Forum Moderator B
Joined: 10 Oct 2012
Posts: 606
Re: Is the number x positive?  [#permalink]

Show Tags

6
3
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.
_________________
Manager  Joined: 03 Dec 2012
Posts: 195
Re: Is the number x positive?  [#permalink]

Show Tags

Forgot to substitute the fractional value ((((
Manager  G
Joined: 30 May 2012
Posts: 200
Location: United States (TX)
Concentration: Finance, Marketing
GPA: 3.3
WE: Information Technology (Consulting)
Re: Is the number x positive?  [#permalink]

Show Tags

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.
Math Expert V
Joined: 02 Sep 2009
Posts: 55801
Re: Is the number x positive?  [#permalink]

Show Tags

1
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.
_________________
Manager  G
Joined: 30 May 2012
Posts: 200
Location: United States (TX)
Concentration: Finance, Marketing
GPA: 3.3
WE: Information Technology (Consulting)
Re: Is the number x positive?  [#permalink]

Show Tags

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 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?
Director  Joined: 25 Apr 2012
Posts: 668
Location: India
GPA: 3.21
Re: Is the number x positive?  [#permalink]

Show Tags

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 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..
_________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”
Board of Directors P
Joined: 17 Jul 2014
Posts: 2540
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30 GPA: 3.92
WE: General Management (Transportation)
Re: Is the number x positive?  [#permalink]

Show Tags

2
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.
Intern  B
Joined: 11 Oct 2015
Posts: 2
Re: Is the number x positive?  [#permalink]

Show Tags

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?
Senior Manager  P
Joined: 29 Jun 2017
Posts: 449
GPA: 4
WE: Engineering (Transportation)
Is the number x positive?  [#permalink]

Show Tags

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
_________________
Give Kudos for correct answer and/or if you like the solution.
Intern  B
Joined: 05 Jan 2019
Posts: 2
Re: Is the number x positive?  [#permalink]

Show Tags

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

Cheers,
Brent

Thank you for this answer! Its by far the clearest. I loved this approach.
Intern  B
Joined: 01 Apr 2019
Posts: 2
Re: Is the number x positive?  [#permalink]

Show Tags

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?

Manager  G
Joined: 29 Nov 2018
Posts: 74
Location: India
Concentration: Entrepreneurship, General Management
GPA: 3.99
WE: Engineering (Computer Hardware)
Re: Is the number x positive?  [#permalink]

Show Tags

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?

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.
CEO  V
Joined: 12 Sep 2015
Posts: 3787
Re: Is the number x positive?  [#permalink]

Show Tags

1
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?

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
_________________
Intern  B
Joined: 15 Apr 2018
Posts: 18
Location: India
Schools: NUS '20
Re: Is the number x positive?  [#permalink]

Show Tags

Bunuel wrote:
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.

Hi Banuel,

If we put x=1/2 in statement 1 then? Re: Is the number x positive?   [#permalink] 19 Apr 2019, 03:55
Display posts from previous: Sort by

Is the number x positive?  