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

 It is currently 21 Sep 2019, 06:23

### 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

# Is x > 0 ? (1) |x+3| < 4 (2) |x-3| < 4 Please assist with above prob

Author Message
TAGS:

### Hide Tags

Manager
Joined: 13 Sep 2016
Posts: 117
GMAT 1: 800 Q51 V51
Is x > 0 ? (1) |x+3| < 4 (2) |x-3| < 4 Please assist with above prob  [#permalink]

### Show Tags

26 Sep 2016, 20:03
1
2
00:00

Difficulty:

25% (medium)

Question Stats:

75% (01:27) correct 25% (01:33) wrong based on 220 sessions

### HideShow timer Statistics

Is x > 0 ?

(1) |x+3| < 4
(2) |x-3| < 4

Intern
Joined: 09 Apr 2018
Posts: 34
Location: India
Schools: IIMA PGPX"20
GPA: 3.5
Re: Is x > 0 ? (1) |x+3| < 4 (2) |x-3| < 4 Please assist with above prob  [#permalink]

### Show Tags

05 Oct 2018, 03:29
2
(1) INSUFFICIENT: We can solve this absolute value inequality by considering both the positive and negative scenarios for the absolute value expression |x + 3|.
If x > -3, making (x + 3) positive, we can rewrite |x + 3| as x + 3:
x + 3 < 4
x < 1
If x < -3, making (x + 3) negative, we can rewrite |x + 3| as -(x + 3):
-(x + 3) < 4
x + 3 > -4
x > -7
If we combine these two solutions we get -7 < x < 1, which means we can’t tell whether x is positive.

(2) INSUFFICIENT: We can solve this absolute value inequality by considering both the positive and negative scenarios for the absolute value expression |x – 3|.
If x > 3, making (x – 3) positive, we can rewrite |x – 3| as x – 3:
x – 3 < 4
x < 7
If x < 3, making (x – 3) negative, we can rewrite |x – 3| as -(x – 3) OR 3 – x
3 – x < 4
x > -1
If we combine these two solutions we get -1 < x < 7, which means we can’t tell whether x is positive.

(1) AND (2) INSUFFICIENT: If we combine the solutions from statements (1) and (2) we get an overlapping range of -1 < x < 1. We still can’t tell whether x is positive.
Math Expert
Joined: 02 Sep 2009
Posts: 58137
Re: Is x > 0 ? (1) |x+3| < 4 (2) |x-3| < 4 Please assist with above prob  [#permalink]

### Show Tags

26 Sep 2016, 21:32
1
1
Is x > 0 ?

(1) |x+3| < 4
-4 < x + 3 < 4
-7 < x < 1.

Not sufficient.

(2) |x-3| < 4
-4 < x - 3 < 4
-1 < x < 7.

Not sufficient.

(1)+(2) -1 < x < 1. Not sufficient.

_________________
Retired Moderator
Joined: 22 Aug 2013
Posts: 1434
Location: India
Re: Is x > 0 ? (1) |x+3| < 4 (2) |x-3| < 4 Please assist with above prob  [#permalink]

### Show Tags

31 May 2018, 03:10
1
101mba101 wrote:
Hi Bunuel,

I have a very basic doubt here.

On combining the statements 1 & 2, how did you get the range of x as -1 < x < 1 ? Why can't the range of x be -7 < x < 7 ?

Bunuel wrote:
Is x > 0 ?

(1) |x+3| < 4
-4 < x + 3 < 4
-7 < x < 1.

Not sufficient.

(2) |x-3| < 4
-4 < x - 3 < 4
-1 < x < 7.

Not sufficient.

(1)+(2) -1 < x < 1. Not sufficient.

HEllo

First statement concludes that -7 < x < 1. It means 'x' is a number which is greater than -7 but less than 1.
Second statement concludes that -1 < x < 7. This means that 'x' is a number which is greater than -1 but less than 7.

Now, combining the two statements. what is common about x? From first, x should be greater than -7 and from second x should be greater than -1. So if a number is both greater than -7 as well as greater than -1, then it has to be greater than -1 (which is the common part).
Similarly, from first x is less than 1 and from second x is less than 7. So if a number is lesser than 1 as well as lesser than 7, then it must be lesser than 1 (which is the common part).
Retired Moderator
Joined: 22 Aug 2013
Posts: 1434
Location: India
Re: Is x > 0? (1) |x + 3| < 4 (2) |x – 3| < 4  [#permalink]

### Show Tags

23 Jan 2018, 23:04
DHINGRACHIRAG24 wrote:
Is x > 0?

(1) |x + 3| < 4
(2) |x – 3| < 4

_________________

Encourage me by pressing the KUDOS if you find my post to be helpful.

(1) |x-(-3)| < 4
This also means that distance of 'x' from '-3' on the number line is within 4 steps. So x is within 4 steps to right and left of -3. 4 steps to right of -3 is 1 and 4 steps to the left of -3 is -7. Thus x lies between -7 and 1. So x could be either positive or negative. Not sufficient.

(2) |x - 3| < 4
This also means that distance of 'x' from '3' on the number line is within 4 steps. So x is within 4 steps to right and left of 3. 4 steps to right of 3 is 7 and 4 steps to the left of 3 is -1. Thus x lies between -1 and 7. So x could be either positive or negative. Not sufficient.

After combining the two statements, x could lie between -1 and 1 (this is the only area on the number line which x can take if it has to satisfy both statement 1 and statement 2 conditions).
But still between -1 and 1, x could be negative or 0 or positive. So not sufficient.

Intern
Joined: 18 Nov 2017
Posts: 43
Re: Is x > 0 ? (1) |x+3| < 4 (2) |x-3| < 4 Please assist with above prob  [#permalink]

### Show Tags

31 May 2018, 02:52
Hi Bunuel,

I have a very basic doubt here.

On combining the statements 1 & 2, how did you get the range of x as -1 < x < 1 ? Why can't the range of x be -7 < x < 7 ?

Bunuel wrote:
Is x > 0 ?

(1) |x+3| < 4
-4 < x + 3 < 4
-7 < x < 1.

Not sufficient.

(2) |x-3| < 4
-4 < x - 3 < 4
-1 < x < 7.

Not sufficient.

(1)+(2) -1 < x < 1. Not sufficient.

Intern
Joined: 18 Nov 2017
Posts: 43
Is x > 0 ? (1) |x+3| < 4 (2) |x-3| < 4 Please assist with above prob  [#permalink]

### Show Tags

31 May 2018, 03:37
Hey amanvermagmat,

Your explanation solved my doubt immediately. You kept it super simple. Thanks a lot!

Cheers!

amanvermagmat wrote:
HEllo

First statement concludes that -7 < x < 1. It means 'x' is a number which is greater than -7 but less than 1.
Second statement concludes that -1 < x < 7. This means that 'x' is a number which is greater than -1 but less than 7.

Now, combining the two statements. what is common about x? From first, x should be greater than -7 and from second x should be greater than -1. So if a number is both greater than -7 as well as greater than -1, then it has to be greater than -1 (which is the common part).
Similarly, from first x is less than 1 and from second x is less than 7. So if a number is lesser than 1 as well as lesser than 7, then it must be lesser than 1 (which is the common part).
Manager
Joined: 02 Jan 2016
Posts: 137
Concentration: General Management, Accounting
Re: Is x > 0 ? (1) |x+3| < 4 (2) |x-3| < 4 Please assist with above prob  [#permalink]

### Show Tags

21 Jun 2018, 15:59
Hi Bunuel,

When statements (1)+(2) -1 < x < 1. that means x has to be "0", however it is not mentioned in the question that "X" is a Integer, so this is insufficient correct ?
Math Expert
Joined: 02 Sep 2009
Posts: 58137
Re: Is x > 0 ? (1) |x+3| < 4 (2) |x-3| < 4 Please assist with above prob  [#permalink]

### Show Tags

21 Jun 2018, 21:37
hero_with_1000_faces wrote:
Hi Bunuel,

When statements (1)+(2) -1 < x < 1. that means x has to be "0", however it is not mentioned in the question that "X" is a Integer, so this is insufficient correct ?

-1 < x < 1 means that x is any number from -1 and 1, not inclusive, not necessarily 0. For example, -3/100, -4/11, -0.000012, 0, 1/2, ... So, x can take infinitely many values, included 0. Hence we cannot say whether x is more than 0.
_________________
Re: Is x > 0 ? (1) |x+3| < 4 (2) |x-3| < 4 Please assist with above prob   [#permalink] 21 Jun 2018, 21:37
Display posts from previous: Sort by