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

 It is currently 22 Jun 2018, 19:17

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# What is the value of integer x?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Intern
Joined: 29 Nov 2014
Posts: 1
What is the value of integer x? [#permalink]

### Show Tags

28 Feb 2015, 07:08
3
6
00:00

Difficulty:

55% (hard)

Question Stats:

65% (01:10) correct 35% (01:19) wrong based on 294 sessions

### HideShow timer Statistics

What is the value of integer x?

(1) |1 - x| - |x + 1| = 0

(2) |7 - x| + |3 + x| = 10
Math Expert
Joined: 02 Aug 2009
Posts: 5928
Re: What is the value of integer x? [#permalink]

### Show Tags

28 Feb 2015, 07:19
jashshah wrote:
What is the value of integer x?

1. |1 - x| - |x + 1| = 0

2. |7 - x| + |3 + x| = 10

ans A..
1) by looking at the statement 1 itself , one can find that x=0.. also by opening the mod, we can find that x gives only one value that is 0.. sufficient
2) 7 and 3 straight way gives one value of x as 0 and by opening mod, we have x can take multiple values 2 ,-2,3,4etc ... so insufficient
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

GMAT online Tutor

Math Expert
Joined: 02 Sep 2009
Posts: 46284
Re: What is the value of integer x? [#permalink]

### Show Tags

28 Feb 2015, 07:33
6
5
What is the value of integer x?

(1) |1 - x| - |x + 1| = 0

|1 - x| = |x + 1| --> square: 1 - 2x + x^2 = x^2 + 2x +1 --> x = 0. Sufficient.

(2) |7 - x| + |3 + x| = 10.

When both 7 - x and 3 + x are positive (so when -3 <= x <= 7), then |7 - x| + |3 + x| = 10 expands as 7 - x + 3 + x = 10 --> 10 = 10, which is true. This means that any x where -3 <= x <= 7 satisfies the equation. Not sufficient.

Answer: A.
_________________
Manager
Joined: 28 Jul 2011
Posts: 208
Re: What is the value of integer x? [#permalink]

### Show Tags

05 Oct 2015, 13:22
1
What is the value of integer x?

1. |1 - x| - |x + 1| = 0
2. |7 - x| + |3 + x| = 10

Can anyone help in how do we open the modules sign for 1 and 2?

this is how i solved it but its time consuming
1. |x-1| - |x+1| = 0
-(x-1) - (x+1) = 0
therefore x= 0
(x-1) + (x+1) = 0
therefore x = 0

any alternate technique to solve this problem
Current Student
Joined: 20 Mar 2014
Posts: 2643
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: What is the value of integer x? [#permalink]

### Show Tags

05 Oct 2015, 17:07
2
kuttingchai wrote:
What is the value of integer x?

1. |1 - x| - |x + 1| = 0
2. |7 - x| + |3 + x| = 10

Can anyone help in how do we open the modules sign for 1 and 2?

this is how i solved it but its time consuming
1. |x-1| - |x+1| = 0
-(x-1) - (x+1) = 0
therefore x= 0
(x-1) + (x+1) = 0
therefore x = 0

any alternate technique to solve this problem

Make sure to format your question in such a way that puts your analysis under "spoiler".

As for your question,

Both statements can be solved in a similar way,

Statement 1, |1-x|-|x+1|=0 , now as |a-x|=|x-a| , you get |x-1|-|x+1|=0 ---> |x-1|=|x+1| ----> $$\pm (x-1) = \pm (x+1)$$ , you only get 2 possible cases giving you x=0 for both cases. Hence this statement is sufficient.

Statement 2, |7 - x| + |3 + x| = 10, using the same principle as shown in statement 1, you get the equation as $$\pm (x-7) \pm (x+3) = 10$$, giving you 2 possible cases again but giving you x=-3 and x=7. Thus this statement is not sufficient.

Hope this helps.
Director
Affiliations: GMATQuantum
Joined: 19 Apr 2009
Posts: 605
Re: What is the value of integer x? [#permalink]

### Show Tags

06 Oct 2015, 00:18
kuttingchai

In statement 2, you will notice that there is a 7 and 3 on the left side and 10 on the right. We also know 7+3=10, and if we choose x=0, we see the equation is indeed satisfied, and if we change x to 1, then also it is satisfied. So just by observation we can come up with two values for x, and say that statement 2 alone is not sufficient.

For statement 1, one could quickly graph the functions |1-x| and |x+1| and show that they only intersect at x=0. Actually, being able to graph these basic types of absolute value equations is important for the GMAT.

And finally, the statement 1 is based on the following official GMAT question from official guide 10th edition, data sufficiency question#81. See the attached image.

Cheers,
Dabral
Attachments

OG10-DS81.png [ 5.98 KiB | Viewed 3403 times ]

Board of Directors
Joined: 17 Jul 2014
Posts: 2730
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Re: What is the value of integer x? [#permalink]

### Show Tags

28 Nov 2015, 10:49
I didn't square, since I didn't know how to tackle this question rather than try the possible options, and although I selected A as the answer I later check and found something interesting:
both positive
both negative
1st positive second negative
1st negative second positive:

1. |1 - x| - |x + 1| = 0
++
1-x-x+1=0=> 0=2x=>x=0
--
-1+x+x+1=>2x=0 => x=0
-+
-1+x-x+1 => 0=0 - doesn't help us much, since there is no way to solve it. or x can take any value.
+-
1-x+x+1 => 2=0 - this is not a solution.

x
2. |7 - x| + |3 + x| = 10

only 2 options tested, which yielded 2 different values for x, thus I dismissed B and D.
Current Student
Joined: 20 Mar 2014
Posts: 2643
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: What is the value of integer x? [#permalink]

### Show Tags

08 Jan 2016, 09:57
2
shasadou wrote:
What is the value of integer x?

(1) |1 - x| - |x + 1| = 0
(2) |7 - x| + |3 + x| = 10

For such questions the most straightforward method to solve is to realize that |x-a| with a = constant is the distance of x from 'a' and |a-x| = |x-a|

Thus |1-x| = |x-1| --> distance of x from 1,

Similarly for |x+1|, |x-7| and |x+3|.

Do remember that x = integer (given information).

Per statement 1, |1 - x| - |x + 1| = 0 ---> |x-1| - |x + 1| = 0 ---> |x-1| = |x + 1| ---> distance of integer x is same from -1 and 1 ---> x can only take 0 as the possible value. Unique value of x ---> sufficient statement.

Per statement 2, |7 - x| + |3 + x| = 10 --> |x-7| + |3 + x| = 10 ---> distance of x from 7 + distance of x from -3 = 10 units. This is satisfied by all integer values of x between -3 and 7. Consider x = 4 , distance from 7 = 3 , distance of x from -3 = 7 , total = 10.

But if x = 0, distance from 7 = 7 and distance of x from -3 = 3 , total = 10 units.

Thus this statement provides multiple values of x ---> not sufficient.

A is thus the correct answer.

Hope this helps.
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 5600
GMAT 1: 800 Q59 V59
GPA: 3.82
Re: What is the value of integer x? [#permalink]

### Show Tags

10 Jan 2016, 19:10
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

What is the value of integer x?

(1) |1 - x| - |x + 1| = 0
(2) |7 - x| + |3 + x| = 10

When it comes to absolute value, it indicates a distance between two dots. That is, it is a distance between |x-y|=x and y in this question.
In the original condition, there is 1 variable(x), which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make C the answer.
For 1), from |1-x|=|x-(-1)|, since a distance from x to 1 is as same as a distance from x to -1, x=0 is derived, which is unique and sufficient.
For 2), from |7-x|+|x-(-3)|=10, the sum of a distance between x and 7, and a distance between x and -3 is 10. That is, all values are possible in -3<=x<=7, which is not unique and not sufficient. Therefore, the answer is A.

 For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only \$99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Current Student
Joined: 28 Nov 2014
Posts: 895
Concentration: Strategy
Schools: Fisher '19 (M)
GPA: 3.71
Re: What is the value of integer x? [#permalink]

### Show Tags

28 Sep 2016, 07:13
Bunuel:
How do I deal with second case -
|7-x| + |3+x| = 10
Now four possibilities can exist
Case 1: 7-x>0 and 3+x>0
-3 < x < 7
On solving
10=10

Case 2: 7-x<0 and 3+x<0
4=10
Dump this!

Case 3: 7-x>0 and 3+x<0
x<7 and x<-3
or x<-3
On solving we get ; x=-3

Case 4: 7-x<0 and 3+x>0
x > -3 and x >7
or x>7
On solving
x = 7

Bunuel: Can you please suggest how do I conclude this.
Math Expert
Joined: 02 Sep 2009
Posts: 46284
Re: What is the value of integer x? [#permalink]

### Show Tags

29 Sep 2016, 04:05
1
Keats wrote:
Bunuel:
How do I deal with second case -
|7-x| + |3+x| = 10
Now four possibilities can exist
Case 1: 7-x>0 and 3+x>0
-3 < x < 7
On solving
10=10

Case 2: 7-x<0 and 3+x<0
4=10
Dump this!

Case 3: 7-x>0 and 3+x<0
x<7 and x<-3
or x<-3
On solving we get ; x=-3

Case 4: 7-x<0 and 3+x>0
x > -3 and x >7
or x>7
On solving
x = 7

Bunuel: Can you please suggest how do I conclude this.

$$|3 + x| + |7 - x| = 10$$

2 key points at -3 and 7.

When $$x < -3$$, then $$3 + x$$ is negative and $$7 - x$$ is positive, thus $$|3 + x| + |7 - x| = 10$$ becomes $$-(3 + x) + (7 - x) = 10$$ --> $$x=-3$$. Discard since -3 is not in the range;

When $$-3 \leq x \leq 7$$, then $$3 + x$$ is positive and $$7 - x$$ is positive, thus $$|3 + x| + |7 - x| = 10$$ becomes $$(3 + x) + (7 - x) = 10$$ --> $$10=10$$. Since this is true, then this means that ANY x from the given range satisfies the equation;

When $$x > 7$$, then $$3 + x$$ is positive and $$7 - x$$ is negative, thus $$|3 + x| + |7 - x| = 10$$ becomes $$(3 + x) - (7 - x) = 10$$ --> $$x=-3$$. Discard since 7 is not in the range.

Therefore, $$|3 + x| + |7 - x| = 10$$ is true for any x where $$-3 \leq x \leq 7$$.

Hope it's clear.
_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 7027
Re: What is the value of integer x? [#permalink]

### Show Tags

03 Oct 2017, 13:49
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: What is the value of integer x?   [#permalink] 03 Oct 2017, 13:49
Display posts from previous: Sort by

# What is the value of integer x?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 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®.