It is currently 18 Oct 2017, 08:11

# Live Now:

### 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

# Events & Promotions

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

# What is the distance between x and y on the number line?

Author Message
TAGS:

### Hide Tags

Manager
Joined: 27 Oct 2011
Posts: 184

Kudos [?]: 211 [2], given: 4

Location: United States
Concentration: Finance, Strategy
GPA: 3.7
WE: Account Management (Consumer Products)
What is the distance between x and y on the number line? [#permalink]

### Show Tags

25 Mar 2012, 18:30
2
KUDOS
7
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

58% (01:36) correct 42% (00:56) wrong based on 431 sessions

### HideShow timer Statistics

What is the distance between x and y on the number line?

(1) |x| – |y| = 5
(2) |x| + |y| = 11
[Reveal] Spoiler: OA

_________________

DETERMINED TO BREAK 700!!!

Kudos [?]: 211 [2], given: 4

Math Expert
Joined: 02 Sep 2009
Posts: 41885

Kudos [?]: 128722 [0], given: 12182

Re: What is the distance between x and y on the number line? [#permalink]

### Show Tags

26 Mar 2012, 00:22
Expert's post
6
This post was
BOOKMARKED
What is the distance between x and y on the number line?

Question: |x-y|=?

(1) |x| – |y| = 5. Not sufficient: consider x=10, y=5 and x=10, y=-5.
(2) |x| + |y| = 11. Not sufficient: consider x=10, y=1 and x=10, y=-1.

(1)+(2) Solve the system of equation for |x| and |y|: sum two equations to get 2|x|=16 --> |x|=8 --> |y|=3. Still not sufficient to get the single numerical value of |x-y|, for example consider: x=8, y=3 and x=8, y=-3. Not sufficient.

_________________

Kudos [?]: 128722 [0], given: 12182

Manager
Joined: 12 Mar 2012
Posts: 93

Kudos [?]: 347 [1], given: 22

Location: India
Concentration: Technology, Strategy
GMAT 1: 710 Q49 V36
GPA: 3.2
WE: Information Technology (Computer Software)
Re: What is the distance between x and y on the number line? [#permalink]

### Show Tags

26 Mar 2012, 01:30
1
KUDOS
Solving the two equations will give x as 8 and y as 3. But since mod sign is there, x and y can take any value, either positive or negative. Hence, both the statements are insufficient.

Kudos [?]: 347 [1], given: 22

Current Student
Joined: 27 Jun 2012
Posts: 405

Kudos [?]: 931 [1], given: 184

Concentration: Strategy, Finance
Re: What is the distance between x and y on the number line? [#permalink]

### Show Tags

18 Dec 2012, 10:16
1
KUDOS
Bunuel can you clarify what can be wrong below approach?

-------------------------------------
By multiplying statements 1 & 2
(1) |x| – |y| = 5
(2) |x| + |y| = 11

$$X^2-Y^2=55$$

i.e. $$(x+y)(x-y)=55 = 11 * 5 = - 11 * - 5$$ (i.e. both factors are either positive or negative)

Hence only two possible solutions for this – i.e. either (x=8 & y=3) OR (x= -8 & y= -3)
In both cases the distance between them is 5.

_________________

Thanks,
Prashant Ponde

Tough 700+ Level RCs: Passage1 | Passage2 | Passage3 | Passage4 | Passage5 | Passage6 | Passage7
VOTE GMAT Practice Tests: Vote Here
PowerScore CR Bible - Official Guide 13 Questions Set Mapped: Click here

Kudos [?]: 931 [1], given: 184

Math Expert
Joined: 02 Sep 2009
Posts: 41885

Kudos [?]: 128722 [0], given: 12182

Re: What is the distance between x and y on the number line? [#permalink]

### Show Tags

23 Dec 2012, 07:55
PraPon wrote:
Bunuel can you clarify what can be wrong below approach?

-------------------------------------
By multiplying statements 1 & 2
(1) |x| – |y| = 5
(2) |x| + |y| = 11

$$X^2-Y^2=55$$

i.e. (x+y)(x-y)=55 = 11 * 5 = - 11 * - 5 (i.e. both factors are either positive or negative)

Hence only two possible solutions for this – i.e. either (x=8 & y=3) OR (x= -8 & y= -3)
In both cases the distance between them is 5.

(x+y)(x-y)=55 does not mean that either (x=8 & y=3) OR (x= -8 & y= -3). There are more integer solutions (for example x=+/-28 and y=+/-27) and infinitely many non-integer solutions.
_________________

Kudos [?]: 128722 [0], given: 12182

Current Student
Joined: 27 Jun 2012
Posts: 405

Kudos [?]: 931 [0], given: 184

Concentration: Strategy, Finance
Re: What is the distance between x and y on the number line? [#permalink]

### Show Tags

23 Dec 2012, 14:41
_________________

Thanks,
Prashant Ponde

Tough 700+ Level RCs: Passage1 | Passage2 | Passage3 | Passage4 | Passage5 | Passage6 | Passage7
VOTE GMAT Practice Tests: Vote Here
PowerScore CR Bible - Official Guide 13 Questions Set Mapped: Click here

Kudos [?]: 931 [0], given: 184

Math Expert
Joined: 02 Sep 2009
Posts: 41885

Kudos [?]: 128722 [0], given: 12182

Re: What is the distance between x and y on the number line? [#permalink]

### Show Tags

17 Jul 2013, 00:22
From 100 hardest questions
Bumping for review and further discussion.
_________________

Kudos [?]: 128722 [0], given: 12182

Senior Manager
Joined: 13 May 2013
Posts: 463

Kudos [?]: 197 [0], given: 134

Re: What is the distance between x and y on the number line? [#permalink]

### Show Tags

18 Jul 2013, 12:56
What is the distance between x and y on the number line?

(1) |x| – |y| = 5

|11|-|6|=5
Distance is five

|11|-|-6|=5
Distance is seventeen
INSUFFICIENT

(2) |x| + |y| = 11

|5|+|6| = 11
Distance is one

|5|+|-6| = 11
Distance is negative eleven

INSUFFICIENT

This problem, to me, seems much easier than a 700 level question. a and b provide us with multiple valid values for x and y, none of which entirely (i.e. are the same) Can someone tell me if I am oversimplifying this problem? Thanks!

Kudos [?]: 197 [0], given: 134

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16707

Kudos [?]: 273 [0], given: 0

Re: What is the distance between x and y on the number line? [#permalink]

### Show Tags

24 Jun 2015, 10:51
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.
_________________

Kudos [?]: 273 [0], given: 0

CEO
Joined: 17 Jul 2014
Posts: 2604

Kudos [?]: 394 [0], given: 182

Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Re: What is the distance between x and y on the number line? [#permalink]

### Show Tags

31 Mar 2016, 18:37
calreg11 wrote:
What is the distance between x and y on the number line?

(1) |x| – |y| = 5
(2) |x| + |y| = 11

i picked 8 and 3
1. x=8, y=3 -> 5 or x=-8, y=3 -> distance is 11. 1 alone is insufficient.
2. x=8, y=3 -> 5 or x=-8, y=3 -> distance is 11. 2 alone is insufficient.

1+2
same info from 1 and 2. C is out, and the answer must be E.

Kudos [?]: 394 [0], given: 182

Intern
Joined: 09 Jan 2015
Posts: 7

Kudos [?]: [0], given: 57

Re: What is the distance between x and y on the number line? [#permalink]

### Show Tags

06 Apr 2016, 22:57
Bunuel wrote:
What is the distance between x and y on the number line?

Question: |x-y|=?

(1) |x| – |y| = 5. Not sufficient: consider x=10, y=5 and x=10, y=-5.
(2) |x| + |y| = 11. Not sufficient: consider x=10, y=1 and x=10, y=-1.

(1)+(2) Solve the system of equation for |x| and |y|: sum two equations to get 2|x|=16 --> |x|=8 --> |y|=3. Still not sufficient to get the single numerical value of |x-y|, for example consider: x=8, y=3 and x=8, y=-3. Not sufficient.

Hi... I have a question when we solve both the eqs tog we get two values for |y|=3 and -13. Right?

Kudos [?]: [0], given: 57

Math Expert
Joined: 02 Sep 2009
Posts: 41885

Kudos [?]: 128722 [0], given: 12182

Re: What is the distance between x and y on the number line? [#permalink]

### Show Tags

07 Apr 2016, 00:33
enasni wrote:
Bunuel wrote:
What is the distance between x and y on the number line?

Question: |x-y|=?

(1) |x| – |y| = 5. Not sufficient: consider x=10, y=5 and x=10, y=-5.
(2) |x| + |y| = 11. Not sufficient: consider x=10, y=1 and x=10, y=-1.

(1)+(2) Solve the system of equation for |x| and |y|: sum two equations to get 2|x|=16 --> |x|=8 --> |y|=3. Still not sufficient to get the single numerical value of |x-y|, for example consider: x=8, y=3 and x=8, y=-3. Not sufficient.

Hi... I have a question when we solve both the eqs tog we get two values for |y|=3 and -13. Right?

|y| is an absolute value of y, so it cannot be negative. When we solve for |y|, we get that |y| = 3, so y = 3, or y = -3.

Hope it's clear.
_________________

Kudos [?]: 128722 [0], given: 12182

Manager
Joined: 23 Dec 2013
Posts: 235

Kudos [?]: 12 [0], given: 21

Location: United States (CA)
GMAT 1: 760 Q49 V44
GPA: 3.76
Re: What is the distance between x and y on the number line? [#permalink]

### Show Tags

22 May 2017, 19:24
calreg11 wrote:
What is the distance between x and y on the number line?

(1) |x| – |y| = 5
(2) |x| + |y| = 11

Picking numbers works well here. The trick is to realize that you can simply make either x or y negative to install a new case to test for sufficiency.

GOAL: What is the distance between x and y? Must be one discrete value, not multiple.

Statement 1: Pick 11 and 6. 11-6 = 5, so this case matches the given information and the distance is 5. Now you can make either 11 or 6 negative, so set x = -11. Now abs(-11) - 6 = 5, but the distance is 17 units. So this case is not sufficient because we have multiple possible distances on the number line.

Statement 2: Here abs(x) + abs(y) = 11. Pick 5 and 6, the most obvious choices. The distance between them is 1. Now turn 5 into -5, and the statement is still valid (abs(-5) + abs(6) =11, but their distance is now 11. Not sufficient.

Combined they are not sufficient. You can test via 8 = x, 3 = y and then -8 = x, 3=y.

Kudos [?]: 12 [0], given: 21

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4127

Kudos [?]: 2886 [0], given: 0

GPA: 3.82
Re: What is the distance between x and y on the number line? [#permalink]

### Show Tags

22 May 2017, 19:47
calreg11 wrote:
What is the distance between x and y on the number line?

(1) |x| – |y| = 5
(2) |x| + |y| = 11

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.

Condition (1)
In the case that $$x = 6$$, $$y = 1$$, the distance $$x$$ and $$y$$, $$| x - y | = 5$$.
In the case that $$x = 6$$, $$y = -1$$, the distance $$x$$ and $$y$$, $$| x - y | = 7$$.
Thus we don't have a unique solution.

Condition (2)
In the case that $$x = 6$$, $$y = 5$$, the distance $$x$$ and $$y$$, $$| x - y | = 1$$.
In the case that $$x = 6$$, $$y = -5$$, the distance $$x$$ and $$y$$, $$| x - y | = 11$$.

Thus we don't have a unique solution.

Condition (1) & (2)
If we add two equation, we have $$2|x| =16$$ or $$|x| = 8$$. Thus $$x = \pm 8$$.
If we subtract the first equation from the second one, we have $$2|y| =6$$ or $$|y| = 3$$. Thus $$y = {\pm}3$$.

In the case that $$x = 8$$ and $$y = 3$$, the distance $$x$$ and $$y$$, $$| x - y | = 5$$.
In the case that $$x = 8$$ and $$y = -3$$, the distance $$x$$ and $$y$$, $$| x - y | = 11$$.
Thus we don't have a unique solution.

Normally for cases where we need 2 more equations, such as original conditions with 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore C has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) together. Here, there is 70% chance that C is the answer, while E has 25% chance. These two are the key questions. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer according to DS definition, we solve the question assuming C would be our answer hence using 1) and 2) together. (It saves us time). Obviously there may be cases where the answer is A, B, D 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.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself

Kudos [?]: 2886 [0], given: 0

Re: What is the distance between x and y on the number line?   [#permalink] 22 May 2017, 19:47
Display posts from previous: Sort by