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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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.

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

Show Tags

26 Mar 2012, 01:30

1

This post received 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.

Bunuel can you clarify what can be wrong below approach?

Answer choice can be (C) ------------------------------------- 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.

-> Hence Answer is C.

(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.
_________________

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!

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.
_________________

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.

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.

Answer: E.

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

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.

Answer: E.

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.

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.

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.

Therefore the answer is E.

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.
_________________

Version 8.1 of the WordPress for Android app is now available, with some great enhancements to publishing: background media uploading. Adding images to a post or page? Now...

Post today is short and sweet for my MBA batchmates! We survived Foundations term, and tomorrow's the start of our Term 1! I'm sharing my pre-MBA notes...

“Keep your head down, and work hard. Don’t attract any attention. You should be grateful to be here.” Why do we keep quiet? Being an immigrant is a constant...