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:

Re: If |a - b| = |b - c| = 2 , what is |a - c| ? [#permalink]

Show Tags

09 Oct 2010, 04:40

2

This post received KUDOS

AndreG wrote:

How do I approach a question like the following:

If \(|a - b| = |b - c| = 2\) , what is \(|a - c|\) ?

1. \(a \lt b \lt c\) 2. \(c - a \gt c - b\)

(C) 2008 GMAT Club - m16#37

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient * Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient * BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient * EACH statement ALONE is sufficient * Statements (1) and (2) TOGETHER are NOT sufficient

\(|a - b| = |b - c| = 2\)

Imagine the points on a number line. There is two possibilities, either a & c are on the same side of the line relative to b, or on the opposite sides. Also remember that |x-y| represents distance between x and y on the number line.

So if a & c ar on the same side then a=c. |a-c|=0 If they are on opposite sides, |a-c|=4

(1) \(a \lt b \lt c\) a and c on opposite sides, answer is 4. Sufficient

(2) \(c - a \gt c - b\) This only implies \(a \lt b\) Insufficient to know where c is, same side or opposite side. Insufficient

Re: If |a - b| = |b - c| = 2 , what is |a - c| ? [#permalink]

Show Tags

09 Oct 2010, 10:14

Thanks to the two of you! While I do understand both solutions, I feel shrouded's is a lot faster, will that always be the case, or is this kind of just lucky for this particular question?

Re: If |a - b| = |b - c| = 2 , what is |a - c| ? [#permalink]

Show Tags

09 Oct 2010, 11:30

Thinking of |x-y| as distance between two points on a number line is a very neat trick and I find it very helpful in a lot of GMAT problems. You should def give it a shot first. Thinking visually is faster than algebraically solving in many cases

Re: If |a - b| = |b - c| = 2 , what is |a - c| ? [#permalink]

Show Tags

09 Oct 2010, 11:38

|a-b| = |b-c| = 2 can be written in 4 ways

1) a-b = b-c = 2 => a>b>c with a diff of 2 2) a-b = c-b = 2 => a=c 3) b-a = b-c = 2 => a=c 4) b-a = c-b = 2 => a<b<c with a diff of 2

A) a<b<c : based on the 4th statement above , we can say that |a-c| = 4 Sufficient B) c-a > c-b : we can understand that a<b but there is no relationship with C. Hence Insufficient

The question is badly framed and is definitely not GMAT.

There is noting wrong with the question. The second statement is NOT sufficient. Consider: b=3, a=1, and c=1 --> |a - c| = 0. b=3, a=1, and c=5 --> |a - c| = 4.

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.

Question

In the original question, there are 3 variables and 2 equations. Thus D is most likely.

For the condition 1), \(| a - b | = b - a = 2\) and \(| b - c | = c - b = 2\). When we add two equations \(c - a = ( b - a ) + ( c - b ) = c - a = 4\). Thus \(| a - c | = 4\). The condition 1) is sufficient.

For the condition 2) \(c - a > c - b\) is equivalent to \(-a > -b\) or \(a < b\). However, we don't know anything about c from the condition 2).

There two cases that satisfy \(| a - b | = | b - c | = 2\).

----a----b----c---->

---a,c----b--------->

Thus \(|a-c| = c - a = ( c - b ) + ( b - a ) = 2 + 2 = 4\) or \(| a - c | = 0\). The condition 2) is 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.
_________________

We’ve given one of our favorite features a boost! You can now manage your profile photo, or avatar , right on WordPress.com. This avatar, powered by a service...

Sometimes it’s the extra touches that make all the difference; on your website, that’s the photos and video that give your content life. You asked for streamlined access...

A lot has been written recently about the big five technology giants (Microsoft, Google, Amazon, Apple, and Facebook) that dominate the technology sector. There are fears about the...

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...