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

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If |a - b| = |b - c| = 2 , what is |a - c| ? [#permalink] New post 09 Oct 2010, 03:09
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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
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Re: If |a - b| = |b - c| = 2 , what is |a - c| ? [#permalink] New post 09 Oct 2010, 03:40
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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

Answer is (A)
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Re: If |a - b| = |b - c| = 2 , what is |a - c| ? [#permalink] New post 09 Oct 2010, 04:51
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Expert's post
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


Generally for |x|:
When x\leq{0}, then |x|=-x;
When x\geq{0}, then |x|=-x.

(1) a<b<c --> as a<b (a-b<0) then |a - b|=2 becomes: -a+b=2, so b=2+a and as b<c ({b-c}<0) then |b-c|=2 becomes: {-b+c}=2. Substituting b --> -2-a+c=2 --> a-c=-4 --> |a - c|=|-4|=4 . Sufficient.

(2) c-a>c-b --> b-a>0 --> |a - b|=2 becomes: -a+b=2, so b=2+a --> |b - c|=|a-c+2| = 2 --> either a-c=0 or a-c=-4. Not sufficient.

Answer: A.
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Re: If |a - b| = |b - c| = 2 , what is |a - c| ? [#permalink] New post 09 Oct 2010, 09:14
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?
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Re: If |a - b| = |b - c| = 2 , what is |a - c| ? [#permalink] New post 09 Oct 2010, 10:30
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

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Re: If |a - b| = |b - c| = 2 , what is |a - c| ? [#permalink] New post 09 Oct 2010, 10:38
|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

Ans : A

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Re: If |a - b| = |b - c| = 2 , what is |a - c| ? [#permalink] New post 16 Oct 2010, 04:38
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I always find these type of questions to be killer..:(
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Re: If |a - b| = |b - c| = 2 , what is |a - c| ? [#permalink] New post 06 Jun 2014, 07:09
I don't think that even the options are required to answer this question

From question itself

|<-------------2------------->|<--------------2-------------->|
A------------------------------B--------------------------------C

|<----------------------------4--------------------------------->|


The question is badly framed and is definitely not GMAT.
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Re: If |a - b| = |b - c| = 2 , what is |a - c| ? [#permalink] New post 06 Jun 2014, 07:36
Expert's post
madn800 wrote:
If |a - b| = |b - c| = 2 , what is |a - c| ?

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

I don't think that even the options are required to answer this question

From question itself

|<-------------2------------->|<--------------2-------------->|
A------------------------------B--------------------------------C

|<----------------------------4--------------------------------->|


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.

Hope it helps.
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PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: If |a - b| = |b - c| = 2 , what is |a - c| ?   [#permalink] 06 Jun 2014, 07:36
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