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# The point A, B, C, and D are on the number line, not necessa

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Manager
Joined: 20 Jan 2016
Posts: 88
Schools: HBS '18
WE: Consulting (Other)
Re: The point A, B, C, and D are on the number line, not necessa  [#permalink]

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26 Aug 2018, 09:06
Hello,

When I saw points ABCD "not necessarily in that order", and AB= 18 and CD = 8, I came up with so many variations of this that I got lost. How did you narrow down your variations before tackling the statements?
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Manager
Joined: 14 Jul 2014
Posts: 96
Location: India
Concentration: Social Entrepreneurship, Strategy
GMAT 1: 620 Q41 V34
WE: Information Technology (Computer Software)
Re: The point A, B, C, and D are on the number line, not necessa  [#permalink]

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28 Aug 2018, 11:52
batmannavneet wrote:
If you draw a number line and plot points ABCD on it, then you will realise that -

1) B can be between A and C
2) C can be between A and B

The above 2 variations is sufficient to prove that the answer is E.

2) C can be between A and B this has to be true from the statement 1
Manager
Joined: 14 Jul 2014
Posts: 96
Location: India
Concentration: Social Entrepreneurship, Strategy
GMAT 1: 620 Q41 V34
WE: Information Technology (Computer Software)
Re: The point A, B, C, and D are on the number line, not necessa  [#permalink]

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28 Aug 2018, 11:53
batmannavneet wrote:
If you draw a number line and plot points ABCD on it, then you will realise that -

1) B can be between A and C
2) C can be between A and B

The above 2 variations is sufficient to prove that the answer is E.

2) C can be between A and B this has to be true from statement 1
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 619
Re: The point A, B, C, and D are on the number line, not necessa  [#permalink]

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02 Dec 2018, 11:42
ronybtl wrote:
The point A, B, C, and D are on the number line, not necessarily in that order. If the distance between A and B is 18 and the distance between C and D is 8, what is the distance between B and D?

(1) The distance between C and A is the same as the distance between C and B.
(2) A is to the left of D on the number line.

\eqalign{ & {\rm{dist}}\left( {A,B} \right) = 18 \cr & {\rm{dist}}\left( {C,D} \right) = 8 \cr}

$${\rm{? = dist}}\left( {B,D} \right)$$

Let´s go straight to (1+2): a bifurcation guarantees the correct answer is (E)!

$$\left( {1 + 2} \right)\,\,\,\,\left\{ \matrix{ \,A < D \hfill \cr \,{\rm{dist}}\left( {C,A} \right) = {\rm{dist}}\left( {C,B} \right) \hfill \cr} \right.\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\,{\rm{Geometric}}\,\,{\rm{Bifurcation}}\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\,\left( {\rm{E}} \right)\,\,\,$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________

Fabio Skilnik :: GMATH method creator (Math for the GMAT)
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Re: The point A, B, C, and D are on the number line, not necessa &nbs [#permalink] 02 Dec 2018, 11:42

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