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

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

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Updated on: 27 May 2014, 07:40
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45% (medium)

Question Stats:

66% (01:53) correct 34% (01:59) wrong based on 1162 sessions

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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.

Originally posted by ronybtl on 17 Nov 2005, 07:25.
Last edited by Bunuel on 27 May 2014, 07:40, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
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Re: The point A, B, C, and D are on the number line, not necessa  [#permalink]

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06 Jan 2017, 06:10
16
19
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.

"If the distance between A and B is 18"
makes me think
A-----------------------------------B
B-----------------------------------A

"the distance between C and D is 8"
C--------------D
D--------------C

Question: Distance between B and D?

(1) The distance between C and A is the same as the distance between C and B.
So C is in the middle of A and B.

A-----------------C-----------------D-B
or
B-----------------C-----------------D-A
or
A-D----------------C------------------B
or
B-D----------------C------------------A

Not sufficient

(2) A is to the left of D on the number line.
No defined relation between B and D. Not sufficient.

Using both statements together, there are two possibilities:
A-----------------C-----------------D-B
or
A-D----------------C------------------B

Still not sufficient.

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Re: Points on a line  [#permalink]

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12 Dec 2011, 18:57
5
1
ABCD can be arranged in any order on the number line, the question stem does not has enough information to rephrase. So, lets move to statements.

1. C is between A and B. There are four sequences possible here: ACDB, ADCB, BCDA, and BDCA. All cases has different distances (2 pairs) between B and D. INSUFFICIENT
2. A is to the left of D. Where is D w.r.t B? INSUFFICIENT

Together, we have ACDB or ADCB as the sequence, both with different distances between B and D. INSUFFICIENT.

E.
##### General Discussion
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17 Nov 2005, 19:02
4
Why couldn't it be E?

Since the points are not in any order...

A and B are 18 apart. C is smack in the middle, and D is 8 from the middle, but couldn't it be on either side? so it could be 1 away from D and also 17 away from D, depending on whether C or D is larger, which I don't think it indicates.

Let me know if I'm overlooking something here. I've been on a roll of careless errors, so I could be wrong big time.
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17 Nov 2005, 22:07
1
1
one more E

Point A,B,C and D are on a number line but not in that order. If distance between A and B is 18 and distance between C and D is 8, what is the distance between B and D?

(a) Distance between C and A is equal to distance between C and B
as this tell us C is in the center of A and B its equidistant from both

if we assume that A is at 0
B at 18
C at 9
then D can be at 17 or at 1 so Insuff

(b) A is left of D on the number line.

does not provide any information about the location of B and D

In suff

taking together

sill the these assumption satisfy both the condition
if we assume that A is at 0
B at 18
C at 9
then D can be at 17 or at 1 so Insuff

but gives different value of distance between B and D

hence E
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Re: points A,B,C,D on a number line  [#permalink]

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02 Sep 2009, 03:03
1
1)insuff,
this says AC=BC=9
2)insuff,
we do not know whether B is left to A or right to A.
Together
insuff. We know BA, BC, AC, CD or do not know BD.
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Re: points A,B,C,D on a number line  [#permalink]

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02 Sep 2009, 17:10
14
7
see figure..
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numberline.gif [ 8.67 KiB | Viewed 105094 times ]

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Re: The point A, B, C, and D are on the number line, not necessa  [#permalink]

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06 Dec 2013, 12:16
1
3
The point A, B, C, and D are on the number line, not necessarily in the 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.

Here is my take.

(1) we know that CA=CB and that the distance between A and B = 18 so A is at 0, C is at 9 and B is at 18 with CA=CB=9. Because C is in the middle, D has to lie somewhere between A and B, 8 units away, specifically at 1 or 17 (9-8 or 9+8) The difference between B and D, therefore, could be 18-17 or 18-1. Insufficient.

(2) This tells us very little, especially considering that the stem gives us no order in which A,B,C,D can be placed. A could be at 1 and D at 2 or D at 1000. Insufficient.

(1+2) (2), when taken into consideration with (1) provides us no new information. From (1) we already know that D lies to the right of A. All we know is that it could be 1 away from A or 17 away from A.

Insufficient, E
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The point A, B, C, and D are on the number line, not necessa  [#permalink]

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14 Jun 2016, 10:04
The point A, B, C, and D are on the number line, not necessarily in the 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.

The GMAT answer to this question is letter E:

1) A_D_______C_________B
2) A_________C_______D_B
3) B_D_______C_________A
4) B_________C_______D_A

It can be seen that the distance between A and B remains 18 in all cases. The distance between C and D remains 8 in all cases. Furthermore as mentioned in the statement one C is in the middle between A and B and therefore the distance from C to A and B is 9 each respectively.
In the cases 2) & 3) the distance between B and D is one and in the cases 1) and 4) the distance between B and D is 17. There the answer choice A is incorrect.
The second statement eliminates the cases 1) and 2). Nethertheless the distance between B and D remains at 1 or 17 in case 3) and 4) respectively.
Therefore both statements together are not suffient and the right answere choice should be E.
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The point A, B, C, and D are on the number line, not necessa  [#permalink]

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14 Jun 2016, 11:19
3
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.

Given ,AB=18 and CD=8 ,
(1)No information of the specifice placement of D,Insufficient

(2) No information of te distance ,Insufficient

(1)+(2) CD<9,So both of C and D points are left of A and their placement and are interchangeable or not specific ,

So the distance between B and D is not specific .Insufficient

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Re: The point A, B, C, and D are on the number line, not necessa  [#permalink]

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29 Jan 2017, 05:11
BC = 8

What is BD?

Statement 1: AC = BC, we can have two possibilities:

-------------A-----------------C----------------B---D------ so BD = 1

-------------A,B---------------C--------------------D------ A and B are on the same point, so BD = 18

Insufficient

Statement 2: A is to the left of D.

There is no info on the position of B relative to A or D. Insufficient.

Both statements together:
Both possibilities shown in statement 1 also satisfies statement 2. So insufficient.

Choose E.
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Re: The point A, B, C, and D are on the number line, not necessa  [#permalink]

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18 Jun 2017, 15:10
1
Here is just an example of how the number line could look.
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answer 2.png [ 318.87 KiB | Viewed 46092 times ]

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

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25 Dec 2017, 11:36
A---------------B(9) -------------C(18)-----D(26) or
A---------------B(9)---D(10)-------C(18)
After even combining these two we are not getting any concrete answer.
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Re: The point A, B, C, and D are on the number line, not necessa  [#permalink]

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02 Dec 2018, 12:42
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.
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Re: The point A, B, C, and D are on the number line, not necessa  [#permalink]

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14 Dec 2019, 11:01
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Re: The point A, B, C, and D are on the number line, not necessa   [#permalink] 14 Dec 2019, 11:01
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