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

"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.

Answer (E)

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.

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.

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

but no information about D

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

1)insuff,
this says AC=BC=9
nothing about BD
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.

see figure..

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

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.

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

Correct Answer E

AD = 18
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.

Here is just an example of how the number line could look.

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.

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

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

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.
_________________

I-----A---D(1)----C---D(2)--B---I

This is the information given by both statements (not drawn to scale). C is in the middle between A and B. However we do not know whether D is on the left side of C or on the right side. Thus, both Statements together are not sufficient.

Similar: https://gmatclub.com/forum/the-points-a ... l#p2729836

From the question data, AB = 18 and CD = 8. The length of BD to be found.

Since A, B, C and D are not necessarily in that order, we do not have a unique diagram. Any information that can help us draw a unique diagram is sufficient information.

From statement I alone, AC = CB. This only tells us that C is exactly half way between A and B.
No information about the positions of A, B and D. So, we could have the positions as shown in the diagram below



We do not have a unique diagram. Statement I alone is insufficient.
Answer options A and D can be eliminated. Possible answer options are B, C or E.

From statement II alone, A is to the left of D on the number line.
We have no information about the positions of C and B

Statement II alone is woefully insufficient. Answer option B can be eliminated. Possible answer options are C or E.

Combining statements I and II, we have the following:

From statement I alone, point C is exactly half way between A and B.
From statement II alone, point A is to the left of D on the number line.

However, we do not know the position of D just yet. We can draw the following diagrams satisfying the combination of data.



The combination of statements is insufficient to give us a unique diagram. Answer option C can be eliminated.

The correct answer option is E.

Hope that helps!
Aravind B T
_________________

KarishmaB Bunuel

Can we do the above question with Mod approach as suggested by Bunuel in one of the questions.

I am not sure which question or method you are talking about. I would need a link to see what Bunuel did there.
As for using absolute values for this question, I wouldn't. It is easy to imagine it all on the number line.

https://gmatclub.com/forum/on-the-numbe ... 89015.html


In the mentioned problem Bunuel solved it through Absolute value. Can we approach the same way here. KarishmaB Bunuel