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

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