The points A, B, C and D are on a number line, not necessarily in this order. If the distance between A and B is 18 and the distance betwen 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.
I think I understand the different cases of positioning these points. However, I thought the answer ic C, instead of E.
Can someone explain how to get to the answer.
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- TakingGMAT
The points A, B, C, and D are on a number line
1) Only tells us that C is between A and B but nothing about D. Insufficient.
2) Tells us that A is to the left of D.
A B D or
--------------------------
A D B
--------------------------
Not sufficient.
1 and 2 together also not sufficient
2) Tells us that A is to the left of D.
A B D or
--------------------------
A D B
--------------------------
Not sufficient.
1 and 2 together also not sufficient
- Kaushik
Re: The points A, B, C, and D are on a number line
Anonymous Wrote:The points A, B, C and D are on a number line, not necessarily in this order. If the distance between A and B is 18 and the distance betwen 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.
I think I understand the different cases of positioning these points. However, I thought the answer ic C, instead of E.
Can someone explain how to get to the answer.
You can ans this question with statement 1 only ......
- Raj
Re: The points A, B, C, and D are on a number line
Hi,
from (1), C has to be half way between A and B. So, AC and CB are each = 9. This does not give any info on D, hence not sufficient. Since CD = 8, D is with in AB but could be on either side of C. It is already clear that A is to the left of D
From (2), from above, this statement does not add any new information, we already know A is to the left of D. insufficient.
Taken together too, insufficient. Ans E.
Can you please share the official Answer.
Thanks,
-Raj.
from (1), C has to be half way between A and B. So, AC and CB are each = 9. This does not give any info on D, hence not sufficient. Since CD = 8, D is with in AB but could be on either side of C. It is already clear that A is to the left of D
From (2), from above, this statement does not add any new information, we already know A is to the left of D. insufficient.
Taken together too, insufficient. Ans E.
Can you please share the official Answer.
Thanks,
-Raj.
Anonymous Wrote:The points A, B, C and D are on a number line, not necessarily in this order. If the distance between A and B is 18 and the distance betwen 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.
I think I understand the different cases of positioning these points. However, I thought the answer ic C, instead of E.
Can someone explain how to get to the answer.
- jwinawer
- ManhattanGMAT Staff
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- Joined: Mon Aug 16, 2004 1:15 pm
Right. As the last poster said, we can deduce from statement 1 that C is halfway between A and B. But we cannot tell D is closer to A or closer to B.
With statement 1, we've got 4 possible layouts (not quite drawn to scale, but almost):
(1)
A --------------------------- B
---------------C------------D
(2)
A----------------------------B
-D-----------C
(3)
B ---------------------------A
------------- C------------D
(4)
B----------------------------A
-D-----------C
This is insufficient. Statement 2 doesn't help at all.
So the right answer is E.
With statement 1, we've got 4 possible layouts (not quite drawn to scale, but almost):
(1)
A --------------------------- B
---------------C------------D
(2)
A----------------------------B
-D-----------C
(3)
B ---------------------------A
------------- C------------D
(4)
B----------------------------A
-D-----------C
This is insufficient. Statement 2 doesn't help at all.
So the right answer is E.
- navrajdhaliwal1
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Re: The points A, B, C, and D are on a number line
Doesn't statement 2 that A is to the left of D, eliminate 3&4 below? What do you mean by "Statement 2 doesn't help at all"?
Answer still remains to be "E" as we cannot choose btw 1&2.
(1)
A --------------------------- B
---------------C------------D
(2)
A----------------------------B
-D-----------C
(3)
B ---------------------------A
------------- C------------D
(4)
B----------------------------A
-D-----------C
Answer still remains to be "E" as we cannot choose btw 1&2.
(1)
A --------------------------- B
---------------C------------D
(2)
A----------------------------B
-D-----------C
(3)
B ---------------------------A
------------- C------------D
(4)
B----------------------------A
-D-----------C
- rachelhong2012
- Course Students
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Re: The points A, B, C, and D are on a number line
Hi instructors,
When I first did this problem it took me more than 3 minutes because I was trying to draw out all the different cases of how ABCD would be arranged on the number line and then eliminate these possible scenarios based on clues given in the question and statement. Still, it was confusing and hard. I'm wondering for these number line questions should I just use the clues the question gives us to draw out the scenarios and thus save time? Is there a strategic or better yet, systematic way to attack this type of problem to be more efficient and effective?
Thanks!
When I first did this problem it took me more than 3 minutes because I was trying to draw out all the different cases of how ABCD would be arranged on the number line and then eliminate these possible scenarios based on clues given in the question and statement. Still, it was confusing and hard. I'm wondering for these number line questions should I just use the clues the question gives us to draw out the scenarios and thus save time? Is there a strategic or better yet, systematic way to attack this type of problem to be more efficient and effective?
Thanks!
- jnelson0612
- ManhattanGMAT Staff
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Re: The points A, B, C, and D are on a number line
rachelhong2012 Wrote:Hi instructors,
When I first did this problem it took me more than 3 minutes because I was trying to draw out all the different cases of how ABCD would be arranged on the number line and then eliminate these possible scenarios based on clues given in the question and statement. Still, it was confusing and hard. I'm wondering for these number line questions should I just use the clues the question gives us to draw out the scenarios and thus save time? Is there a strategic or better yet, systematic way to attack this type of problem to be more efficient and effective?
Thanks!
You know, it totally depends on the question. In something like this the question does not give you enough information to really narrow things down, so go to the statements. Use statement 1 to draw out a few possibilities and quickly establish that it's insufficient. Same with 2. Same with them together. Our objective on Data Sufficiency is to try to show that a statement is insufficient as quickly as possible, unless you've rephrased the original question upfront and you can see that the statement clearly is sufficient. Great question!
Jamie Nelson
ManhattanGMAT Instructor
ManhattanGMAT Instructor
- ghong14
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Re: The points A, B, C, and D are on a number line
This problem has been bother me for a while finally came up with the solution on the board. Thought I share the solution because I was having a really hard time finding a good example that showed sufficiency and insufficiency.
We know that A B C D are 4 points on a line. The big thing we need to notice from the question prompt is that there is a combination of ways to order this. In fact there are 4! ways(happy number counting;)). The other thing is we need to notice there is a relationship between the points which will help us later.
Step 1. Look at statement and deduce scenarios that fit the requirement.
C is equal distant from A and B. SO we could have the following combinations
Starting with A
A C B D
A C D B
A D C B
Starting with B
B C A D
B C D A
B D C A
Starting with C
D A C B
D B C A
Notice C cannot come first because it needs to be in between A and B.
Step 2. Find insufficiency
IF A B equals 18 and CD equals 8 let's just plug that into one of our scenarios
A C B D, that means A....(9 units away)....C.....(9)......B...(1)....D
In this case BD = 1
Now pick a case where BD does not equal 1
A D C B, that means A...(1)...D....(8)....C.....(9)...B
In this case BD = 17
CLEARLY INSUFFICIENT CROSS A AND D
Step 3. look at statement 2.
A is to the left of D on the number line
Guess what, we just used two scenarios where A was both to the left of D and there was insufficiency.
Eliminate B
Step 4. Combine both statement to limit your scenarios
When combined statement 1 and 2 we eliminate alot of the scenarios that were first presented because A must be to the left of D. I will BOLD the combinations that fit both of the criteria of statement 1 and 2.
Starting with A
A C B D
A C D B
A D C B
Starting with B
B C A D
B C D A
B D C A
Starting with C
D A C B
D B C A
WOW that just decreased the number of possibilities to 4. Well can we still find insufficiency? YEP because A C B D and A D C B is still there. So overall E.
GOOD LUCK :)
We know that A B C D are 4 points on a line. The big thing we need to notice from the question prompt is that there is a combination of ways to order this. In fact there are 4! ways(happy number counting;)). The other thing is we need to notice there is a relationship between the points which will help us later.
Step 1. Look at statement and deduce scenarios that fit the requirement.
C is equal distant from A and B. SO we could have the following combinations
Starting with A
A C B D
A C D B
A D C B
Starting with B
B C A D
B C D A
B D C A
Starting with C
D A C B
D B C A
Notice C cannot come first because it needs to be in between A and B.
Step 2. Find insufficiency
IF A B equals 18 and CD equals 8 let's just plug that into one of our scenarios
A C B D, that means A....(9 units away)....C.....(9)......B...(1)....D
In this case BD = 1
Now pick a case where BD does not equal 1
A D C B, that means A...(1)...D....(8)....C.....(9)...B
In this case BD = 17
CLEARLY INSUFFICIENT CROSS A AND D
Step 3. look at statement 2.
A is to the left of D on the number line
Guess what, we just used two scenarios where A was both to the left of D and there was insufficiency.
Eliminate B
Step 4. Combine both statement to limit your scenarios
When combined statement 1 and 2 we eliminate alot of the scenarios that were first presented because A must be to the left of D. I will BOLD the combinations that fit both of the criteria of statement 1 and 2.
Starting with A
A C B D
A C D B
A D C B
Starting with B
B C A D
B C D A
B D C A
Starting with C
D A C B
D B C A
WOW that just decreased the number of possibilities to 4. Well can we still find insufficiency? YEP because A C B D and A D C B is still there. So overall E.
GOOD LUCK :)
- RonPurewal
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Re: The points A, B, C, and D are on a number line
ghong14, that's a valid solution, but it's way too much work -- suggesting that you may not be sufficiently focused on the goal of the problem.
in particular, you listed a whole ton of cases for statement #1, before even thinking about what to do with those cases.
if you are more focused on what you're actually trying to accomplish here, you don't need more than two cases.
statement 1:
as you noticed, C is the midpoint between A and B, so AC and BC are both 9 units.
point D is only 8 units away from C (the middle point), so point D must be inside AB -- but we don't know on which side.
all you need is two cases:
A-D--------C-----------B
A-----------C---------D-B
you don't even have to figure out the actual distances in these cases, because they are clearly different (the distance DB is way, way smaller in the second picture than in the first one).
insufficient.
--
statement 2:
with this statement, D can be absolutely anywhere to the right of A.
* D can be 100 units to the right of A. In that case, DB will be somewhere around 100 units.
* D can be 1,000,000 units to the right of A. In that case, DB will be somewhere around 1,000,000 units.
etc.
no need to waste the time to test specific cases, since there's so much freedom to move point D around all over town.
--
together:
both cases from statement 1 actually work in statement 2, so, we're done.
(if you drew them the other way around -- with B on the left and A on the right -- then you'd just reverse them. but, since A comes before B in the alphabet, it's unlikely that you won't have drawn the versions above.)
it's E.
you need to solve these problems efficiently. that doesn't mean you have to be super-fast or super-"smart"; it just means that you need to have a DEFINITE GOAL OR PURPOSE at each step of the way.
if you are just listing random possibilities, then there's a (somewhat slim) chance that you'll just accidentally walk into a valid solution -- but it's more likely that you'll just keep wandering around the problem.
in particular, you listed a whole ton of cases for statement #1, before even thinking about what to do with those cases.
if you are more focused on what you're actually trying to accomplish here, you don't need more than two cases.
statement 1:
as you noticed, C is the midpoint between A and B, so AC and BC are both 9 units.
point D is only 8 units away from C (the middle point), so point D must be inside AB -- but we don't know on which side.
all you need is two cases:
A-D--------C-----------B
A-----------C---------D-B
you don't even have to figure out the actual distances in these cases, because they are clearly different (the distance DB is way, way smaller in the second picture than in the first one).
insufficient.
--
statement 2:
with this statement, D can be absolutely anywhere to the right of A.
* D can be 100 units to the right of A. In that case, DB will be somewhere around 100 units.
* D can be 1,000,000 units to the right of A. In that case, DB will be somewhere around 1,000,000 units.
etc.
no need to waste the time to test specific cases, since there's so much freedom to move point D around all over town.
--
together:
both cases from statement 1 actually work in statement 2, so, we're done.
(if you drew them the other way around -- with B on the left and A on the right -- then you'd just reverse them. but, since A comes before B in the alphabet, it's unlikely that you won't have drawn the versions above.)
it's E.
you need to solve these problems efficiently. that doesn't mean you have to be super-fast or super-"smart"; it just means that you need to have a DEFINITE GOAL OR PURPOSE at each step of the way.
if you are just listing random possibilities, then there's a (somewhat slim) chance that you'll just accidentally walk into a valid solution -- but it's more likely that you'll just keep wandering around the problem.
- ghong14
- Course Students
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- Joined: Wed Dec 31, 1969 8:00 pm
Re: The points A, B, C, and D are on a number line
statement 1:
as you noticed, C is the midpoint between A and B, so AC and BC are both 9 units.
point D is only 8 units away from C (the middle point), so point D must be inside AB -- but we don't know on which side.
all you need is two cases:
A-D--------C-----------B
A-----------C---------D-B
you don't even have to figure out the actual distances in these cases, because they are clearly different (the distance DB is way, way smaller in the second picture than in the first one).
insufficient.
Why can't you have B....D............C.............................A
OR
B...............C..................D.....A
Ron, if I am reading this correctly, its because these are unnecessary considerations since the two examples mentioned will show insufficiency already?
- RonPurewal
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Re: The points A, B, C, and D are on a number line
ghong14 Wrote:Ron, if I am reading this correctly, its because these are unnecessary considerations since the two examples mentioned will show insufficiency already?
ya, that's the main point -- don't do unnecessary / pointless work.
lazy = efficient
--
(there's also the fact that those two cases aren't really different anyway, as far as statement 1 is concerned -- they are just mirror images of the existing cases.
if you had a relevant notion of left vs. right -- as you do in statement 2 -- then you might have to think about those cases, IF the first two cases didn't already the issue.)
- ColinF686
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Re: The points A, B, C, and D are on a number line
we can think of this an arrangement problem. how many ways can you arrange ABCD given the constraints. Does the arrangement give a unique value of BD in these constraints.
1. Only way this is possible is if C is midway between A & B giving ACBD, BCAD, DACB, DBCA- BD varies in these arrangement.
2. XXXD, XXD(BorC), ADXX- lots of arrangement possible with different BD values.
1&2 --> ACBD,BCAD - two different BDs
1. Only way this is possible is if C is midway between A & B giving ACBD, BCAD, DACB, DBCA- BD varies in these arrangement.
2. XXXD, XXD(BorC), ADXX- lots of arrangement possible with different BD values.
1&2 --> ACBD,BCAD - two different BDs
- tim
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Re: The points A, B, C, and D are on a number line
This approach does not take into account the numerical distances, so you cannot be sure it will yield a correct result.
Tim Sanders
Manhattan GMAT Instructor
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Follow this link for some important tips to get the most out of your forum experience:
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- RonPurewal
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Re: The points A, B, C, and D are on a number line
colin, do you have a question?
this discussion has been dormant for 3 years, so, i think it's safe to assume that you aren't just adding a random comment... but, i can't tell what you are trying to ask. what are you trying to ask?
this discussion has been dormant for 3 years, so, i think it's safe to assume that you aren't just adding a random comment... but, i can't tell what you are trying to ask. what are you trying to ask?
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