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m9 q34

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Re: m9 q34 [#permalink] New post 17 Sep 2011, 19:15
I got B as answer...
My logic was

AB + AC> 10
hence AB > (10- AC)

Since A, B and C are three different point, AB, BC,and AC are all positive values.
so AC will have a value defines as 0 < AC < 10.
because if AC> 10, AB becomes negative.
SO this inturn gives the value of AB as : 10 > AB > 0.
So AB is less than 10.

Pls tell me where I went wrong!!
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Re: m9 q34 [#permalink] New post 11 Sep 2012, 04:10
Expert's post
sset009 wrote:
A , B , and C are points on the plane. Is AB \lt 10 ?

1. AC + BC = 10
2. AB + AC \gt 10

[Reveal] Spoiler: OA
E

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Couldnt understand the official explanation


New edition of this question reads:

If A, B, and C are distinct points on the number line. Is the length of the line segment AB less than 10?

(1) The sum of the lengths of line segments AC and BC is 10
(2) The sum of the lengths of line segments AB and AC is more than 10

Even when we consider both statements together we can not have a definite answer. Consider two examples below:
Attachment:
Number line.png
Number line.png [ 8.54 KiB | Viewed 1017 times ]
Answer: E.
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Re: m9 q34 [#permalink] New post 11 Sep 2012, 04:37
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Re: m9 q34 [#permalink] New post 11 Sep 2012, 04:39
Could not understand the question

None of he options seem interesting

Choose E! - strategic guess
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Re: m9 q34 [#permalink] New post 11 Sep 2012, 04:55
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A , B , and C are points on the plane. Is AB < 10 ?

1. AC + BC = 10
2. AB + AC > 10

Since we already know that individual statements are insufficient, let's combine:

From 1, we know that AC= 10 - BC. Let's substitute this into 2.
AB + 10 - BC > 10 =====> AB > BC

From 1, we know that BC < 10, since AC must be some value greater than zero.
Combining AB > BC with BC < 10, we have AB > 0, and this is not enough to tell us whether AB < 10.

Therefore, E.

Cheers,
Der alte Fritz.
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Re: m9 q34 [#permalink] New post 11 Sep 2012, 04:59
It's a tough question because I got to the point where it was between C and E. I didn't know what cases to choose to rule out C convincingly.

This is my attempt at a methodical approach or ruling out answers.

Lets take two cases:
1) Where C is in between A and B

--A-----------------C-------------------B-----
----------4-----------------6------------------

AC+BC = 10 YES
AB+AC>10 YES
AB<10?? NO

2) Where C is outside of A and B

--A-----------------B-------------------C-----
----------2-----------------4------------------

AC+BC = 10 YES
AB+AC>10 NO
AB<10?? YES

But this case is invalid because in this case :AB+AC>10 NO

2) Where C is outside of A and B

--A-----------------B-------------------C-----
----------2-----------------8------------------

AC+BC = 10 YES
AB+AC>10 YES
AB<10?? YES


Choose E and move on.
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Re: m9 q34 [#permalink] New post 11 Sep 2012, 05:23
E is the answer.

(1) does not give any relation about AB at all
(2) gives vague information about AB as we donot know about AC

so AD and B are not the answers
C .. when combined also we cannot land on a perfect solution, so C is also not the choice.

Hence E.
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Re: m9 q34 [#permalink] New post 11 Sep 2012, 08:57
Answer:E

Because the points are on plane so they can be anywhere .
Look at the scenario when the points are in line A____C____B
in that case

If AC + BC =10 then AB =10 which is not less than 10
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Re: m9 q34 [#permalink] New post 11 Sep 2012, 09:03
the answer is E, and a quick dirty way to do it is by plugging in numbers. First thing to note is that it the original question does not say A B or C are distinct, implying that A could equal B and so on. Also, the way the equations are set up it is just easier to think about the points as numbers.

so is stmt 1 enough?
AC + BC = 10. plug in A=2, B=0, C=5
in this case AB<10
now plug in A = 5, B =5, C=1
in this case AB>10.
Therefore stmnt 1 is not enough.

is stmt 2 enough?
AB +AC >10
A = 11, B = 1, C = 1 and AB >10
A = 1, B = 1, C =10 and AB<10
therefore stmnt 2 is not enough

Together?
AC + BC = 10 and AB+AC>10
A=3, B = 2, C =2 and AB<10
A=18, B = 2, C =.5 and AB>10

therefore together not enough
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Re: M09 #34 [#permalink] New post 11 Sep 2012, 09:22
matt3030 wrote:
Interesting. I assume that if the question prompt was something like "A, B and C are distinct points on a plane" that the answer would be (a)?


I assume, irrespective of points are distinct or not, the ans is E

The ans is A only if it is given that the 3 points don't lie on the same line.
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Re: M09 #34 [#permalink] New post 11 Sep 2012, 09:31
giridharkumar wrote:
matt3030 wrote:
Interesting. I assume that if the question prompt was something like "A, B and C are distinct points on a plane" that the answer would be (a)?


I assume, irrespective of points are distinct or not, the ans is E

The ans is A only if it is given that the 3 points don't lie on the same line.


yes, even if they were distinct A is not enough:

AC + BC = 10.
plug in A=2, B=0, C=5
in this case AB<10
now plug in A = 14, B =6, C=.5
in this case AB>10.
Therefore stmnt 1 is not enough.
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Re: m9 q34 [#permalink] New post 11 Sep 2012, 09:53
Expert's post
OldFritz wrote:
A , B , and C are points on the plane. Is AB < 10 ?

1. AC + BC = 10
2. AB + AC > 10

Since we already know that individual statements are insufficient, let's combine:

From 1, we know that AC= 10 - BC. Let's substitute this into 2.
AB + 10 - BC > 10 =====> AB > BC

From 1, we know that BC < 10, since AC must be some value greater than zero.
Combining AB > BC with BC < 10, we have AB > 0, and this is not enough to tell us whether AB < 10.

Therefore, E.

Cheers,
Der alte Fritz.



the Bunuel approach of course is the faster........but yours is pretty good :)
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Re: m9 q34 [#permalink] New post 11 Sep 2012, 23:48
My pick is also E.
If we have been provided with some additional information on the location of the points, for example whether it is a triangle, a straight line or something then provided statements could have been sufficient.
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Re: m9 q34 [#permalink] New post 12 Sep 2012, 23:50
But if we solve for the inequality in equation 2, we get AB>10-AC. Since AC cannot be negative or zero, AB will be < 10 no matter if the points are in a triangle or collinear. Isn't the second statement enough and answer B?
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Re: m9 q34 [#permalink] New post 10 Sep 2013, 09:44
Hi! I've got E too since we do not know in what order the points are in the plan (whether a triangle or another shape)!

==> Do someone know the difficulty of this question plz?

Thank you very much!
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Re: m9 q34 [#permalink] New post 11 Sep 2013, 01:56
Expert's post
Paris75 wrote:
Hi! I've got E too since we do not know in what order the points are in the plan (whether a triangle or another shape)!

==> Do someone know the difficulty of this question plz?

Thank you very much!


The difficulty level is ~650.

Revised version (m9-q34-70894-20.html#p1120622) is a bit easier.
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Re: m9 q34 [#permalink] New post 27 Jun 2014, 12:50
Bunuel wrote:
sset009 wrote:
A , B , and C are points on the plane. Is AB \lt 10 ?

1. AC + BC = 10
2. AB + AC \gt 10

[Reveal] Spoiler: OA
E

Source: GMAT Club Tests - hardest GMAT questions

Couldnt understand the official explanation


New edition of this question reads:

If A, B, and C are distinct points on the number line. Is the length of the line segment AB less than 10?

(1) The sum of the lengths of line segments AC and BC is 10
(2) The sum of the lengths of line segments AB and AC is more than 10

Even when we consider both statements together we can not have a definite answer. Consider two examples below:
Attachment:
Number line.png
Answer: E.


This was a tough question for me. Since there are three distinct points, there are 6 ways to arrange those three points. What is an efficient approach to this problem?
Re: m9 q34   [#permalink] 27 Jun 2014, 12:50
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