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# m09 #34

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VP
Joined: 18 May 2008
Posts: 1261

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10 Nov 2008, 04:10
A, B, and C are points on the plane. Is AB<10 ?
(1) AC+BC=10
(2) AB+BC>10

OA is E. But cant we consider these points as a triangle then the third side is smaller than the sum of other tow sides. This way, (1) is sufficient.
What is wrong in this reasoning?
SVP
Joined: 17 Jun 2008
Posts: 1548

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10 Nov 2008, 06:42
Since the question is not explicitly saying that these three points are not on the same line, from stmt1 you get AB <= 10 and that is the reason stmt1 is not sufficient.
SVP
Joined: 29 Aug 2007
Posts: 2473

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10 Nov 2008, 21:04
ritula wrote:
A, B, and C are points on the plane. Is AB<10 ?
(1) AC+BC=10
(2) AB+BC>10

OA is E. But cant we consider these points as a triangle then the third side is smaller than the sum of other tow sides. This way, (1) is sufficient.
What is wrong in this reasoning?

1. You assumed that a, b and c makes a triangle but how do we know that a, b and c are on on the same plane. If so, then ab = ac + bc = 10.

2. ab > 0.

So E.
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VP
Joined: 18 May 2008
Posts: 1261

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10 Nov 2008, 23:26
In that case also AB cant be 10. It has to be less than 10 (the third side is smaller than the sum of other two sides)
GMAT TIGER wrote:
ritula wrote:
A, B, and C are points on the plane. Is AB<10 ?
(1) AC+BC=10
(2) AB+BC>10

OA is E. But cant we consider these points as a triangle then the third side is smaller than the sum of other tow sides. This way, (1) is sufficient.
What is wrong in this reasoning?

1. You assumed that a, b and c makes a triangle but how do we know that a, b and c are on on the same plane. If so, then ab = ac + bc = 10.

2. ab > 0.

So E.
SVP
Joined: 29 Aug 2007
Posts: 2473

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10 Nov 2008, 23:39
ritula wrote:
In that case also AB cant be 10. It has to be less than 10 (the third side is smaller than the sum of other two sides)
GMAT TIGER wrote:
ritula wrote:
A, B, and C are points on the plane. Is AB<10 ?
(1) AC+BC=10
(2) AB+BC>10

OA is E. But cant we consider these points as a triangle then the third side is smaller than the sum of other tow sides. This way, (1) is sufficient.
What is wrong in this reasoning?

1. You assumed that a, b and c makes a triangle but how do we know that a, b and c are on on the same plane. If so, then ab = ac + bc = 10.

2. ab > 0.

So E.

Thats the point here. We do not know whether a, b and c make a triangle or a line.

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Manager
Status: Prospective Applicant
Joined: 06 Mar 2011
Posts: 80
Concentration: General Management, Marketing

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10 Jun 2011, 13:28
Can anyone explain how statement 1 tells us that AB <= 10?

If AC + BC = 10, and I assume C=1 then AB can be between 0 and 25 (if A & B are 5)?

Thanks!
Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2010

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10 Jun 2011, 14:28
ritula wrote:
A, B, and C are points on the plane. Is AB<10 ?
(1) AC+BC=10
(2) AB+BC>10

OA is E. But cant we consider these points as a triangle then the third side is smaller than the sum of other tow sides. This way, (1) is sufficient.
What is wrong in this reasoning?

Just try these two sets:
************************
Case I:
A(0,0), B(6,0), C(3,4)
AC=BC=5
AB+BC=6+5=11>10
AB=6<10
************************
A(0,0), B(10,0), C(5,0)
AC=BC=5
AB+BC=10+5=15>10
AB=10=10
************************
Thus, AB can be equal to 10 OR less than 10.

Ans: "E"
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Re: m09 #34   [#permalink] 10 Jun 2011, 14:28
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# m09 #34

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