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What is the area of triangle ABC? (1) AB = 5, AC = 12 (2) ABC is a ri

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Hoozan
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What is the area of triangle ABC? (1) AB = 5, AC = 12 (2) ABC is a ri [#permalink] New post   21 Feb 2021, 08:26
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What is the area of triangle ABC?

(1) AB = 5, AC = 12
(2) ABC is a right triangle
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E
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GMATinsight
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Re: What is the area of triangle ABC? (1) AB = 5, AC = 12 (2) ABC is a ri [#permalink] New post   22 Feb 2021, 01:12
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Hoozan wrote:
What is the area of triangle ABC?

(1) AB = 5, AC = 12
(2) ABC is a right triangle


It's a common trap for takers to answer this question as Option C. The reason for this trap is that we don't probe enough. We always need to test if there is unique triangle that we are getting with given input or there are more than one possible triangles.

IMPORTANT QUESTION TO PROBE:


- WHere is the right angle being formed??? Is it between sides of length 5 and 12 or 12 may be Hypotenuse as well because the question doesn't specify that the length of all sides are integers


Combining the statements

Case 1: AB = 5, AC = 12 and BC \(= √(12^2+5^2) = 13\) (Assuming that 13 is hypotenuse)
Case 2: AB = 5, AC = 12 and BC \(= √(12^2-5^2) = √119\) (Assuming that 12 is hypotenuse)

Two possible triangles and two possible areas hence

NOT SUFFICIENT

Answer: Option E
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Re: What is the area of triangle ABC? (1) AB = 5, AC = 12 (2) ABC is a ri [#permalink] New post   21 Feb 2021, 09:58
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St 1 & St2 are clearly NOT sufficient individually.

Combining ST 1 & 2, We dont know which angle is 90 deg.

There is NO need to find the area in different cases, since we don't know which angle is 90, different triangles (different areas) can be drawn. it is NOT Sufficient.
Answer E.

(PS: If Angle A is 90, Area = AB*AC/2 = 5*12/2 = 30
If Angle B is 90, AC would be the hypotenuse. So BC = \(\sqrt{(12^2 -5^2)}\). hence the area AB*BC/2 would be different.)

Hoozan wrote:
What is the area of triangle ABC?

(1) AB = 5, AC = 12
(2) ABC is a right triangle
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Re: What is the area of triangle ABC? (1) AB = 5, AC = 12 (2) ABC is a ri [#permalink] New post   22 Feb 2021, 21:09
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jrk23 wrote:
Can't we say if "ABC is a right angle triangle" than angle B is right angle?


jrk23

No, we can't.

The assumptions in GMAT exam could very dangerous so avoid assuming anything unless it's clearly stated or depicted in question's input.
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Re: What is the area of triangle ABC? (1) AB = 5, AC = 12 (2) ABC is a ri [#permalink] New post   22 Feb 2021, 21:23
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"ABC is a right angle triangle" translates to " one of the three angles in the triangle is 90 deg. The 90 deg angle can be between any 2 sides.


jrk23 wrote:
GMATBusters wrote:
St 1 & St2 are clearly NOT sufficient individually.

Combining ST 1 & 2, We dont know which angle is 90 deg.

There is NO need to find the area in different cases, since we don't know which angle is 90, different triangles (different areas) can be drawn. it is NOT Sufficient.
Answer E.

(PS: If Angle A is 90, Area = AB*AC/2 = 5*12/2 = 30
If Angle B is 90, AC would be the hypotenuse. So BC = \(\sqrt{(12^2 -5^2)}\). hence the area AB*BC/2 would be different.)

Hoozan wrote:
What is the area of triangle ABC?

(1) AB = 5, AC = 12
(2) ABC is a right triangle


Can't we say if "ABC is a right angle triangle" than angle B is right angle?
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Re: What is the area of triangle ABC? (1) AB = 5, AC = 12 (2) ABC is a ri [#permalink] New post   22 Feb 2021, 22:02
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jrk23 wrote:
GMATBusters wrote:
St 1 & St2 are clearly NOT sufficient individually.

Combining ST 1 & 2, We dont know which angle is 90 deg.

There is NO need to find the area in different cases, since we don't know which angle is 90, different triangles (different areas) can be drawn. it is NOT Sufficient.
Answer E.

(PS: If Angle A is 90, Area = AB*AC/2 = 5*12/2 = 30
If Angle B is 90, AC would be the hypotenuse. So BC = \(\sqrt{(12^2 -5^2)}\). hence the area AB*BC/2 would be different.)

Hoozan wrote:
What is the area of triangle ABC?

(1) AB = 5, AC = 12
(2) ABC is a right triangle


Can't we say if "ABC is a right angle triangle" than angle B is right angle?


Hi,

The right angle can be between two sides one of which will be the smaller of the given two, so between 12 and 5, or between 5 and the other unknown.

The moment the right angle is taken as the angle between 12 and the other unknown, the side 5 becomes hypotenuse, and 5<12.
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Re: What is the area of triangle ABC? (1) AB = 5, AC = 12 (2) ABC is a ri [#permalink] New post   21 Feb 2021, 08:48
GMATBusters is this similar to what we were discussing? Could you probably attach a few links that test this concept
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Re: What is the area of triangle ABC? (1) AB = 5, AC = 12 (2) ABC is a ri [#permalink] New post   22 Feb 2021, 02:36
Got caught up in the same trap of choosing C over E... Thanks GMATinsight

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Re: What is the area of triangle ABC? (1) AB = 5, AC = 12 (2) ABC is a ri [#permalink] New post   22 Feb 2021, 14:53
GMATBusters wrote:
St 1 & St2 are clearly NOT sufficient individually.

Combining ST 1 & 2, We dont know which angle is 90 deg.

There is NO need to find the area in different cases, since we don't know which angle is 90, different triangles (different areas) can be drawn. it is NOT Sufficient.
Answer E.

(PS: If Angle A is 90, Area = AB*AC/2 = 5*12/2 = 30
If Angle B is 90, AC would be the hypotenuse. So BC = \(\sqrt{(12^2 -5^2)}\). hence the area AB*BC/2 would be different.)

Hoozan wrote:
What is the area of triangle ABC?

(1) AB = 5, AC = 12
(2) ABC is a right triangle


Can't we say if "ABC is a right angle triangle" than angle B is right angle?
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Hoozan
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Re: What is the area of triangle ABC? (1) AB = 5, AC = 12 (2) ABC is a ri [#permalink] New post   23 Feb 2021, 01:03
GMATinsight wrote:
Hoozan wrote:
What is the area of triangle ABC?

(1) AB = 5, AC = 12
(2) ABC is a right triangle


It's a common trap for takers to answer this question as Option C. The reason for this trap is that we don't probe enough. We always need to test if there is unique triangle that we are getting with given input or there are more than one possible triangles.

IMPORTANT QUESTION TO PROBE:


- WHere is the right angle being formed??? Is it between sides of length 5 and 12 or 12 may be Hypotenuse as well because the question doesn't specify that the length of all sides are integers


Combining the statements

Case 1: AB = 5, AC = 12 and BC \(= √(12^2+5^2) = 13\) (Assuming that 13 is hypotenuse)
Case 2: AB = 5, AC = 12 and BC \(= √(12^2-5^2) = √119\) (Assuming that 12 is hypotenuse)

Two possible triangles and two possible areas hence

NOT SUFFICIENT

Answer: Option E
Hoozan


Thanks GMATinsight

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Re: What is the area of triangle ABC? (1) AB = 5, AC = 12 (2) ABC is a ri [#permalink] New post   18 Apr 2023, 11:49
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Re: What is the area of triangle ABC? (1) AB = 5, AC = 12 (2) ABC is a ri [#permalink]
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