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705-805 Level|   Geometry|      
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In the given figure, ABC is a triangle and DEFG is a square. Find the 08 Dec 2018, 10:25
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GMATbuster's Weekly Quant Quiz#12 Ques #10


For Questions from earlier quizzes: Click Here


In the given figure, ABC is a triangle and DEFG is a square. Find the area of the square.


(1) ∠DAG = 60 deg

(2) Area of triangle CDE = 30√3 m2


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In the given figure, ABC is a triangle and DEFG is a square. Find the 10 Dec 2018, 07:51
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Official Solution



Steps 1 & 2: Understand Question and Draw Inferences

In the given figure, DEFG is a square.
Thus, ∠DGF = ∠GFE = ∠FED = ∠EDG = 90 deg
Since, we do not have any other information with us, let us analyse each statement.

Step 3: Analyze Statement 1 independently

∠DAG = 60 deg


From the above information, we can find all the angles in the triangle, as shown in the diagram, but as we do not have any information about the length of any side, therefore, we won’t be able to find the area of the square.

Step 4: Analyze Statement 2 independently

Area of the triangle CDE = 30√3 m2
This information does not tell us anything about the length or angles in triangle CDE.
Hence statement 2 is also not sufficient to answer the question.

Step 5: Combining both the statements:
After combining both the statements, we can write –
Area of the triangle CDE = 30√3 m2
And ∠CDE = 60 deg
But does that help us find the length of the sides of triangle CDE?
No it does not! Hence, even after combining both the statements, we cannot find the area of the square.
The correct answer is Option E.


Note: If we know the value of ∠CED that would have helped us in find the length of the sides of CDE and once we had the value of ED, which is the length of the square, we could have found the area of the square.

Show Spoiler
Attachment:
Sol...jpg
Sol...jpg [ 14.74 KiB | Viewed 11517 times ]
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In the given figure, ABC is a triangle and DEFG is a square. Find the 08 Dec 2018, 10:59
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To calculate the area of the square, we either know the side length or the both the area of the triangle and its sub triangles.
1) Only one angle given; nothing can be said about the properties of the triangle. None of the quantities stated above can be determined. Insufficient.
2) Only area of large triangle is given but no area of sub triangles. Insufficient.
Taken together, both (1) and (2) remain insufficient.
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In the given figure, ABC is a triangle and DEFG is a square. Find the 08 Dec 2018, 11:00
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In the given figure, ABC is a triangle and DEFG is a square. Find the area of the square.


(1) ∠DAG = 60 deg

(2) Area of triangle CDE = 30√3 m2


Stmnt 1 : is not sufficient

but since given that DEFG is a square so angle DGA is 90 and angle ADG is 30

stmt 2: area of triagnle CDE given but not sure what type of triangle it is so again in sufficient

From 1& 2

we can say that angle EDC & angle CED are both 60 degree , triangle CDE is equilaterial triangle
so side DE = 2swrt 30 , so area of square DEFG would be 120 m^2
IMO C
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In the given figure, ABC is a triangle and DEFG is a square. Find the 08 Dec 2018, 22:49
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Statement 1 : Only angle cannot help you find the area of square. Insufficient data
Statement 2 : We don't know anything about the triangle.

Using 1 & 2 together , we can find out it's an equilateral triangle and find the area of the square
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In the given figure, ABC is a triangle and DEFG is a square. Find the 10 Dec 2018, 09:47
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gmatbusters

Official Solution



Steps 1 & 2: Understand Question and Draw Inferences

In the given figure, DEFG is a square.
Thus, ∠DGF = ∠GFE = ∠FED = ∠EDG = 90 deg
Since, we do not have any other information with us, let us analyse each statement.

Step 3: Analyze Statement 1 independently

∠DAG = 60 deg


From the above information, we can find all the angles in the triangle, as shown in the diagram, but as we do not have any information about the length of any side, therefore, we won’t be able to find the area of the square.

Step 4: Analyze Statement 2 independently

Area of the triangle CDE = 30√3 m2
This information does not tell us anything about the length or angles in triangle CDE.
Hence statement 2 is also not sufficient to answer the question.

Step 5: Combining both the statements:
After combining both the statements, we can write –
Area of the triangle CDE = 30√3 m2
And ∠CDE = 60 deg
But does that help us find the length of the sides of triangle CDE?
No it does not! Hence, even after combining both the statements, we cannot find the area of the square.
The correct answer is Option E.


Note: If we know the value of ∠CED that would have helped us in find the length of the sides of CDE and once we had the value of ED, which is the length of the square, we could have found the area of the square.

Show Spoiler
Attachment:
Sol...jpg
Show more

gmatbusters

while you have combined the 2 statements you clearly deduced that angle CDE is 60* , similarly wont angle CED be 60* and triangle CDE equilateral.. hence it would sufficient to answer...

DEGF is a rectangle so finding other sides like you have done earlier wont be difficult to derive and corresponding sides can determined accordingly..
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In the given figure, ABC is a triangle and DEFG is a square. Find the 10 Dec 2018, 10:09
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Archit3110
similarly wont angle CED be 60*
Show more


Angle CDE is not necessarily be 60deg.
See the sketch



Archit3110
gmatbusters

Official Solution



Steps 1 & 2: Understand Question and Draw Inferences

In the given figure, DEFG is a square.
Thus, ∠DGF = ∠GFE = ∠FED = ∠EDG = 90 deg
Since, we do not have any other information with us, let us analyse each statement.

Step 3: Analyze Statement 1 independently

∠DAG = 60 deg


From the above information, we can find all the angles in the triangle, as shown in the diagram, but as we do not have any information about the length of any side, therefore, we won’t be able to find the area of the square.

Step 4: Analyze Statement 2 independently

Area of the triangle CDE = 30√3 m2
This information does not tell us anything about the length or angles in triangle CDE.
Hence statement 2 is also not sufficient to answer the question.

Step 5: Combining both the statements:
After combining both the statements, we can write –
Area of the triangle CDE = 30√3 m2
And ∠CDE = 60 deg
But does that help us find the length of the sides of triangle CDE?
No it does not! Hence, even after combining both the statements, we cannot find the area of the square.
The correct answer is Option E.


Note: If we know the value of ∠CED that would have helped us in find the length of the sides of CDE and once we had the value of ED, which is the length of the square, we could have found the area of the square.

Show Spoiler
Attachment:
The attachment Sol...jpg is no longer available

gmatbusters

while you have combined the 2 statements you clearly deduced that angle CDE is 60* , similarly wont angle CED be 60* and triangle CDE equilateral.. hence it would sufficient to answer...

DEGF is a rectangle so finding other sides like you have done earlier wont be difficult to derive and corresponding sides can determined accordingly..
Show more
Show Spoiler
Attachment:
WhatsApp Image 2018-12-10 at 22.34.46.jpeg
WhatsApp Image 2018-12-10 at 22.34.46.jpeg [ 82.62 KiB | Viewed 10512 times ]
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In the given figure, ABC is a triangle and DEFG is a square. Find the 10 Dec 2018, 21:51
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gmatbusters
Archit3110
similarly wont angle CED be 60*


Angle CDE is not necessarily be 60deg.
See the sketch



Archit3110
gmatbusters

Official Solution



Steps 1 & 2: Understand Question and Draw Inferences

In the given figure, DEFG is a square.
Thus, ∠DGF = ∠GFE = ∠FED = ∠EDG = 90 deg
Since, we do not have any other information with us, let us analyse each statement.

Step 3: Analyze Statement 1 independently

∠DAG = 60 deg


From the above information, we can find all the angles in the triangle, as shown in the diagram, but as we do not have any information about the length of any side, therefore, we won’t be able to find the area of the square.

Step 4: Analyze Statement 2 independently

Area of the triangle CDE = 30√3 m2
This information does not tell us anything about the length or angles in triangle CDE.
Hence statement 2 is also not sufficient to answer the question.

Step 5: Combining both the statements:
After combining both the statements, we can write –
Area of the triangle CDE = 30√3 m2
And ∠CDE = 60 deg
But does that help us find the length of the sides of triangle CDE?
No it does not! Hence, even after combining both the statements, we cannot find the area of the square.
The correct answer is Option E.


Note: If we know the value of ∠CED that would have helped us in find the length of the sides of CDE and once we had the value of ED, which is the length of the square, we could have found the area of the square.

Show Spoiler
Attachment:
Sol...jpg

gmatbusters

while you have combined the 2 statements you clearly deduced that angle CDE is 60* , similarly wont angle CED be 60* and triangle CDE equilateral.. hence it would sufficient to answer...

DEGF is a rectangle so finding other sides like you have done earlier wont be difficult to derive and corresponding sides can determined accordingly..
Show Spoiler
Attachment:
WhatsApp Image 2018-12-10 at 22.34.46.jpeg
Show more
thanks


Sent from my iPhone using GMAT Club Forum mobile app
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In the given figure, ABC is a triangle and DEFG is a square. Find the 11 Dec 2018, 01:18
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gmatbusters
Archit3110
similarly wont angle CED be 60*


Angle CDE is not necessarily be 60deg.
See the sketch



Archit3110
gmatbusters

Official Solution



Steps 1 & 2: Understand Question and Draw Inferences

In the given figure, DEFG is a square.
Thus, ∠DGF = ∠GFE = ∠FED = ∠EDG = 90 deg
Since, we do not have any other information with us, let us analyse each statement.

Step 3: Analyze Statement 1 independently

∠DAG = 60 deg


From the above information, we can find all the angles in the triangle, as shown in the diagram, but as we do not have any information about the length of any side, therefore, we won’t be able to find the area of the square.

Step 4: Analyze Statement 2 independently

Area of the triangle CDE = 30√3 m2
This information does not tell us anything about the length or angles in triangle CDE.
Hence statement 2 is also not sufficient to answer the question.

Step 5: Combining both the statements:
After combining both the statements, we can write –
Area of the triangle CDE = 30√3 m2
And ∠CDE = 60 deg
But does that help us find the length of the sides of triangle CDE?
No it does not! Hence, even after combining both the statements, we cannot find the area of the square.
The correct answer is Option E.


Note: If we know the value of ∠CED that would have helped us in find the length of the sides of CDE and once we had the value of ED, which is the length of the square, we could have found the area of the square.

Show Spoiler
Attachment:
Sol...jpg

gmatbusters

while you have combined the 2 statements you clearly deduced that angle CDE is 60* , similarly wont angle CED be 60* and triangle CDE equilateral.. hence it would sufficient to answer...

DEGF is a rectangle so finding other sides like you have done earlier wont be difficult to derive and corresponding sides can determined accordingly..
Show Spoiler
Attachment:
WhatsApp Image 2018-12-10 at 22.34.46.jpeg
Show more


gmatbusters : thanks for the detailed explanation..

although no offence to anybody or source of question , but I honestly feel that such questions are not close enough to official or GMAT kind .. in questions where in figures are given its usually given as not drawn to scale or some relation and info is given which was not at all clearly given in this case ..
for instances you have also quoted "Angle CDE is not necessarily be 60deg. " , saying not necessarily does not prove that CDE cannot be equilateral triangle..

anyways like most of the people I am also in the phase of learning so i guess on the route to gmat study one surely comes across such bumpers...
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In the given figure, ABC is a triangle and DEFG is a square. Find the 11 Dec 2018, 01:27
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Hi
Please note the following:

1) unless explicitly mentioned, figures are never assumed to be drawn to scale.

2) yes triangle CDE can be equilateral but it can be scalene also. So it is not sufficient to answer.

Thanks

Archit3110
gmatbusters


Angle CDE is not necessarily be 60deg.
See the sketch



Archit3110"[quote="gmatbusters

Official Solution



Steps 1 & 2: Understand Question and Draw Inferences

In the given figure, DEFG is a square.
Thus, ∠DGF = ∠GFE = ∠FED = ∠EDG = 90 deg
Since, we do not have any other information with us, let us analyse each statement.

Step 3: Analyze Statement 1 independently

∠DAG = 60 deg


From the above information, we can find all the angles in the triangle, as shown in the diagram, but as we do not have any information about the length of any side, therefore, we won’t be able to find the area of the square.

Step 4: Analyze Statement 2 independently

Area of the triangle CDE = 30√3 m2
This information does not tell us anything about the length or angles in triangle CDE.
Hence statement 2 is also not sufficient to answer the question.

Step 5: Combining both the statements:
After combining both the statements, we can write –
Area of the triangle CDE = 30√3 m2
And ∠CDE = 60 deg
But does that help us find the length of the sides of triangle CDE?
No it does not! Hence, even after combining both the statements, we cannot find the area of the square.
The correct answer is Option E.


Note: If we know the value of ∠CED that would have helped us in find the length of the sides of CDE and once we had the value of ED, which is the length of the square, we could have found the area of the square.

Show Spoiler
Attachment:
Sol...jpg

gmatbusters

while you have combined the 2 statements you clearly deduced that angle CDE is 60* , similarly wont angle CED be 60* and triangle CDE equilateral.. hence it would sufficient to answer...

DEGF is a rectangle so finding other sides like you have done earlier wont be difficult to derive and corresponding sides can determined accordingly..
Show Spoiler
Attachment:
WhatsApp Image 2018-12-10 at 22.34.46.jpeg
Show more


gmatbusters : thanks for the detailed explanation..

although no offence to anybody or source of question , but I honestly feel that such questions are not close enough to official or GMAT kind .. in questions where in figures are given its usually given as not drawn to scale or some relation and info is given which was not at all clearly given in this case ..
for instances you have also quoted "Angle CDE is not necessarily be 60deg. " , saying not necessarily does not prove that CDE cannot be equilateral triangle..

anyways like most of the people I am also in the phase of learning so i guess on the route to gmat study one surely comes across such bumpers...[/quote]

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