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The figure above shows the dimensions of a square picture frame that

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Bunuel
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The figure above shows the dimensions of a square picture frame that [#permalink] New post  15 Dec 2014, 08:00
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The figure above shows the dimensions of a square picture frame that was constructed using four identical pieces of frame as shown. If w is the width of each piece of the frame, what is the area of the front surface of each piece? (1 ft = 12 inches)

(1) w = 3 inches
(2) PQ = \(\sqrt{18}\) inches


DS87602.01

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skrmsiva
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Re: The figure above shows the dimensions of a square picture frame that [#permalink] New post  16 Dec 2014, 01:20
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Statement A: Sufficient: By knowing the value of w, we can know the area of the inner square (3ft-2w is the length of inner square). and by subtracting the inner square area from the outer square area, we can know the area of the frame.

Statement B: Sufficient: we can find out the diagonal value out the square, and using the value of this statement, we can get the diagonal value of inner square and its area. subtract the inner square area from the outer square area.

Need not get the exact value of the area of the frame.

Answer:D
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vietnammba
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Re: The figure above shows the dimensions of a square picture frame that [#permalink] New post  16 Dec 2014, 00:23
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I think the answer is D.

Area of each piece S= (3ft*3ft-(3f-w)*(3ft-w))/4
Statement 1: w=3inch => we can calculate S. Suff
Statement 2: We know PQ and PQ is hypotenuse of a right isolece triangle w, we can calculate w => we can calculate S. Suff
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DangerPenguin
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Re: The figure above shows the dimensions of a square picture frame that [#permalink] New post  15 Dec 2014, 09:52
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statement 1: insufficient
we need the length of the square

statement 2: insufficient
we do not know the height of the trapezoid (w) and therefore cannot figure out the are of it and we also don't know the length of the square

statement 1+2: insufficient
the only part missing for us to find the area of each piece is the length of the square and we do not have that

Answer E!
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Re: The figure above shows the dimensions of a square picture frame that [#permalink] New post  19 Dec 2014, 22:40
Solution: 3ft=36in
Area= Length * Width - 2*Area of triangle having base and height as w = 36*w - 2*w*(w/2) ---- eq 1
To determine the area of each piece, we need to know the value of w:

Statement 1: w = 3 inches
Plugging the value of w in eq 1 we can get the area - Sufficient

Statement 2: PQ = \sqrt{18} inches
PQ is hypotenuse of Isosceles triangle with other sides as w.
w^2 + w^2 = PQ --> w=3
Plugging the value of w in eq 1 we can get the area - Sufficient

Each statement alone is sufficient, Answer D
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GMATGuruNY
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The figure above shows the dimensions of a square picture frame that [#permalink] New post  Updated on: 09 Aug 2020, 16:22
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Bunuel wrote:

Tough and Tricky questions: Geometry.




The figure above shows the dimensions of a square picture frame that was constructed using four pieces of frame as shown. If w is the width of each piece of the frame, what is the area of each piece?

(1) w = 3 inches
(2) PQ = \(\sqrt{18}\) inches


Statement 1:
The following figure is yielded:


Since the frame is divided into 4 equal pieces, we get:
Each piece = \(\frac{(4-red-rectangles) + (4-blue-squares)}{4}\).
Thus, the area of each piece can be determined.
SUFFICIENT.

Statement 2:
In the figure for Statement 1, PQ = \(\frac{(diagonal-of-the-frame) - (diagonal-of-the-picture)}{2}\) = \(\frac{36√2 - 30√2}{2}\) = \(\frac{6√2}{2}\) = 3√2 = √18 inches.
Thus, Statement 2 implies the same figure as Statement 1.
Since Statement 1 is sufficient, so is Statement 2.
SUFFICIENT.

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D

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Originally posted by GMATGuruNY on 14 Jun 2018, 15:42.
Last edited by GMATGuruNY on 09 Aug 2020, 16:22, edited 1 time in total.
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coreyander
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Re: The figure above shows the dimensions of a square picture frame that [#permalink] New post  11 Jun 2020, 10:13
vietnammba wrote:
I think the answer is D.

Area of each piece S= (3ft*3ft-(3f-w)*(3ft-w))/4
Statement 1: w=3inch => we can calculate S. Suff
Statement 2: We know PQ and PQ is hypotenuse of a right isolece triangle w, we can calculate w => we can calculate S. Suff


The highlighted should be (3f-2w)
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coreyander
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Re: The figure above shows the dimensions of a square picture frame that [#permalink] New post  11 Jun 2020, 10:20
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Bunuel wrote:

The figure above shows the dimensions of a square picture frame that was constructed using four pieces of frame as shown. If w is the width of each piece of the frame, what is the area of each piece?

(1) w = 3 inches
(2) PQ = \(\sqrt{18}\) inches


DS87602.01

Show Spoiler
Attachment:
2007-01-02_114321_z.jpg


Bunuel The below highlighted part in the question is left out. Requesting you to add the same.
The figure above shows the dimensions of a square picture frame that was constructed using four identical pieces of frame as shown. If w is the width of each piece of the frame, what is the area of the front surface of each piece? (1 ft = 12 inches)
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Bunuel
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Re: The figure above shows the dimensions of a square picture frame that [#permalink] New post  11 Jun 2020, 10:35
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coreyander wrote:
Bunuel wrote:

The figure above shows the dimensions of a square picture frame that was constructed using four pieces of frame as shown. If w is the width of each piece of the frame, what is the area of each piece?

(1) w = 3 inches
(2) PQ = \(\sqrt{18}\) inches


DS87602.01

Show Spoiler
Attachment:
2007-01-02_114321_z.jpg


Bunuel The below highlighted part in the question is left out. Requesting you to add the same.
The figure above shows the dimensions of a square picture frame that was constructed using four identical pieces of frame as shown. If w is the width of each piece of the frame, what is the area of the front surface of each piece? (1 ft = 12 inches)


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Fixed. Thank you.
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The figure above shows the dimensions of a square picture frame that [#permalink] New post  11 Jun 2020, 11:56
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IMO :- D

Area of Frame is Trapezium

Area is Only dependent on "w"

1) W is given - Sufficient

2) PQ is given, PQ= Sqrt(2) * w - Sufficient
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The figure above shows the dimensions of a square picture frame that [#permalink] New post  11 Jun 2020, 22:21
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yashikaaggarwal wrote:
Bunuel Sir, can you also post the official explanation? I still didn't get what the question is asking for total surface area or area of frame. Please.

Posted from my mobile device


PFA the OFFICIAL EXPLANATION

IMO, TSA and area are the same for a 2D object.
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Re: The figure above shows the dimensions of a square picture frame that [#permalink] New post  07 Aug 2020, 10:02
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Bunuel wrote:

The figure above shows the dimensions of a square picture frame that was constructed using four identical pieces of frame as shown. If w is the width of each piece of the frame, what is the area of the front surface of each piece? (1 ft = 12 inches)

(1) w = 3 inches
(2) PQ = \(\sqrt{18}\) inches


DS87602.01

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The attachment 2007-01-02_114321_z.jpg is no longer available



Superb question. Please find attached the explanation for the question.

Answer D
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mcolbert
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The figure above shows the dimensions of a square picture frame that [#permalink] New post  Updated on: 09 Aug 2020, 12:38
Why is everyone assuming that sides of the inner square are parallel to the sides of the outer square? Could not the inner square be rotated within the outer square in different ways such that the four pieces of frame are still identical but the sides of the inner square are not parallel with those of the outer square? The problem does not state that they are parallel so we cannot assume it. It does not state that PQ bisects the right angle. I believe the answer should be E.

Example shown below:
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Originally posted by mcolbert on 09 Aug 2020, 12:32.
Last edited by mcolbert on 09 Aug 2020, 12:38, edited 1 time in total.
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sk7075
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Re: The figure above shows the dimensions of a square picture frame that [#permalink] New post  11 Aug 2020, 06:53
mcolbert wrote:
Why is everyone assuming that sides of the inner square are parallel to the sides of the outer square? Could not the inner square be rotated within the outer square in different ways such that the four pieces of frame are still identical but the sides of the inner square are not parallel with those of the outer square? The problem does not state that they are parallel so we cannot assume it. It does not state that PQ bisects the right angle. I believe the answer should be E.

Example shown below:



In this case, how can you consider the width of each frame w?
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Re: The figure above shows the dimensions of a square picture frame that [#permalink] New post  07 Aug 2023, 22:17
Bunuel wrote:

The figure above shows the dimensions of a square picture frame that was constructed using four identical pieces of frame as shown. If w is the width of each piece of the frame, what is the area of the front surface of each piece? (1 ft = 12 inches)

(1) w = 3 inches
(2) PQ = \(\sqrt{18}\) inches


DS87602.01

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Attachment:
2007-01-02_114321_z.jpg


Bunuel I didn't understand why each angle will be 45 degrees for the trapezium. Can you please help me understand?
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Re: The figure above shows the dimensions of a square picture frame that [#permalink]
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