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

Question

https://gmatclub.com/forum/download/file.php?id=25050 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 2007-01-02_114321_z.jpg

skrmsiva · Accepted Answer

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

vietnammba · Answer

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

DangerPenguin · Answer

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!

beattheheat · Answer

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

GMATGuruNY · Answer

Statement 1: 
The following figure is yielded:
 https://thumb.ibb.co/eN9JHy/framed_picture.png

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.

D

coreyander · Answer

The highlighted should be (3f-2w)

coreyander · Answer

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)

Bunuel · Answer

__________________
Fixed. Thank you.

Superman249 · Answer

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

coreyander · Answer

PFA the   OFFICIAL EXPLANATION

IMO, TSA and area are the same for a 2D object.

hemantbafna · Answer

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

Answer  D

mcolbert · Answer

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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Example shown below:

sk7075 · Answer

In this case, how can you consider the width of each frame w?

Krishnahelps · Answer

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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