Data Suffi abt quadrilateral

[gmatready]

If a certain quadrilateral has 4 equal angles, what is its area?

1. if lenght id doubled, Area would increase by 64 sqare feet.
2. if width is reduced by half, the area would decrease by 32 Square
feet


GR.

[gmatready]

My solution:

PR says ans is D. I say ans. is C.
How?


condition is fulfilled by both Square and Rectangle

l*w = A

condition 1,
if rect, 2l*w = A + 64
hence we know its area is 64


if square, 2l*2w = A + 64
the value of l*w = 64/3
they are different.

similarly, for condition 2,

only when you put these two conditions togather that you get just one
answer for Area A
hence ans should be C
what do you think?




If a certain quadrilateral has 4 equal angles, what is its area?

1. if lenght id doubled, Area would increase by 64 sqare feet.
2. if width is reduced by half, the area would decrease by 32 Square
feet


GR.

[isha]

Condition 1

l*w = A
If length doubled area will increase by 64.
Therefore,
(2*l)*w = A +64
2*A = A + 64 since lw = A
A = 64

Condition 2

l*w = A
If width is halved area will decrease by 32.
Therefore,
l*(w/2) = A - 32

[umka24]

You have to remember it's a "square". So L=W.
Then, LxL=A or 2Lx2L=A+64, or 4LxL=LxL+64 do Statment 1 should be sufficient.
The same for Statement 2 where Width is reduced, so: W/2xW/2=A-32 or: W/2xW/2=WxW-32. Stat. 2 also sufficient


My solution:

PR says ans is D. I say ans. is C.
How?


condition is fulfilled by both Square and Rectangle

l*w = A

condition 1,
if rect, 2l*w = A + 64
hence we know its area is 64


if square, 2l*2w = A + 64
the value of l*w = 64/3
they are different.

similarly, for condition 2,

only when you put these two conditions togather that you get just one
answer for Area A
hence ans should be C
what do you think?




If a certain quadrilateral has 4 equal angles, what is its area?

1. if lenght id doubled, Area would increase by 64 sqare feet.
2. if width is reduced by half, the area would decrease by 32 Square
feet


GR.





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[/quote]

[ysnath]

Hello All,
I feel Isha's approach is correct, but she couldn't able to complete the problem. Lets do like this:

1. It is given that

If a certain quadrilateral has 4 equal angles, what is its area?

So it is obvious that the quadrilateral will be either a sqare or a rectangle. For either of them the formula for Area will be:

Area = lenght * width.(diff. will be for a square length = width)
shortcut : A = L * W.

3. And in the problem it is clearly stated that :

1. if lenght id doubled, Area would increase by 64 sqare feet.
2. if width is reduced by half, the area would decrease by 32 Square
feet

So in each of these statements it is understood that we have to change only one side of either square or rectangle. Not as umka24 calculated 2L*2L or W/2 * W/2. This is wrong.

So..lets continue...
4. So first statement states that:

1. if lenght id doubled, Area would increase by 64 sqare feet.

So.. we have A = L * W.

2*L*W = A + 64
2* A = A + 64. ie. A = 64

5. Second statement states that:

2. if width is reduced by half, the area would decrease by 32 Square
feet

We have A = L * W.
L * (W/2) = A - 32
L * W = 2A - 64.
A = 2A - 64 ie. A = 64.

6. So in our steps ( steps 4 & 5) we have derived A= 64 without help of other statement. So it is enough that any one of given statements(statement 1 & 2) are sufficient to find the result. Means ans. D(Is it correct??)

7. Here we are considering that the LENGTH and WIDTH is assumed to be only for one side and not for both as mentioned by umka24.


I feel I am enough explanative. And you are satisfied with the answer.


Regards,
Surendra

[tobe]

equal angles ==> quadrilateral = rectangle.
original length: L, original length: B, LB = ?
1) (L + 2) * B = LB + 64 ==> B = 32. insuff to find LB.
2) L * B/2 = LB - 32 ==> LB = 64. suff
Answer: B

[pitts20042006]

tobe .. in the first condition why did you add 2 to the length. It is given as the length is doubled .. so it will be 2 * L and not L + 2

[Kal]

Surendra's answer is perfect. I also came up with D.