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Re: geometry, data sufficiency [#permalink]
05 Apr 2011, 15:28

2

This post received KUDOS

Knesl wrote:

What is the area of parallelogram ABCD ?

1. AB = BC = CD = DA = 1 2. AC = BD = \sqrt{2}

(C) 2008 GMAT Club - s10#1

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient * Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient * BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient * EACH statement ALONE is sufficient * Statements (1) and (2) TOGETHER are NOT sufficient

why is statement 2 not sufficient? when the two diagonals are to be the same then it is possible only in case of square. Therefore, the sides are defined as well. Or am I wrong?

1. Can be square or rhombus.

2. Diagonals are same for rectangle and square.

For square the area will be: Area = 1*1 as the side will be 1. Diagonal is sqrt{2}, Diagonal=hypotenuse of 45-90-45 right triangle. Side= 1.

For rectangle the sides can be: 0.5, 1.12; Area = 0.56 OR 0.75, 1.2; Area = 0.9

Basically, all combination of l and w that satisfies: l^2+w^2=2. And there are infinite such possibilities.

Re: geometry, data sufficiency [#permalink]
05 Apr 2011, 16:50

The answer is C as fluke has explained. To add a bit more, it were a square then there is no need to calculate the sides, the area can be simply 1/2 * d1 * d2. _________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

Re: What is the area of parallelogram ABCD ? 1. AB = BC = CD = [#permalink]
19 Mar 2014, 10:43

I have a doubt in the explanation of this question. The official ans says that all four sides of parallelogram ABCD are equal, which implies that ABCD is a rhombus but this is the property of square(a parallelogram) as well...?\ _________________

Re: What is the area of parallelogram ABCD ? 1. AB = BC = CD = [#permalink]
20 Mar 2014, 00:56

Expert's post

swati007 wrote:

I have a doubt in the explanation of this question. The official ans says that all four sides of parallelogram ABCD are equal, which implies that ABCD is a rhombus but this is the property of square(a parallelogram) as well...?

Yes, both a rhombus and a square have equal sides. From (1) we know that ABCD is a rhombus. A rhombus is a special type of a square, so from (1) ABCD is a rhombus and can be a square.

What is the area of parallelogram ABCD?

Notice that we are told that ABCD is a parallelogram.

(1) AB = BC =CD = DA = 1 --> all four sides of parallelogram ABCD are equal, which implies that ABCD is a rhombus. Area of a rhombus equals to \frac{d_1*d_2}{2} (where d_1 and d_2 are the lengths of the diagonals) or bh (where b is the length of the base and h is the altitude), so we don't have enough data to calculate the area. Not sufficient.

(2) AC = BD = \sqrt{2} --> the diagonals of parallelogram ABCD are equal, which implies that ABCD is a rectangle. Area of a rectangle equals to length*width, so again we don't have enough data to calculate the area. Not sufficient. Notice that you cannot find the area of a rectangle just knowing the length of its diagonal.

(1)+(2) ABCD is a rectangle and a rhombus, so it's a square --> area=side^2=1^2=1. Sufficient.

Re: What is the area of parallelogram ABCD ? 1. AB = BC = CD = [#permalink]
17 Apr 2014, 06:16

Bunuel wrote:

swati007 wrote:

I have a doubt in the explanation of this question. The official ans says that all four sides of parallelogram ABCD are equal, which implies that ABCD is a rhombus but this is the property of square(a parallelogram) as well...?

Yes, both a rhombus and a square have equal sides. From (1) we know that ABCD is a rhombus. A rhombus is a special type of a square, so from (1) ABCD is a rhombus and can be a square.

What is the area of parallelogram ABCD?

Notice that we are told that ABCD is a parallelogram.

(1) AB = BC =CD = DA = 1 --> all four sides of parallelogram ABCD are equal, which implies that ABCD is a rhombus. Area of a rhombus equals to \frac{d_1*d_2}{2} (where d_1 and d_2 are the lengths of the diagonals) or bh (where b is the length of the base and h is the altitude), so we don't have enough data to calculate the area. Not sufficient.

(2) AC = BD = \sqrt{2} --> the diagonals of parallelogram ABCD are equal, which implies that ABCD is a rectangle. Area of a rectangle equals to length*width, so again we don't have enough data to calculate the area. Not sufficient. Notice that you cannot find the area of a rectangle just knowing the length of its diagonal.

(1)+(2) ABCD is a rectangle and a rhombus, so it's a square --> area=side^2=1^2=1. Sufficient.

Answer: C.

Hope it's clear.

HI Bunnel,

Diagonal of a square is also equals. then if both the diagonals are equal and root 2 then we have side as 1 and we can calculate the area.

Re: What is the area of parallelogram ABCD ? 1. AB = BC = CD = [#permalink]
17 Apr 2014, 06:27

Expert's post

PathFinder007 wrote:

Bunuel wrote:

swati007 wrote:

I have a doubt in the explanation of this question. The official ans says that all four sides of parallelogram ABCD are equal, which implies that ABCD is a rhombus but this is the property of square(a parallelogram) as well...?

Yes, both a rhombus and a square have equal sides. From (1) we know that ABCD is a rhombus. A rhombus is a special type of a square, so from (1) ABCD is a rhombus and can be a square.

What is the area of parallelogram ABCD?

Notice that we are told that ABCD is a parallelogram.

(1) AB = BC =CD = DA = 1 --> all four sides of parallelogram ABCD are equal, which implies that ABCD is a rhombus. Area of a rhombus equals to \frac{d_1*d_2}{2} (where d_1 and d_2 are the lengths of the diagonals) or bh (where b is the length of the base and h is the altitude), so we don't have enough data to calculate the area. Not sufficient.

(2) AC = BD = \sqrt{2} --> the diagonals of parallelogram ABCD are equal, which implies that ABCD is a rectangle. Area of a rectangle equals to length*width, so again we don't have enough data to calculate the area. Not sufficient. Notice that you cannot find the area of a rectangle just knowing the length of its diagonal.

(1)+(2) ABCD is a rectangle and a rhombus, so it's a square --> area=side^2=1^2=1. Sufficient.

Answer: C.

Hope it's clear.

HI Bunnel,

Diagonal of a square is also equals. then if both the diagonals are equal and root 2 then we have side as 1 and we can calculate the area.

Please clarify.

Please read the red part in my solution. Why should the sides equal to 1? Why cannot they be any numbers satisfying x^2+y^2=2? _________________

Re: What is the area of parallelogram ABCD ? 1. AB = BC = CD = [#permalink]
17 Apr 2014, 06:32

Expert's post

Bunuel wrote:

PathFinder007 wrote:

Bunuel wrote:

Yes, both a rhombus and a square have equal sides. From (1) we know that ABCD is a rhombus. A rhombus is a special type of a square, so from (1) ABCD is a rhombus and can be a square.

What is the area of parallelogram ABCD?

Notice that we are told that ABCD is a parallelogram.

(1) AB = BC =CD = DA = 1 --> all four sides of parallelogram ABCD are equal, which implies that ABCD is a rhombus. Area of a rhombus equals to \frac{d_1*d_2}{2} (where d_1 and d_2 are the lengths of the diagonals) or bh (where b is the length of the base and h is the altitude), so we don't have enough data to calculate the area. Not sufficient.

(2) AC = BD = \sqrt{2} --> the diagonals of parallelogram ABCD are equal, which implies that ABCD is a rectangle. Area of a rectangle equals to length*width, so again we don't have enough data to calculate the area. Not sufficient. Notice that you cannot find the area of a rectangle just knowing the length of its diagonal.

(1)+(2) ABCD is a rectangle and a rhombus, so it's a square --> area=side^2=1^2=1. Sufficient.

Answer: C.

Hope it's clear.

HI Bunnel,

Diagonal of a square is also equals. then if both the diagonals are equal and root 2 then we have side as 1 and we can calculate the area.

Please clarify.

Please read the red part in my solution. Why should the sides equal to 1? Why cannot they be any numbers satisfying x^2+y^2=2?

Re: What is the area of parallelogram ABCD ? 1. AB = BC = CD = [#permalink]
17 Apr 2014, 07:01

Because diagonal of a square = site root2

now as it is given diagonals are equal and this is also property of a square . so if diagonal is root 2 then my site will be 1. and area of a square would be one.

Re: What is the area of parallelogram ABCD ? 1. AB = BC = CD = [#permalink]
17 Apr 2014, 07:28

Expert's post

PathFinder007 wrote:

Because diagonal of a square = site root2

now as it is given diagonals are equal and this is also property of a square . so if diagonal is root 2 then my site will be 1. and area of a square would be one.

Thanks

First of all from (2) we know that ABCD is a rectangle, not necessarily a square.

Next, the fact that the diagonals equals to \sqrt{2} does not mean that the sides must be equal to 1. The sides can be:

\frac{1}{2} and \frac{\sqrt{7}}{2}; \frac{1}{3} and \frac{\sqrt{7}}{\sqrt{3}}; ...

Basically the lengths of the sides can be any positive (x, y) satisfying x^2+y^2=(\sqrt{2})^2.

Please follow the links in my post above for questions which use the same trap. _________________

Re: What is the area of parallelogram ABCD ? 1. AB = BC = CD = [#permalink]
17 Apr 2014, 09:41

Bunuel wrote:

PathFinder007 wrote:

Because diagonal of a square = site root2

now as it is given diagonals are equal and this is also property of a square . so if diagonal is root 2 then my site will be 1. and area of a square would be one.

Thanks

First of all from (2) we know that ABCD is a rectangle, not necessarily a square.

Next, the fact that the diagonals equals to \sqrt{2} does not mean that the sides must be equal to 1. The sides can be:

\frac{1}{2} and \frac{\sqrt{7}}{2}; \frac{1}{3} and \frac{\sqrt{7}}{\sqrt{3}}; ...

Basically the lengths of the sides can be any positive (x, y) satisfying x^2+y^2=(\sqrt{2})^2.

Please follow the links in my post above for questions which use the same trap.

Clear. Thanks for your valuable input.

gmatclubot

Re: What is the area of parallelogram ABCD ? 1. AB = BC = CD =
[#permalink]
17 Apr 2014, 09:41