Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized for You
we will pick new questions that match your level based on your Timer History
Track Your Progress
every week, we’ll send you an estimated GMAT score based on your performance
Practice Pays
we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
It appears that you are browsing the GMAT Club forum unregistered!
Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club
Registration gives you:
Tests
Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.
Applicant Stats
View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more
Books/Downloads
Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
Re: geometry, data sufficiency [#permalink]
05 Apr 2011, 15:28
2
This post received KUDOS
1
This post was BOOKMARKED
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
1
This post received KUDOS
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...?\ _________________
What is the area of parallelogram ABCD ? [#permalink]
20 Mar 2014, 00:56
1
This post received KUDOS
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 square is a special type of a rhombus, 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.
Re: What is the area of parallelogram ABCD ? [#permalink]
04 Feb 2015, 16:42
1
This post received KUDOS
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.
Thanks as always for your valuable and detailed explanations. However, you've mentioned that a 'rhombus is a special type of square', where as a square is a special type of rhombus. Parallelogram->Rectangle/Rhombus->Square. _________________
"Hardwork is the easiest way to success." - Aviram
One more shot at the GMAT...aiming for a more balanced score.
Re: What is the area of parallelogram ABCD ? [#permalink]
04 Feb 2015, 16:47
Expert's post
aviram 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.
Thanks as always for your valuable and detailed explanations. However, you've mentioned that a 'rhombus is a special type of square', where as a square is a special type of rhombus. Parallelogram->Rectangle/Rhombus->Square.
As I’m halfway through my second year now, graduation is now rapidly approaching. I’ve neglected this blog in the last year, mainly because I felt I didn’...
Perhaps known best for its men’s basketball team – winners of five national championships, including last year’s – Duke University is also home to an elite full-time MBA...