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: NEED SOME Help on this DS question [#permalink]
26 Nov 2010, 13:07

6

This post received KUDOS

Expert's post

1

This post was BOOKMARKED

ajit257 wrote:

What is the area of rectangular region R ? (1) Each diagonal of R has length 5 (2) The perimeter of R is 14

Please could someone explain this question ...thanks.

Let the sides of the rectangle be \(x\) and \(y\). Question: \(area=xy=?\)

(1) Each diagonal of R has length 5 --> as the diagonals in a rectangle are the hypotenuses for the sides then: \(x^2+y^2=5^2\), but we can not get the value of \(xy\) from this info. Not sufficient.

(2) The perimeter of R is 14 --> \(P=2(x+y)=14\) --> \(x+y=7\). Again we can not get the value of \(xy\) from this info. Not sufficient.

(1)+(2) We have \(x^2+y^2=25\) and \(x+y=7\). Square the second expression: \(x^2+2xy+y^2=49\), as \(x^2+y^2=5^2\) then \(25+2xy=49\) --> \(xy=12\). Sufficient.

Re: NEED SOME Help on this DS question [#permalink]
27 Nov 2010, 09:22

1

This post received KUDOS

Expert's post

1

This post was BOOKMARKED

rockroars wrote:

I thought "Statement 1" alone is sufficient to solve this problem.

3,4,5 is the only Pythagorean triplet which supports 5 a diagonal of a right angled triangle.

Why can't the answer be A?

We are not told that the lengths of the sides are integers. So knowing that hypotenuse equals to 5 DOES NOT mean that the sides of the right triangle necessarily must be in the ratio of Pythagorean triple - 3:4:5. Or in other words: if \(x^2+y^2=5^2\) DOES NOT mean that \(x=3\) and \(y=4\). Certainly this is one of the possibilities but definitely not the only one. In fact \(x^2+y^2=5^2\) has infinitely many solutions for \(x\) and \(y\) and only one of them is \(x=3\) and \(y=4\).

For example: \(x=1\) and \(y=\sqrt{24}\) or \(x=2\) and \(y=\sqrt{21}\)...

So knowing that the diagonal of a rectangle (hypotenuse) equals to one of the Pythagorean triple hypotenuse value is not sufficient to calculate the sides of this rectangle.

Re: What is the area of rectangular region R? [#permalink]
29 Feb 2012, 01:30

1

This post received KUDOS

From what I understand of rectangular diagonals or quadrilateral diagonals is that if they are the same length, then all sides should be of equal length. Also area of Rhombus = 1/2 * diagonal * diagonal? Correct me if I'm wrong here, just need clarification

Re: What is the area of rectangular region R? [#permalink]
29 Feb 2012, 01:40

1

This post received KUDOS

Expert's post

calvin1984 wrote:

From what I understand of rectangular diagonals or quadrilateral diagonals is that if they are the same length, then all sides should be of equal length. Also area of Rhombus = 1/2 * diagonal * diagonal? Correct me if I'm wrong here, just need clarification

All rectangles have the diagonals of equal length, so (1) doesn't necessarily means that given rectangle is a rhombus.

Re: NEED SOME Help on this DS question [#permalink]
21 Sep 2012, 08:15

Bunuel wrote:

ajit257 wrote:

What is the area of rectangular region R ? (1) Each diagonal of R has length 5 (2) The perimeter of R is 14

Please could someone explain this question ...thanks.

Let the sides of the rectangle be \(x\) and \(y\). Question: \(area=xy=?\)

(1) Each diagonal of R has length 5 --> as the diagonals in a rectangle are the hypotenuses for the sides then: \(x^2+y^2=5^2\), but we can not get the value of \(xy\) from this info. Not sufficient.

(2) The perimeter of R is 14 --> \(P=2(x+y)=14\) --> \(x+y=7\). Again we can not get the value of \(xy\) from this info. Not sufficient.

(1)+(2) We have \(x^2+y^2=25\) and \(x+y=7\). Square the second expression: \(x^2+2xy+y^2=49\), as \(x^2+y^2=5^2\) then \(25+2xy=49\) --> \(xy=12\). Sufficient.

Answer: C.

Area of a rectangular region = Product of two diagonals/2 We are given both are diagonals are equal to 5 So area would be = 25/2 = 12.5 Thus A is sufficient

Let me know why i am wrong.

Waiting for reply. _________________

If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS. Kudos always maximizes GMATCLUB worth-Game Theory

If you have any question regarding my post, kindly pm me or else I won't be able to reply

Re: NEED SOME Help on this DS question [#permalink]
21 Sep 2012, 08:23

Expert's post

fameatop wrote:

Bunuel wrote:

ajit257 wrote:

What is the area of rectangular region R ? (1) Each diagonal of R has length 5 (2) The perimeter of R is 14

Please could someone explain this question ...thanks.

Let the sides of the rectangle be \(x\) and \(y\). Question: \(area=xy=?\)

(1) Each diagonal of R has length 5 --> as the diagonals in a rectangle are the hypotenuses for the sides then: \(x^2+y^2=5^2\), but we can not get the value of \(xy\) from this info. Not sufficient.

(2) The perimeter of R is 14 --> \(P=2(x+y)=14\) --> \(x+y=7\). Again we can not get the value of \(xy\) from this info. Not sufficient.

(1)+(2) We have \(x^2+y^2=25\) and \(x+y=7\). Square the second expression: \(x^2+2xy+y^2=49\), as \(x^2+y^2=5^2\) then \(25+2xy=49\) --> \(xy=12\). Sufficient.

Answer: C.

Area of a rectangular region = Product of two diagonals/2 We are given both are diagonals are equal to 5 So area would be = 25/2 = 12.5 Thus A is sufficient

Let me know why i am wrong.

Waiting for reply.

The red part is not correct. It's true about squares: \(area_{square}=\frac{diagonal^2}{2}\).

Re: What is the area of rectangular region R ? [#permalink]
08 Dec 2012, 10:06

I screwed up on this one like an earlier poster. So hypothetically, if the question stem stated that the sides were integers, would A be sufficient alone?

I'm nervous on the DS. I got one wrong on the PS in the official guide and 6 wrong already on DS and I'm only on question 50 .

Re: What is the area of rectangular region R ? [#permalink]
09 Dec 2012, 08:49

Expert's post

RonBagel wrote:

I screwed up on this one like an earlier poster. So hypothetically, if the question stem stated that the sides were integers, would A be sufficient alone?

Yes, if we were told that the lengths of the sides of the rectangle are integers, then the first statement would be sufficient: x^2+y^2=25 --> x=3 and y=4 or vise -versa --> xy=12. _________________

Re: NEED SOME Help on this DS question [#permalink]
11 Apr 2014, 00:04

Bunuel wrote:

ajit257 wrote:

What is the area of rectangular region R ? (1) Each diagonal of R has length 5 (2) The perimeter of R is 14

Please could someone explain this question ...thanks.

Let the sides of the rectangle be \(x\) and \(y\). Question: \(area=xy=?\)

(1) Each diagonal of R has length 5 --> as the diagonals in a rectangle are the hypotenuses for the sides then: \(x^2+y^2=5^2\), but we can not get the value of \(xy\) from this info. Not sufficient.

(2) The perimeter of R is 14 --> \(P=2(x+y)=14\) --> \(x+y=7\). Again we can not get the value of \(xy\) from this info. Not sufficient.

(1)+(2) We have \(x^2+y^2=25\) and \(x+y=7\). Square the second expression: \(x^2+2xy+y^2=49\), as \(x^2+y^2=5^2\) then \(25+2xy=49\) --> \(xy=12\). Sufficient.

Answer: C.

Hi Bunuel,

Can't we apply the 1 sqrt3 2 theory to statement one? Since it's a rectangular then the angle created by the diagonal must be 90 and leaving the rest 30 and 60. So the sides must be 5/2 and 5/2(sqrt3).

Re: NEED SOME Help on this DS question [#permalink]
11 Apr 2014, 01:35

Expert's post

aquax wrote:

Bunuel wrote:

ajit257 wrote:

What is the area of rectangular region R ? (1) Each diagonal of R has length 5 (2) The perimeter of R is 14

Please could someone explain this question ...thanks.

Let the sides of the rectangle be \(x\) and \(y\). Question: \(area=xy=?\)

(1) Each diagonal of R has length 5 --> as the diagonals in a rectangle are the hypotenuses for the sides then: \(x^2+y^2=5^2\), but we can not get the value of \(xy\) from this info. Not sufficient.

(2) The perimeter of R is 14 --> \(P=2(x+y)=14\) --> \(x+y=7\). Again we can not get the value of \(xy\) from this info. Not sufficient.

(1)+(2) We have \(x^2+y^2=25\) and \(x+y=7\). Square the second expression: \(x^2+2xy+y^2=49\), as \(x^2+y^2=5^2\) then \(25+2xy=49\) --> \(xy=12\). Sufficient.

Answer: C.

Hi Bunuel,

Can't we apply the 1 sqrt3 2 theory to statement one? Since it's a rectangular then the angle created by the diagonal must be 90 and leaving the rest 30 and 60. So the sides must be 5/2 and 5/2(sqrt3).

What's wrong with this explanation?

Thanks.

Let me ask you a question: why must the remaining angles be 30 and 60 degrees? Why cannot they be 25 or 65? Or 20 and 70? Basically any pair totaling 90? _________________

Re: NEED SOME Help on this DS question [#permalink]
11 Apr 2014, 02:29

aquax wrote:

Bunuel wrote:

ajit257 wrote:

What is the area of rectangular region R ? (1) Each diagonal of R has length 5 (2) The perimeter of R is 14

Please could someone explain this question ...thanks.

Let the sides of the rectangle be \(x\) and \(y\). Question: \(area=xy=?\)

(1) Each diagonal of R has length 5 --> as the diagonals in a rectangle are the hypotenuses for the sides then: \(x^2+y^2=5^2\), but we can not get the value of \(xy\) from this info. Not sufficient.

(2) The perimeter of R is 14 --> \(P=2(x+y)=14\) --> \(x+y=7\). Again we can not get the value of \(xy\) from this info. Not sufficient.

(1)+(2) We have \(x^2+y^2=25\) and \(x+y=7\). Square the second expression: \(x^2+2xy+y^2=49\), as \(x^2+y^2=5^2\) then \(25+2xy=49\) --> \(xy=12\). Sufficient.

Answer: C.

Hi Bunuel,

Can't we apply the 1 sqrt3 2 theory to statement one? Since it's a rectangular then the angle created by the diagonal must be 90 and leaving the rest 30 and 60. So the sides must be 5/2 and 5/2(sqrt3).

What's wrong with this explanation?

Thanks.

Probably you are getting confused because of this example: "a rectangle is inscribed in a circle of radius r...."

The diagonal divides the rectangle in two right triangles, so sum of two angles need to be 90 but it can be 30: 60, 45:45...and so on...

Re: What is the area of rectangular region R ? [#permalink]
22 Jul 2014, 07:33

Hi Bunuel,

To keep it straight, just because it says its a rectangle does not mean we have to have two 30-60-90 triangles, but if we put together two 30-60-90 triangles we get a rectangle? Correct? I picked "A" because I thought that since it said we had a rectangle, we had to have two of these triangles. From the discussion above, it looks like this is not a mandatory condition of a rectangle.

Re: What is the area of rectangular region R ? [#permalink]
22 Jul 2014, 07:36

1

This post received KUDOS

Expert's post

jbdoyl3 wrote:

Hi Bunuel,

To keep it straight, just because it says its a rectangle does not mean we have to have two 30-60-90 triangles, but if we put together two 30-60-90 triangles we get a rectangle? Correct? I picked "A" because I thought that since it said we had a rectangle, we had to have two of these triangles. From the discussion above, it looks like this is not a mandatory condition of a rectangle.

Correct. But you can get a rectangle by putting together any two congruent right triangles, not necessarily 30-60-90 triangles. _________________

Re: What is the area of rectangular region R ? [#permalink]
25 Oct 2015, 06:19

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Low GPA MBA Acceptance Rate Analysis Many applicants worry about applying to business school if they have a low GPA. I analyzed the low GPA MBA acceptance rate at...

http://blog.davidbbaker.com/wp-content/uploads/2015/11/12249800_10153820891439090_8007573611012789132_n.jpg When you think about an MBA program, usually the last thing you think of is professional collegiate sport. (Yes American’s I’m going...