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:

If p is the perimeter of rectangle Q, what is the value of p?

Question: \(P=2(a+b)=?\)

(1) Each diagonal of rectangle Q has length 10. \(d^2=a^2+b^2=100\). Not sufficient. (2) The area of rectangle Q is 48. \(ab=48\). Not sufficient.

(1)+(2) Square P --> \(P^2=4(a^2+b^2+2ab)\). Now as from (1) \(a^2+b^2=100\) and from (2) \(ab=48\), then \(P^2=4(a^2+b^2+2ab)=4(100+2*48)=4*196\) --> \(P=\sqrt{4*196}=2*14=28\). Sufficient.

If instead, Q were a square, would 1 be sufficient?

In a rectangle, why can't we use the Isosceles Triangle to figure out the third side since the diagonals bisect each other?

If we were told that Q is a square instead of a rectangle, then the answer would be D.

As for the second question: can you please explain what you mean? Generally you cannot find the sides of a rectangle just knowing the length of its diagonal, since knowing the length of hypotenuse (diagonal) in a right triangle (created by length and width), is not enough to find the legs of it (length and width).

Re: If p is the perimeter of rectangle Q, what is the value of p [#permalink]

Show Tags

12 Dec 2012, 13:40

I'm sorry I'm still not seeing how this is not answer "A". I understand the logic at arriving at answer "C", I just don't understand why you NEED to combine statements "1" and "2", contradicts my entire understanding of Data Sufficiency logic.

A rectangle is comprised of 4 right angles, no?

So ultimately the "diagonal" represents the hypotenuse forming two right triangles, no?

Can you form a right triangle with a hypotenuse of 10 with any other legs besides 6 and 8? Or do I have that wrong?

Re: If p is the perimeter of rectangle Q, what is the value of p [#permalink]

Show Tags

13 Dec 2012, 02:21

1

This post received KUDOS

1

This post was BOOKMARKED

kelleygrad05 wrote:

I'm sorry I'm still not seeing how this is not answer "A". I understand the logic at arriving at answer "C", I just don't understand why you NEED to combine statements "1" and "2", contradicts my entire understanding of Data Sufficiency logic.

A rectangle is comprised of 4 right angles, no?

So ultimately the "diagonal" represents the hypotenuse forming two right triangles, no?

Can you form a right triangle with a hypotenuse of 10 with any other legs besides 6 and 8? Or do I have that wrong?

(pythagorean triplet (3, 4, 5) , (6, 8, 10))

Hi Kellygrad05,

There was a similar problem I was attempting yesterday on the forum.

Basically we are told that it is a rectangle but we aren't sure if the sides are Integers or not. For ex.

Diagonal-10, sides can be 6 and 8 (because of PT) or something like Square root 99 and 1...and such other combination

When you consider the st2 with above then we can figure out sides will be 6 and 8 as only in that condition Area will be 48 and Diagonal as 10.

Thanks
_________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

I'm sorry I'm still not seeing how this is not answer "A". I understand the logic at arriving at answer "C", I just don't understand why you NEED to combine statements "1" and "2", contradicts my entire understanding of Data Sufficiency logic.

A rectangle is comprised of 4 right angles, no?

So ultimately the "diagonal" represents the hypotenuse forming two right triangles, no?

Can you form a right triangle with a hypotenuse of 10 with any other legs besides 6 and 8? Or do I have that wrong?

(pythagorean triplet (3, 4, 5) , (6, 8, 10))

A right triangle with hypotenuse 10, doesn't mean that we have (6, 8, 10) right triangle. If we are told that the lengths of all sides are integers, then yes: the only integer solution for right triangle with hypotenuse 10 would be (6, 8, 10).

To check this: consider the right triangle with hypotenuse 10 inscribed in circle. We know that a right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s side, then that triangle is a right triangle.

So ANY point on circumference of a circle with diameter of 10 would make the right triangle with diameter. Not necessarily sides to be 6 and 8. For example we can have isosceles right triangle, which would be 45-45-90: and the sides would be \(\frac{10}{\sqrt{2}}\). OR if we have 30-60-90 triangle and hypotenuse is \(10\), sides would be \(5\) and \(5*\sqrt{3}\). Of course there could be many other combinations.

Re: If p is the perimeter of rectangle Q, what is the value of p [#permalink]

Show Tags

13 Dec 2012, 07:37

Thank you Bunuel, it's clear my understanding of pythagorean triplets was incomplete. The example of the triangle within the circle was quite illuminating. So to summarize, if it is given that all sides of the triangle are integers, and the hypotenuse was given, only then I could have deduced it was part of a pythagorean triple, correct? Was that my only misstep at arriving at answer "A"?

Thank you Bunuel, it's clear my understanding of pythagorean triplets was incomplete. The example of the triangle within the circle was quite illuminating. So to summarize, if it is given that all sides of the triangle are integers, and the hypotenuse was given, only then I could have deduced it was part of a pythagorean triple, correct? Was that my only misstep at arriving at answer "A"?

Re: If p is the perimeter of rectangle Q, what is the value of p [#permalink]

Show Tags

17 Dec 2013, 11:07

Bunuel wrote:

If p is the perimeter of rectangle Q, what is the value of p?

(1) Each diagonal of rectangle Q has length 10. (2) The area of rectangle Q is 48.

Diagnostic Test Question: 48 Page: 26 Difficulty: 650

1) Basically, in saying that the diagonal is 10, they are giving us the hypotenuse of a right triangle. There is no info about the two other sides though, so insufficient.

2) They are simply telling us the area, which is not enough for us to know the perimeter since there are many different products of two that can yield 48.

However, taking 1 and 2 together, they are giving us the hypothenuse (in 1) and the RELATION between the two other sides of the triangle (in statement 2). Since the pythagoran theorem restricts which size two sides can have, if we are given the third (hypothenuse), then this relation between the other two sides is enough.

Notice that I did not do any calculation at all. The DS questions are more about "does this make sense?" than they are about testing if exact boundaries and relations hold up.

Re: If p is the perimeter of rectangle Q, what is the value of p [#permalink]

Show Tags

17 Mar 2015, 03:23

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.
_________________

Re: If p is the perimeter of rectangle Q, what is the value of p [#permalink]

Show Tags

18 Mar 2015, 20:46

I'm was baffled at how the answer wasn't A as well, since when applying the 30-60-90 x, \sqrt{3} , and 2x you could technically get the other sides. We know the hypotenuse is 10, so we have 2x = 10, so x would be 5 and the last side would be 5\sqrt{3}...

But the second statement contradicts this I guess... something to look out for! I thought I was being clever applying that concept.

Re: If p is the perimeter of rectangle Q, what is the value of p [#permalink]

Show Tags

16 May 2015, 07:54

Hi,

I am surprised as well that A was not the correct answer but not for the reasons explained in the previous posts (except if I missed something).

The question is stating that we have a rectangle to consider.

1) tells us that each diagonal of rectangle Q has length 10.

I would guess a rectangle that has its diagonals equal is always a square. If this is a square then knowing the hypotenuse (the diagonal) is enough to guess the perimeter.

I am surprised as well that A was not the correct answer but not for the reasons explained in the previous posts (except if I missed something).

The question is stating that we have a rectangle to consider.

1) tells us that each diagonal of rectangle Q has length 10.

I would guess a rectangle that has its diagonals equal is always a square. If this is a square then knowing the hypotenuse (the diagonal) is enough to guess the perimeter.

Anyone to help me on this? Thanks

The diagonals of a rectangle are always equal.
_________________

Re: If p is the perimeter of rectangle Q, what is the value of p [#permalink]

Show Tags

16 May 2015, 08:29

Bunuel wrote:

tsunagaru wrote:

Hi,

I am surprised as well that A was not the correct answer but not for the reasons explained in the previous posts (except if I missed something).

The question is stating that we have a rectangle to consider.

1) tells us that each diagonal of rectangle Q has length 10.

I would guess a rectangle that has its diagonals equal is always a square. If this is a square then knowing the hypotenuse (the diagonal) is enough to guess the perimeter.

Anyone to help me on this? Thanks

The diagonals of a rectangle are always equal.

Indeed... I have been a bit quick in my guess. Thanks a lot!

Re: If p is the perimeter of rectangle Q, what is the value of p [#permalink]

Show Tags

21 Jul 2015, 14:05

1

This post received KUDOS

I did not use the math way this is how I did it

it is given that 2L +2w= the perimeter of a rectangle 1. each diagnal of a rectangle is length of 10 which makes the rectangle in half so it cant, but just know the triangle height = not sufficient 2. the area of a rectangle is 48 so l*w= area not sufficent

both will tell us 2 equations and can find the length an width to get p so it is C thanks

Happy New Year everyone! Before I get started on this post, and well, restarted on this blog in general, I wanted to mention something. For the past several months...

It’s quickly approaching two years since I last wrote anything on this blog. A lot has happened since then. When I last posted, I had just gotten back from...

Post-MBA I became very intrigued by how senior leaders navigated their career progression. It was also at this time that I realized I learned nothing about this during my...