If p is the perimeter of rectangle Q, what is the value of p : GMAT Data Sufficiency (DS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 23 Feb 2017, 20:16

### GMAT Club Daily Prep

#### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 37102
Followers: 7251

Kudos [?]: 96451 [0], given: 10751

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

### Show Tags

16 Jul 2012, 03:56
Expert's post
15
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

69% (01:58) correct 31% (01:04) wrong based on 871 sessions

### HideShow timer Statistics

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
[Reveal] Spoiler: OA

_________________
Director
Status: Tutor - BrushMyQuant
Joined: 05 Apr 2011
Posts: 583
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 570 Q49 V19
GMAT 2: 700 Q51 V31
GPA: 3
WE: Information Technology (Computer Software)
Followers: 102

Kudos [?]: 578 [2] , given: 55

Re: If p is the perimeter of rectangle 0, what is the value of p [#permalink]

### Show Tags

16 Jul 2012, 10:00
2
KUDOS
2
This post was
BOOKMARKED
Let x and y be two sides of the rectangle.. then p =x+y

Stat1
Diagonal = 10
=> x^2 + y^2 = 10^2
we cannot find p i.e. x+y using this info so NOT SUFFICIENT

Sta2
Area = 48
=> xy =48
we cannot find p i.e. x+y using this info so NOT SUFFICIENT

Combining (1) and (2)
we will get
value of x+y = sqrt (x+y)^2 = sqrt(x^2 + y^2 + 2xy) = sqrt ( 10^2 + 2*48)
sqrt(196) = 14

SUFFICIENT
_________________

Ankit

Check my Tutoring Site -> Brush My Quant

GMAT Quant Tutor
How to start GMAT preparations?
How to Improve Quant Score?
Gmatclub Topic Tags
Check out my GMAT debrief

How to Solve :
Statistics || Reflection of a line || Remainder Problems || Inequalities

Math Expert
Joined: 02 Sep 2009
Posts: 37102
Followers: 7251

Kudos [?]: 96451 [4] , given: 10751

Re: If p is the perimeter of rectangle 0, what is the value of p [#permalink]

### Show Tags

20 Jul 2012, 03:40
4
KUDOS
Expert's post
3
This post was
BOOKMARKED
SOLUTION

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.

Similar questions to practice:
if-the-diagonal-of-rectangle-z-is-d-and-the-perimeter-of-104205.html
what-is-the-area-of-rectangular-region-r-105414.html
what-is-the-perimeter-of-rectangle-r-96381.html

Hope it helps.
_________________
Intern
Joined: 20 Feb 2012
Posts: 5
Followers: 0

Kudos [?]: 0 [0], given: 1

Re: If p is the perimeter of rectangle 0, what is the value of p [#permalink]

### Show Tags

28 Jul 2012, 14:42
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?
Math Expert
Joined: 02 Sep 2009
Posts: 37102
Followers: 7251

Kudos [?]: 96451 [0], given: 10751

Re: If p is the perimeter of rectangle 0, what is the value of p [#permalink]

### Show Tags

29 Jul 2012, 00:36
ctiger100 wrote:
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).

Hope it's clear.
_________________
Intern
Joined: 06 Dec 2012
Posts: 6
Followers: 0

Kudos [?]: 2 [0], given: 5

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?

(pythagorean triplet (3, 4, 5) , (6, 8, 10))
Director
Joined: 25 Apr 2012
Posts: 728
Location: India
GPA: 3.21
Followers: 43

Kudos [?]: 707 [1] , given: 723

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

### Show Tags

13 Dec 2012, 02:21
1
KUDOS
1
This post was
BOOKMARKED
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))

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.”

Math Expert
Joined: 02 Sep 2009
Posts: 37102
Followers: 7251

Kudos [?]: 96451 [3] , given: 10751

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

### Show Tags

13 Dec 2012, 03:18
3
KUDOS
Expert's post
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.

Similar questions to practice:
if-the-diagonal-of-rectangle-z-is-d-and-the-perimeter-of-104205.html
what-is-the-area-of-rectangular-region-r-105414.html
what-is-the-perimeter-of-rectangle-r-96381.html

Hope it helps.
_________________
Intern
Joined: 06 Dec 2012
Posts: 6
Followers: 0

Kudos [?]: 2 [0], given: 5

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"?
Math Expert
Joined: 02 Sep 2009
Posts: 37102
Followers: 7251

Kudos [?]: 96451 [0], given: 10751

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

### Show Tags

13 Dec 2012, 07:43
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"?

Yes, that's correct.

For more check Triangles chapter of out Math Book: math-triangles-87197.html

DS geometry questions: search.php?search_id=tag&tag_id=32
PS geometry questions: search.php?search_id=tag&tag_id=53

Hope it helps.
_________________
Manager
Joined: 12 Jan 2013
Posts: 244
Followers: 4

Kudos [?]: 70 [0], given: 47

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.
Manager
Joined: 12 Jan 2013
Posts: 244
Followers: 4

Kudos [?]: 70 [0], given: 47

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

### Show Tags

09 Jan 2014, 10:26
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

Please, correct me if Im wrong because I really need to make sure my "process" is correct:

Statement one tells us that: (length)^2 + (width)^2 = 100

Statement two tells us that: (length)*(width) = 48

Obviously, the two statements alone are not sufficient.. So it's between C and E.

Basically, we are given two equations and two unknowns, so we can solve for both X and Y, and thus we can solve for 2x + 2y = p.

That's why C is correct.

Bunuel, is this process valid?
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13938
Followers: 590

Kudos [?]: 167 [0], given: 0

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.
_________________
Manager
Joined: 27 Jan 2015
Posts: 132
Concentration: General Management, Entrepreneurship
GMAT 1: 670 Q44 V38
Followers: 0

Kudos [?]: 22 [0], given: 51

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.
Intern
Joined: 01 Oct 2014
Posts: 4
Followers: 0

Kudos [?]: 0 [0], given: 10

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.

Anyone to help me on this?
Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 37102
Followers: 7251

Kudos [?]: 96451 [0], given: 10751

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

### Show Tags

16 May 2015, 08:10
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.
_________________
Intern
Joined: 01 Oct 2014
Posts: 4
Followers: 0

Kudos [?]: 0 [0], given: 10

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!
Intern
Joined: 18 Jul 2015
Posts: 26
Followers: 0

Kudos [?]: 1 [1] , given: 36

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

### Show Tags

21 Jul 2015, 14:05
1
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
Intern
Joined: 18 Jul 2015
Posts: 26
Followers: 0

Kudos [?]: 1 [0], given: 36

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

### Show Tags

21 Jul 2015, 14:09
we cant use the isoceles because its not equal on both sides
Intern
Joined: 18 Jul 2015
Posts: 26
Followers: 0

Kudos [?]: 1 [0], given: 36

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

### Show Tags

21 Jul 2015, 14:14
I understand that you are right, but the 30 60 90 right traingle we cant do with rectangles because we dont know if it is a right triangle.

thanks Hyder
Re: If p is the perimeter of rectangle Q, what is the value of p   [#permalink] 21 Jul 2015, 14:14

Go to page    1   2    Next  [ 30 posts ]

Similar topics Replies Last post
Similar
Topics:
If P and Q are both positive, what is the value of P? 2 30 Jul 2016, 02:06
3 If p and q are positive integers, what is the value of q? 3 28 Jun 2012, 05:56
If p is the perimeter of rectangle X, what is the value of 5 02 Nov 2011, 11:11
4 If (p - q) is not equal to zero, what is the value of p/(p - 3 15 Sep 2011, 05:25
4 If p is the perimeter of rectangle Q, what is the value of p 9 05 Oct 2010, 01:11
Display posts from previous: Sort by