Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 27 Jul 2010
Posts: 24

If p is the perimeter of rectangle Q, what is the value of p
[#permalink]
Show Tags
05 Oct 2010, 02:11
Question Stats:
77% (00:46) correct 23% (01:04) wrong based on 203 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.
Official Answer and Stats are available only to registered users. Register/ Login.



Math Expert
Joined: 02 Sep 2009
Posts: 47920

Re: OG12 D48
[#permalink]
Show Tags
05 Oct 2010, 02:27



Intern
Joined: 27 Jul 2010
Posts: 24

Re: OG12 D48
[#permalink]
Show Tags
05 Oct 2010, 03:57
Great Method! Thank you so much Bunuel, +1



Manager
Joined: 25 Aug 2010
Posts: 68

Re: OG12 D48
[#permalink]
Show Tags
05 Oct 2010, 04:23
Since it is a rectangle, the diagnal opposite side would make 90 degrees, so the diagnal = a^2 + b^2 which is equal to 10  from (i)
I can nt determine the p value from the (i)
From (2), ab = 48 not sufficient. now combine both, we know that (a+b)^2 = a^2 + b^2 + 2ab .... we have all the values ..
so the ans is : C



Manager
Joined: 15 Apr 2010
Posts: 134

Re: OG12 D48
[#permalink]
Show Tags
06 Oct 2010, 07:20
Perimeter = p = 2* (l+b)
To caluculate the perimeter, we need both l and b
1) Length of diagonal = 10 Length of a diagonal = sqrt{l^2 + b^2} = 10 Squaring both sides, we get (l^2 + b^2) = 100 This is not sufficient since we have one equation and 2 variables.
2) Area = l*b = 48 This is not sufficient since we have one equation and 2 variables.
(l+b)^2 = l^2 + b^2 + 2*l*b Substituting the values obtained in 1) and 2), we can get the value of (l+b) and thus we can calculate the perimeter.
Hence C.



Intern
Joined: 06 Dec 2010
Posts: 2

Perimeter of rectangle Q ?
[#permalink]
Show Tags
30 Jan 2011, 08:14
Hi,
in the book "GMAT review 12th edt.", there is diagnostic test question #48 (DS).  If p is the perimeter of rectangle Q, what is the value of p? 1) Each diagonal of rectangle Q has length of 10. 2) The area of rectangle Q is 48.  Now, the answer explanation says C is correct. However, when looking at answer 1), I know the hypotenuse of both triangles is 10. Using the Pythagorean theorem, I know that my sides are 8 and 6 > (5:4:3) x 2.
So p = 2l + 2w = 16 + 12... hence A is sufficient to determine the value.
Where is my error?



Math Expert
Joined: 02 Sep 2009
Posts: 47920

Re: Perimeter of rectangle Q ?
[#permalink]
Show Tags
30 Jan 2011, 08:33
Merging similar topics. demeuse81 wrote: Hi,
in the book "GMAT review 12th edt.", there is diagnostic test question #48 (DS).  If p is the perimeter of rectangle Q, what is the value of p? 1) Each diagonal of rectangle Q has length of 10. 2) The area of rectangle Q is 48.  Now, the answer explanation says C is correct. However, when looking at answer 1), I know the hypotenuse of both triangles is 10. Using the Pythagorean theorem, I know that my sides are 8 and 6 > (5:4:3) x 2.
So p = 2l + 2w = 16 + 12... hence A is sufficient to determine the value.
Where is my error? Check this post: onemoregeometry96381.html#p742164You assume with no ground for it that the lengths of the sides are integers. Knowing that hypotenuse equals to 10 DOES NOT mean that the sides of the right triangle necessarily must be in the ratio of Pythagorean triple  6:8:10. Or in other words: if \(a^2+b^2=10^2\) DOES NOT mean that \(a=6\) and \(b=8\), certainly this is one of the possibilities but definitely not the only one. In fact \(a^2+b^2=10^2\) has infinitely many solutions for \(a\) and \(b\) and only one of them is \(a=6\) and \(b=8\). For example: \(a=1\) and \(b=\sqrt{99}\) or \(a=2\) and \(b=\sqrt{96}\) or \(a=4\) and \(b=\sqrt{84}\) ... 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. Check this post for more on triangles: mathtriangles87197.htmlHope it helps.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Retired Moderator
Joined: 20 Dec 2010
Posts: 1879

Re: OG12 D48
[#permalink]
Show Tags
30 Jan 2011, 10:27
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 For the rectangle; if Diagonal=d length=l width=w Rephrasing: What is 2(l+w) or simply what is (l+w) 1) d=10 \(l^2+w^2=d^2\) \((l+w)^22lw=d^2\) \((l+w)^2=d^2+2lw=10^2+2lw=100+2lw\) \((l+w)=sqrt{100+2lw}\) If we knew lw; we would have known l+w; but we don't know that Not Sufficient. 2) Area=48 lw=48 \(l^2+w^2=d^2\) \((l+w)^22lw=d^2\) \((l+w)^2=d^2+2lw=d^2+2*48=d^2+96\) \((l+w)=sqrt{d^2+96}\) If we knew diagonal "d"; we would have known l+w; but we don't know that Not Sufficient. Using both the statements; We know lw=48 and d=10 \(l^2+w^2=d^2\) \((l+w)^22lw=d^2\) \((l+w)^2=d^2+2lw=10^2+2*48=100+96\) \((l+w)=sqrt{196}=14\) Sufficient using both statements. Ans: "C"
_________________
~fluke
GMAT Club Premium Membership  big benefits and savings



Intern
Joined: 21 Mar 2011
Posts: 10

Official Guide  12  Question D48
[#permalink]
Show Tags
15 Sep 2011, 00:13
Hi.. am a member for some while now, however this is my 1st ever post. In Q 48 (data sufficiency) of diagnostic test of OG12, the diagonal length of rectangle is given as 10 inches, and we need to find the perimeter. According to me, the statement is sufficient in that the sides have to be 6 and 8 inhes (using the pythagorean triple 6810). However, book says it's not sufficient. Can someone plz clarify or explain? Tx



Manager
Status: MBA Aspirant
Joined: 12 Jun 2010
Posts: 144
Location: India
Concentration: Finance, International Business
WE: Information Technology (Investment Banking)

Re: Official Guide  12  Question D48
[#permalink]
Show Tags
17 Sep 2011, 01:05
deephoenix wrote: Hi.. am a member for some while now, however this is my 1st ever post. In Q 48 (data sufficiency) of diagnostic test of OG12, the diagonal length of rectangle is given as 10 inches, and we need to find the perimeter. According to me, the statement is sufficient in that the sides have to be 6 and 8 inhes (using the pythagorean triple 6810). However, book says it's not sufficient. Can someone plz clarify or explain? Tx OG is right. You cannot take 6810 to solve this quesion. In the above posts Bunnel and fluke have explained the solution of this question using the right approach. Please refer their posts and reply back if you have any doubts.



Intern
Joined: 24 Sep 2017
Posts: 2

Re: If p is the perimeter of rectangle Q, what is the value of p
[#permalink]
Show Tags
09 Dec 2017, 06:47
i chose answer A since this is a rectangle and the diagonal will bisect the right angles, forming 454590 triangle with sides ratios of 1:1:root 2. using Pythagorean theory , we can get the value of both sides
what did i do wrong here ?



Math Expert
Joined: 02 Sep 2009
Posts: 47920

If p is the perimeter of rectangle Q, what is the value of p
[#permalink]
Show Tags
09 Dec 2017, 06:54




If p is the perimeter of rectangle Q, what is the value of p &nbs
[#permalink]
09 Dec 2017, 06:54






