|
Author |
Message |
|
TAGS:
|
|
|
Intern
Joined: 27 Jul 2010
Posts: 24
Followers: 1
Kudos [?]:
9
[1] , given: 37
|
If p is the perimeter of rectangle Q, what is the value of p [#permalink]
 05 Oct 2010, 02:11
1
This post received
KUDOS
Question Stats:
77% (01:40) correct
22% (00:44) wrong based on 4 sessions
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.
|
|
|
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11570
Followers: 1797
Kudos [?]:
9580
[2] , given: 826
|
2
This post received
KUDOS
wininblue 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
I am not able to understand how do you solve a quadratic eqn of this size and conclude that length and breadth can have 2 distinct values.
Please help! Question: P=2(a+b)=?(1) d^2=a^2+b^2=100. Not sufficient. (2) 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}=28. Sufficient. Answer: C. So you can see that it's not necessary to solve quadratic equation for a and b to get P. Similar question: one-more-geometry-96381.html?hilit=perimeter%20rectangle#p742145Hope it helps.
_________________
PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory
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. NEW!!!
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. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
Intern
Joined: 27 Jul 2010
Posts: 24
Followers: 1
Kudos [?]:
9
[0], given: 37
|
Great Method!
Thank you so much Bunuel, +1
|
|
|
|
|
|
Manager
Joined: 25 Aug 2010
Posts: 102
Followers: 1
Kudos [?]:
4
[0], given: 1
|
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: 174
Followers: 4
Kudos [?]:
19
[0], given: 3
|
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
Followers: 0
Kudos [?]:
0
[0], given: 2
|
Perimeter of rectangle Q ? [#permalink]
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?
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11570
Followers: 1797
Kudos [?]:
9580
[1] , given: 826
|
Re: Perimeter of rectangle Q ? [#permalink]
30 Jan 2011, 08:33
1
This post received
KUDOS
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: one-more-geometry-96381.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: math-triangles-87197.htmlHope it helps.
_________________
PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory
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. NEW!!!
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. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2100
Followers: 108
Kudos [?]:
655
[0], given: 376
|
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)^2-2lw=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)^2-2lw=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)^2-2lw=d^2(l+w)^2=d^2+2lw=10^2+2*48=100+96(l+w)=sqrt{196}=14Sufficient using both statements. Ans: "C"
_________________
~fluke
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
Intern
Joined: 21 Mar 2011
Posts: 10
Followers: 0
Kudos [?]:
0
[0], given: 0
|
Official Guide - 12 - Question D48 [#permalink]
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 OG-12, 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 6-8-10). However, book says it's not sufficient.
Can someone plz clarify or explain? Tx
|
|
|
|
|
|
Manager
Status: MBA Aspirant
Joined: 12 Jun 2010
Posts: 190
Location: India
Concentration: Finance, International Business
WE: Information Technology (Investment Banking)
Followers: 3
Kudos [?]:
14
[0], given: 1
|
Re: Official Guide - 12 - Question D48 [#permalink]
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 OG-12, 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 6-8-10). However, book says it's not sufficient.
Can someone plz clarify or explain? Tx OG is right. You cannot take 6-8-10 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.
|
|
|
|
|
|
|
Re: Official Guide - 12 - Question D48
[#permalink]
17 Sep 2011, 01:05
|
|
|
|
|
|
|
|
|
Similar topics |
Author |
Replies |
Last post |
|
Similar
Topics:
|
 |
|
|
If p is the perimeter of rectangle Q, what is the value of
|
omomo |
3 |
13 Nov 2005, 10:41 |
|
|
|
|
If p is the perimeter of rectangle Q, what is the value of
|
netcaesar |
1 |
12 Jan 2008, 11:57 |
 |
|
|
If p is the perimeter of rectangle Q, what is the value of
|
fwl200 |
12 |
08 Jul 2008, 23:17 |
|
|
|
 |
If p is the perimeter of rectangle X, what is the value of
|
gnothobiot |
5 |
02 Nov 2011, 12:11 |
|
|
3
|
|
If p is the perimeter of rectangle Q, what is the value of p
|
Bunuel |
9 |
16 Jul 2012, 04:56 |
|
|
|
|
|
|
close
