GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Oct 2019, 06:31 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  If l and w represent the length and width, respectively, of the rectan

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

CEO  D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2978
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
If l and w represent the length and width, respectively, of the rectan  [#permalink]

Show Tags

2 00:00

Difficulty:   25% (medium)

Question Stats: 73% (01:19) correct 27% (01:21) wrong based on 123 sessions

HideShow timer Statistics

If l and w represent the length and width, respectively, of the rectangle, what is the perimeter of Rectangle?

(1) The area of the rectangle is 48.
(2) The length of a diagonal of the rectangle is 10.

_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Intern  Joined: 10 Jan 2013
Posts: 36
Location: United States
Concentration: General Management, Operations
GMAT 1: 710 Q49 V38 GPA: 3.02
WE: Design (Telecommunications)
Re: If l and w represent the length and width, respectively, of the rectan  [#permalink]

Show Tags

1
we have to find out the perimeter of the rectangle which is 2( l+w) :

1. The area of the rectangle is 48 --> not sufficient as possible (l,w) can be (4,12),(8,6),( 2,24),(16,3).
2. The length of a diagonal of the rectangle is 10.--> sufficient. As rectangle is right angled and only (8,6) satisfy the equation 10^2= 8^2+6^2.

Can somebody explain the problem.
CEO  D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2978
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: If l and w represent the length and width, respectively, of the rectan  [#permalink]

Show Tags

1
GMATinsight wrote:
If l and w represent the length and width, respectively, of the rectangle, what is the perimeter of Rectangle?

(1) The area of the rectangle is 48.
(2) The length of a diagonal of the rectangle is 10.

Perimeter = l + w

Statement 1: The area of the rectangle is 48
i.e. l*w = 48
Case 1: l = 6 and w = 8
Case 2: l = 1 and w = 48, Hence,
NOT SUFFICIENT

Statement 2: l^2 + w^2 = 10^2 = 100
Case 1: l = 6 and w = 8
Case 2: l = $$5\sqrt{2}$$ and w = $$5\sqrt{2}$$, Hence,
NOT SUFFICIENT

Combining the two statements
l and w can only be 6 and 8 (or vice versa)
but in each case Perimeter = 2(6+8) = 28
SUFFICIENT

I hope this helps! _________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Board of Directors P
Joined: 17 Jul 2014
Posts: 2510
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30 GPA: 3.92
WE: General Management (Transportation)
If l and w represent the length and width, respectively, of the rectan  [#permalink]

Show Tags

i spent more time on thinking whether B is a trap or not, since 10 is 2x5, and we know the pythagorean triplet 3-4-5 multiplied by 2 or 6-8-10.
even the first statement might suggest that l=8 and w=6 since 6*8 = 48
but!!!
if you do the math, you see that lw = 48, and l^2 + w^2 = 100
knowing that (a+b)^2 = a^2+2ab+b^2, we can easily see that l^2+2lw+w^2 = 196 or (l+w)^2 = 196
l+w will thus be 14 and the perimeter 32. we can get to the correct answer only by combining the two statements.
C is the answer.
Intern  B
Status: Prepping for GMAT
Joined: 06 Nov 2017
Posts: 23
Location: France
GPA: 4
If l and w represent the length and width, respectively, of the rectan  [#permalink]

Show Tags

1
GMATinsight wrote:
If l and w represent the length and width, respectively, of the rectangle, what is the perimeter of Rectangle?

(1) The area of the rectangle is 48.
(2) The length of a diagonal of the rectangle is 10.

Rephrasing the question: "what is the perimeter of the rectangle?" i.e. $$2*(l+w) = ?$$

(1) The area of the rectangle is 48
Mathematically, this means that $$l*w = 48$$. This piece of information is not sufficient by itself.
Hence, the statement is insufficient (eliminate A and D).

(2) The length of a diagonal of the rectangle is 10
Since rectangles have right angles in their corners, the diagonal of any rectangle can be obtained through Pythagoras' theorem. Mathematically, this means that $$\sqrt{l^2+w^2} = 10$$. This piece of information is not sufficient by itself.
Hence, the statement is insufficient (eliminate B).

(1) + (2) The area of the rectangle is 48 and the length of a diagonal of the rectangle is 10
This statement gives us two mathematical formulas:
$$l*w = 48$$
$$\sqrt{l^2+w^2} = 10$$
If one recalls, one of the basic mathematical identities is $$(a+b)^2 = a^2 + 2*ab + b^2$$. Hence, if we plug the two formulas above into the latter identity, we get:
$$(l+w)^2 = l^2 + w^2 + 2*l*w = 10^2 + 2*48 = 196 = 14^2$$
Thus, $$2*(l+w) = 2*14 = 28$$.
This is sufficient to answer the question. If l and w represent the length and width, respectively, of the rectan   [#permalink] 01 Mar 2018, 05:31
Display posts from previous: Sort by

If l and w represent the length and width, respectively, of the rectan

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  