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

 It is currently 19 Aug 2018, 21:36

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

What is the area of the rectangular region above?

Author Message
TAGS:

Hide Tags

Senior Manager
Joined: 18 Oct 2010
Posts: 392
What is the area of the rectangular region above?  [#permalink]

Show Tags

Updated on: 30 Jan 2018, 21:00
2
6
00:00

Difficulty:

25% (medium)

Question Stats:

73% (00:44) correct 27% (00:53) wrong based on 274 sessions

HideShow timer Statistics

What is the area of the rectangular region above?

(1) l + w = 6.
(2) d^2 = 20

Attachment:

untitled.PNG [ 1.94 KiB | Viewed 7752 times ]

Originally posted by heygirl on 24 Feb 2011, 11:39.
Last edited by Bunuel on 30 Jan 2018, 21:00, edited 2 times in total.
Edited the question
Retired Moderator
Joined: 20 Dec 2010
Posts: 1877
Re: What is the area of the rectangular region above?  [#permalink]

Show Tags

24 Feb 2011, 11:46
5
1
(1)
$$l+w = 6$$
$$(l+w)^2 = l^2+w^2+2w*l=36$$
$$w*l=\frac{36-l^2-w^2}{2}$$
Not Sufficient.

(2)
$$d^2=l^2+w^2=20$$
Not Sufficient.

Combining both;
$$w*l=\frac{36-(l^2+w^2)}{2}$$
$$w*l=\frac{36-20}{2}$$
$$w*l=\frac{16}{2}$$
$$w*l=8$$(Area is w*l)

Sufficient.

Ans: "C"
_________________
General Discussion
Senior Manager
Joined: 18 Oct 2010
Posts: 392
Re: What is the area of the rectangular region above?  [#permalink]

Show Tags

24 Feb 2011, 11:49
Thanks!
Actually, can we not use the pythagorean theorem and 45-45-90 triangle rule to get l and w using (2)?
Math Expert
Joined: 02 Sep 2009
Posts: 48037
What is the area of the rectangular region above?  [#permalink]

Show Tags

24 Feb 2011, 12:10
2
1

What is the area of the rectangular region above?

$$area=lw=?$$

(1) l + w = 6. Not sufficient to get the value of $$lw$$.
(2) d^2 = 20 --> $$l^2 +w^2 = 20$$. Not sufficient to get the value of $$lw$$.

(1)+(2) Square (1): $$l^2+2lw+w^2=36$$, as from (2) $$l^2 +w^2 = 20$$ then $$2lw+20=36$$ --> $$lw=8$$. Sufficient.

heygirl wrote:
Thanks!
Actually, can we not use the pythagorean theorem and 45-45-90 triangle rule to get l and w using (2)?

Usually the diagonal does not divide a rectangle into two 45-45-90 triangles (it'll be correct only for squares, so when l=w).

Similar questions:
http://gmatclub.com/forum/need-some-hel ... 05414.html
http://gmatclub.com/forum/og12-d48-102246.html
http://gmatclub.com/forum/one-more-geometry-96381.html
_________________
Senior Manager
Joined: 18 Oct 2010
Posts: 392
Re: What is the area of the rectangular region above?  [#permalink]

Show Tags

24 Feb 2011, 12:12
1
Thanks for letting me know Bunuel. I shall follow the rules henceforth!!
I actually thought b could be the right answer here. I made a wrong assumption : diag of a rect make 45 degrees!
Manager
Joined: 14 Feb 2011
Posts: 179
Re: What is the area of the rectangular region above?  [#permalink]

Show Tags

09 Mar 2011, 00:19
Lolaergasheva wrote:
What is the area of the rectangular region ?
(1) l + w = 6
(2) d^2 = 20

Area of rectangular region is given by $$l*w$$.

Statement 1 gives us,$$l+w=6$$, but l and w can take any values, so insufficient

Statement 2 gives us $$d^2 = 20$$ . Assuming that d refers to length of diagonal, we have $$d^2 = l^2 + w^2 = 20$$. Again l and w can take multiple values, so insufficient.

Combining 1 and 2,

we get $$l+w=6$$ ... (1)

and $$l^2 + w^2 = 20$$.... (2)

Squaring both sides of (1), we get

so, $$l^2 + w^2 + 2l*w = 36$$

Putting $$l^2 + w^2 = 20$$ in above we get $$2l*w = 16$$ or $$l*w = 8$$

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6038
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: What is the area of the rectangular region above?  [#permalink]

Show Tags

07 Sep 2015, 07:28
1
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and equations ensures a solution.

What is the area of the rectangular region above?

(1) l + w = 6. Not sufficient to get the value of .
(2) d^2 = 20

In the original condition we have 2 variables for the rectangle(width, length) and thus we need 2 variables to match the number of variables and equations. Since there is 1 each in 1) and 2), C is likely the answer.
Attachments

untitled.PNG [ 1.94 KiB | Viewed 3565 times ]

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only \$99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Intern
Joined: 16 Oct 2017
Posts: 38
Re: What is the area of the rectangular region above?  [#permalink]

Show Tags

30 Jan 2018, 19:03
Bunuel wrote:
heygirl wrote:
What is the area of a rectangle with length l and width w?
(1)l+w=6
(2)d^2=20(d is the diagonal)

Make sure you type the question in exactly as it was stated from the source. Yuo should not reword or/and shorten the questions.

Original question:

Attachment:
untitled.PNG
What is the area of the rectangular region above?

$$area=lw=?$$

(1) l + w = 6. Not sufficient to get the value of $$lw$$.
(2) d^2 = 20 --> $$l^2 +w^2 = 20$$. Not sufficient to get the value of $$lw$$.

(1)+(2) Square (1): $$l^2+2lw+w^2=36$$, as from (2) $$l^2 +w^2 = 20$$ then $$2lw+20=36$$ --> $$lw=8$$. Sufficient.

heygirl wrote:
Thanks!
Actually, can we not use the pythagorean theorem and 45-45-90 triangle rule to get l and w using (2)?

Usually the diagonal does not divide a rectangle into two 45-45-90 triangles (it'll be correct only for squares, so when l=w).

Similar questions:
http://gmatclub.com/forum/need-some-hel ... 05414.html
http://gmatclub.com/forum/og12-d48-102246.html
http://gmatclub.com/forum/one-more-geometry-96381.html

Bunuel, I screwed up and assumed I was to use the 30:60:90 triangle rule for statement #2 (since it's a rectangle).

How am I supposed to know that rule won't work for this question? Is it because d^2 = 20 -> d= 4 square root 5, but not 4 square root 3?
Math Expert
Joined: 02 Sep 2009
Posts: 48037
Re: What is the area of the rectangular region above?  [#permalink]

Show Tags

30 Jan 2018, 21:07
OCDianaOC wrote:
Bunuel wrote:
heygirl wrote:
What is the area of a rectangle with length l and width w?
(1)l+w=6
(2)d^2=20(d is the diagonal)

Make sure you type the question in exactly as it was stated from the source. Yuo should not reword or/and shorten the questions.

Original question:

Attachment:
untitled.PNG
What is the area of the rectangular region above?

$$area=lw=?$$

(1) l + w = 6. Not sufficient to get the value of $$lw$$.
(2) d^2 = 20 --> $$l^2 +w^2 = 20$$. Not sufficient to get the value of $$lw$$.

(1)+(2) Square (1): $$l^2+2lw+w^2=36$$, as from (2) $$l^2 +w^2 = 20$$ then $$2lw+20=36$$ --> $$lw=8$$. Sufficient.

heygirl wrote:
Thanks!
Actually, can we not use the pythagorean theorem and 45-45-90 triangle rule to get l and w using (2)?

Usually the diagonal does not divide a rectangle into two 45-45-90 triangles (it'll be correct only for squares, so when l=w).

Similar questions:
http://gmatclub.com/forum/need-some-hel ... 05414.html
http://gmatclub.com/forum/og12-d48-102246.html
http://gmatclub.com/forum/one-more-geometry-96381.html

Bunuel, I screwed up and assumed I was to use the 30:60:90 triangle rule for statement #2 (since it's a rectangle).

How am I supposed to know that rule won't work for this question? Is it because d^2 = 20 -> d= 4 square root 5, but not 4 square root 3?

Knowing only the length of a diagonal of a rectangle does not allow to find its adjacent angles. You can squeeze or stretch a rectangle with any length of a diagonal along one of its sides to get any adjacent lengths from 0 to 90 not inclusive.
_________________
Director
Joined: 09 Mar 2016
Posts: 769
Re: What is the area of the rectangular region above?  [#permalink]

Show Tags

22 Apr 2018, 04:38
Bunuel wrote:

What is the area of the rectangular region above?

$$area=lw=?$$

(1) l + w = 6. Not sufficient to get the value of $$lw$$.
(2) d^2 = 20 --> $$l^2 +w^2 = 20$$. Not sufficient to get the value of $$lw$$.

(1)+(2) Square (1): $$l^2+2lw+w^2=36$$, as from (2) $$l^2 +w^2 = 20$$ then $$2lw+20=36$$ --> $$lw=8$$. Sufficient.

heygirl wrote:
Thanks!
Actually, can we not use the pythagorean theorem and 45-45-90 triangle rule to get l and w using (2)?

Usually the diagonal does not divide a rectangle into two 45-45-90 triangles (it'll be correct only for squares, so when l=w).

Similar questions:
http://gmatclub.com/forum/need-some-hel ... 05414.html
http://gmatclub.com/forum/og12-d48-102246.html
http://gmatclub.com/forum/one-more-geometry-96381.html

Bunuel why are you squaring statement one l + w = 6 ?? the formula for area of rectangle is L*W , isnt it
_________________

In English I speak with a dictionary, and with people I am shy.

DS Forum Moderator
Joined: 22 Aug 2013
Posts: 1343
Location: India
Re: What is the area of the rectangular region above?  [#permalink]

Show Tags

22 Apr 2018, 11:17
1
dave13 wrote:
Bunuel wrote:

What is the area of the rectangular region above?

$$area=lw=?$$

(1) l + w = 6. Not sufficient to get the value of $$lw$$.
(2) d^2 = 20 --> $$l^2 +w^2 = 20$$. Not sufficient to get the value of $$lw$$.

(1)+(2) Square (1): $$l^2+2lw+w^2=36$$, as from (2) $$l^2 +w^2 = 20$$ then $$2lw+20=36$$ --> $$lw=8$$. Sufficient.

heygirl wrote:
Thanks!
Actually, can we not use the pythagorean theorem and 45-45-90 triangle rule to get l and w using (2)?

Usually the diagonal does not divide a rectangle into two 45-45-90 triangles (it'll be correct only for squares, so when l=w).

Similar questions:
http://gmatclub.com/forum/need-some-hel ... 05414.html
http://gmatclub.com/forum/og12-d48-102246.html
http://gmatclub.com/forum/one-more-geometry-96381.html

Bunuel why are you squaring statement one l + w = 6 ?? the formula for area of rectangle is L*W , isnt it

Hello Dave

I think Bunuel is doing this because he sees two equations from two statements: one equation says that l + w = 6 and the other says that l^2 + w^2 = 20. But he has to find l*w. So how to find l*w from l+w and l^2 + w^2. Immediately the formula which comes to mind is:
(l+w)^2 = l^2 + w^2 + 2*l*w.
We can substitute the values of l+w and l^2 + w^2 in the above formula and we can get the value of l*w. Hope this is clear.
Intern
Joined: 25 Sep 2017
Posts: 15
Location: India
Concentration: Strategy, Nonprofit
WE: Web Development (Computer Software)
Re: What is the area of the rectangular region above?  [#permalink]

Show Tags

24 Apr 2018, 01:44
4
Need to find area = l*w
1. l+w=6 --> sqrn both sides --> l^2 + w^2 + 2wl=36 -eqn(a)
INSUFFICIENT
2. d^2=20 --> l^2+w^2=d^2=20 -eqn(b)
INSUFFICIENT

Consider eqn (a) and (b)
20 +2wl=36 --> Solve for wl

Ans -> C
Director
Joined: 02 Oct 2017
Posts: 616
Re: What is the area of the rectangular region above?  [#permalink]

Show Tags

08 May 2018, 07:59
Area=LW
We got L*L + W*W=D*D
Converted to

=(L+W)^2 -2LW=20

=36-20=2LW

2LW=16

LW =8

Both statements are required

Posted from my mobile device
Intern
Joined: 10 Jul 2018
Posts: 4
Re: What is the area of the rectangular region above?  [#permalink]

Show Tags

26 Jul 2018, 17:49
Bunuel

When you square statement 1 why do you are you doing this: (l+w)^2 and not l^2+w^2. When squaring, I've never done it like this.
Math Expert
Joined: 02 Sep 2009
Posts: 48037
Re: What is the area of the rectangular region above?  [#permalink]

Show Tags

26 Jul 2018, 20:20
akoundourakis wrote:
Bunuel

When you square statement 1 why do you are you doing this: (l+w)^2 and not l^2+w^2. When squaring, I've never done it like this.

Because we are squaring the sum and not individual terms.
_________________
Re: What is the area of the rectangular region above? &nbs [#permalink] 26 Jul 2018, 20:20
Display posts from previous: Sort by

Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.