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

 It is currently 18 Sep 2018, 16:30

### 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 rectangular region R? 1. Each diagonal

Author Message
Manager
Joined: 05 Sep 2007
Posts: 144
Location: New York
What is the area of rectangular region R? 1. Each diagonal  [#permalink]

### Show Tags

17 Feb 2008, 17:17
1
2
00:00

Difficulty:

35% (medium)

Question Stats:

73% (00:46) correct 27% (01:05) wrong based on 75 sessions

### HideShow timer Statistics

What is the area of rectangular region R?

1. Each diagonal of R has length 5.
2. the perimeter of R is 14.
Manager
Joined: 20 Dec 2004
Posts: 249
Re: What is the area of rectangular region R? 1. Each diagonal  [#permalink]

### Show Tags

17 Feb 2008, 18:59
el1981 wrote:
What is the area of rectangular region R?
1. Each diagonal of R has length 5.
2. the perimeter of R is 14.

1) $$L^2+B^2 = 25$$ -- Not sufficient

2) $$2 (L+B) = 14$$ => $$L+B = 7$$ -- Not sufficient

But with both 1 & 2 $$L^2+B^2 = 25$$ => $$(L+B)^2 - 2(L*B) = 25$$ => $$L*B = \frac{(49 - 25)}{2}$$
_________________

Stay Hungry, Stay Foolish

VP
Joined: 28 Dec 2005
Posts: 1473
Re: What is the area of rectangular region R? 1. Each diagonal  [#permalink]

### Show Tags

17 Feb 2008, 19:59
since we know its a rectangle, and we know the length of the diagonal is 5, cant we say that the other two sides are 3 and 4 ?

if so, then the answer is A
Director
Joined: 12 Jul 2007
Posts: 850
Re: What is the area of rectangular region R? 1. Each diagonal  [#permalink]

### Show Tags

17 Feb 2008, 20:09
pmenon wrote:
since we know its a rectangle, and we know the length of the diagonal is 5, cant we say that the other two sides are 3 and 4 ?

if so, then the answer is A

That's assuming the sides and diagonal form a perfect square. We can't assume that.
VP
Joined: 28 Dec 2005
Posts: 1473
Re: What is the area of rectangular region R? 1. Each diagonal  [#permalink]

### Show Tags

17 Feb 2008, 20:15
oh, okay. i had thought that with rectangles, their corners were always 90 degrees. I guess we cant assume that because of shapes like rhombuses, etc ?

edit: wait a sec, if the corners arent 90 degrees, then why can we use pythagorean theorem and say that ^2+b^2 = 5 ?
Director
Joined: 12 Jul 2007
Posts: 850
Re: What is the area of rectangular region R? 1. Each diagonal  [#permalink]

### Show Tags

17 Feb 2008, 20:58

3-4-5 triangle works for an area of 12 (3*4)

but so does:

sqrt(20)-sqrt(5)-5 because 20+5 = 25 and that would give you an area of 10

so yes, it has a 90 degree angle, but you need to know more about the side lengths to get an area.
Manager
Joined: 05 Sep 2007
Posts: 144
Location: New York
Re: What is the area of rectangular region R? 1. Each diagonal  [#permalink]

### Show Tags

18 Feb 2008, 14:50
neelesh wrote:
el1981 wrote:
What is the area of rectangular region R?
1. Each diagonal of R has length 5.
2. the perimeter of R is 14.

1) $$L^2+B^2 = 25$$ -- Not sufficient

2) $$2 (L+B) = 14$$ => $$L+B = 7$$ -- Not sufficient

But with both 1 & 2 $$L^2+B^2 = 25$$ => $$(L+B)^2 - 2(L*B) = 25$$ => $$L*B = \frac{(49 - 25)}{2}$$

neelesh, could you please clarify why 1&2 sufficient. Thanks.
Manager
Joined: 20 Dec 2004
Posts: 249
Re: What is the area of rectangular region R? 1. Each diagonal  [#permalink]

### Show Tags

18 Feb 2008, 19:22
el1981 wrote:
neelesh wrote:
el1981 wrote:
What is the area of rectangular region R?
1. Each diagonal of R has length 5.
2. the perimeter of R is 14.

1) $$L^2+B^2 = 25$$ -- Not sufficient

2) $$2 (L+B) = 14$$ => $$L+B = 7$$ -- Not sufficient

But with both 1 & 2 $$L^2+B^2 = 25$$ => $$(L+B)^2 - 2(L*B) = 25$$ => $$L*B = \frac{(49 - 25)}{2}$$

neelesh, could you please clarify why 1&2 sufficient. Thanks.

Because I am taking the Statement 2 and using it in statement 1

$$L^2+B^2 = 25$$
=> $$L^2 + B^2 + 2(L*B) - 2(L*B) = 25$$
=> $$(L+B)^2 - 2(L*B) = 25$$
=> $$(7)^2 - 2(L*B) = 25$$ /* Using statement-2 */

Hence C.
_________________

Stay Hungry, Stay Foolish

Senior Manager
Joined: 06 Jul 2006
Posts: 278
Location: SFO Bay Area
Schools: Berkeley Haas
Re: What is the area of rectangular region R? 1. Each diagonal  [#permalink]

### Show Tags

19 Feb 2008, 01:17
pmenon wrote:
oh, okay. i had thought that with rectangles, their corners were always 90 degrees. I guess we cant assume that because of shapes like rhombuses, etc ?

edit: wait a sec, if the corners arent 90 degrees, then why can we use pythagorean theorem and say that ^2+b^2 = 5 ?

The angles of a rectangle are ALWAYS 90 degrees.

But if the hypo is 5, its not necessary that the other two sides will always be 3 and 4.
Director
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 546
Re: What is the area of rectangular region R? 1. Each diagonal  [#permalink]

### Show Tags

20 May 2011, 12:09
1) L^2 + W^2 = 25 Not sufficient

2) L + W = 7 Not sufficient

But with both 1 & 2
(L+W)^2 = 7^2
=> L^2 +W^2 = 49
=> L^2 +W^2 + 2LW = 49
=> 25+ LW = 49
=> 2LW = 49 – 25
=> LW = 12

Ans. C
_________________

Collections:-
PSof OG solved by GC members: http://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html
DS of OG solved by GC members: http://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html
100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html
Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html
Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html

Intern
Joined: 17 May 2011
Posts: 2
Re: What is the area of rectangular region R? 1. Each diagonal  [#permalink]

### Show Tags

20 May 2011, 17:12
Rectangle is a parallelogram of which all angles are 90 degree, and opposite sides are equal.

So, two sides of the rectangle are 3 and 4. Therefore, we can derive the area of rectangle from option 1 making it sufficient enough.

But option 2 alone is not sufficient.

_________________

~BM

Retired Moderator
Joined: 20 Dec 2010
Posts: 1869
Re: What is the area of rectangular region R? 1. Each diagonal  [#permalink]

### Show Tags

20 May 2011, 17:47
bibhas wrote:
Rectangle is a parallelogram of which all angles are 90 degree, and opposite sides are equal.

So, two sides of the rectangle are 3 and 4. Therefore, we can derive the area of rectangle from option 1 making it sufficient enough.

But option 2 alone is not sufficient.

According to you; Area=3*4=12

What if:
one side$$=1$$; other side$$=4\sqrt{6}$$ and hypotenuse$$=5$$
$$Area = 1*4\sqrt{6}=4\sqrt{6}$$

OR

one side$$=\sqrt{12.5}$$; other side$$=\sqrt{12.5}$$ and hypotenuse$$=5$$
$$Area = \sqrt{12.5}*\sqrt{12.5}=12.5$$

There are infinite such possibilities because we are NOT GIVEN THAT SIDES ARE INTEGERS.

OA: "C" is correct.
_________________
Intern
Joined: 17 May 2011
Posts: 2
Re: What is the area of rectangular region R? 1. Each diagonal  [#permalink]

### Show Tags

20 May 2011, 18:07
Your option cannot form a triangle and second option makes the parallelogram a Square (questions says Rectangular region). So neither of them is sufficient enough to justify your answer.
_________________

~BM

Retired Moderator
Joined: 20 Dec 2010
Posts: 1869
Re: What is the area of rectangular region R? 1. Each diagonal  [#permalink]

### Show Tags

20 May 2011, 18:33
bibhas wrote:
Your option cannot form a triangle and second option makes the parallelogram a Square (questions says Rectangular region). So neither of them is sufficient enough to justify your answer.

I meant to say; any combination of two positive numbers whose squares add up to 25 i.e. 5^2 will form a triangle with hypotenuse 5.

one side: $$2\sqrt{6}$$ and other side: $$1$$; hypotenuse: $$5$$

$$1^2+(2\sqrt{6})^2=5^2$$

And a square is a specialized rectangle in GMAT.
_________________
VP
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1098
Re: What is the area of rectangular region R? 1. Each diagonal  [#permalink]

### Show Tags

20 May 2011, 21:38
a+b gives,

l^2 -7l + 12 = 0 l = length

(l-3)(l-4)=0
hence lw = 12 in either cases, as l+w = 7.

C
_________________

Visit -- http://www.sustainable-sphere.com/
Promote Green Business,Sustainable Living and Green Earth !!

Intern
Joined: 10 May 2011
Posts: 6
Re: What is the area of rectangular region R? 1. Each diagonal  [#permalink]

### Show Tags

23 Jun 2011, 11:52
fluke wrote:
bibhas wrote:
Your option cannot form a triangle and second option makes the parallelogram a Square (questions says Rectangular region). So neither of them is sufficient enough to justify your answer.

I meant to say; any combination of two positive numbers whose squares add up to 25 i.e. 5^2 will form a triangle with hypotenuse 5.

one side: $$2\sqrt{6}$$ and other side: $$1$$; hypotenuse: $$5$$

$$1^2+(2\sqrt{6})^2=5^2$$

And a square is a specialized rectangle in GMAT.

Hi ,
Your statement "any combination of two positive numbers whose squares add up to 25 i.e. 5^2 will form a triangle with hypotenuse 5. " is not true if its a right angle traingle with diagonal as 5. as per Pythagoras theorem other 2 sides should be 3 and 4 so A is sufficient alone
Pl clarify incase I am missing anything
Current Student
Joined: 26 May 2005
Posts: 525
Re: What is the area of rectangular region R? 1. Each diagonal  [#permalink]

### Show Tags

23 Jun 2011, 12:01
sameershintrein wrote:
fluke wrote:
bibhas wrote:
Your option cannot form a triangle and second option makes the parallelogram a Square (questions says Rectangular region). So neither of them is sufficient enough to justify your answer.

I meant to say; any combination of two positive numbers whose squares add up to 25 i.e. 5^2 will form a triangle with hypotenuse 5.

one side: $$2\sqrt{6}$$ and other side: $$1$$; hypotenuse: $$5$$

$$1^2+(2\sqrt{6})^2=5^2$$

And a square is a specialized rectangle in GMAT.

Hi ,
Your statement "any combination of two positive numbers whose squares add up to 25 i.e. 5^2 will form a triangle with hypotenuse 5. " is not true if its a right angle traingle with diagonal as 5. as per Pythagoras theorem other 2 sides should be 3 and 4 so A is sufficient alone
Pl clarify incase I am missing anything

Pythagoras theorem says ..
Hyp^2 = sum of the squares of other 2 sides..
it never said the all the sides are phythagoras triplets like 3,4,5 and 9,12,15
so if the hyp = 5, yes its easier to assume that other 2 sides follow the triplet format and are 3 and 4
but nothing stops us from assuming that they can be 1 and 2 sqrt 6.
Retired Moderator
Joined: 20 Dec 2010
Posts: 1869
Re: What is the area of rectangular region R? 1. Each diagonal  [#permalink]

### Show Tags

23 Jun 2011, 12:14
sameershintrein wrote:
fluke wrote:
bibhas wrote:
Your option cannot form a triangle and second option makes the parallelogram a Square (questions says Rectangular region). So neither of them is sufficient enough to justify your answer.

I meant to say; any combination of two positive numbers whose squares add up to 25 i.e. 5^2 will form a triangle with hypotenuse 5.

one side: $$2\sqrt{6}$$ and other side: $$1$$; hypotenuse: $$5$$

$$1^2+(2\sqrt{6})^2=5^2$$

And a square is a specialized rectangle in GMAT.

Hi ,
Your statement "any combination of two positive numbers whose squares add up to 25 i.e. 5^2 will form a triangle with hypotenuse 5. " is not true if its a right angle traingle with diagonal as 5. as per Pythagoras theorem other 2 sides should be 3 and 4 so A is sufficient alone
Pl clarify incase I am missing anything

3,4,5 is just one of the infinite possibilities.

Why don't you draw it and see it yourself.

Draw a horizontal line-segment(AB) of 1 unit . Draw a perpendicular ray directly upward from point A. Now, using divider pointing at point B, and setting the divider to 5 units, make a small arc so that it cuts the ray at some point, say C. Join BC. You now have a right triangle with hypotenuse 5, one side 1 unit, and another side $$\sqrt{5^2-1} = \sqrt{24}= 2 \sqrt{6} \approx 4.9$$

Like this, we have infinite possibilities because there are infinite real numbers between 0 and 5, exclusive.
_________________
Director
Joined: 01 Feb 2011
Posts: 670
Re: What is the area of rectangular region R? 1. Each diagonal  [#permalink]

### Show Tags

23 Jun 2011, 22:35
1. Not sufficient

l^2+w^2 = 25

l ,w can have different values . for different values we will have different areas.

2. Not sufficient

we know the l+w =7,

still we can chose different combinations of l , w and different values yield different area.

together,

consider (l+w)^2 = l^2+w^w+2lw
we can find lw with the values we have from 1 and 2.

Math Expert
Joined: 02 Sep 2009
Posts: 49206
Re: What is the area of rectangular region R? 1. Each diagonal  [#permalink]

### Show Tags

01 Jul 2018, 21:13
el1981 wrote:
What is the area of rectangular region R?

1. Each diagonal of R has length 5.
2. the perimeter of R is 14.

What is the area of rectangular region R?

Let the sides of the rectangle be $$x$$ and $$y$$. Question: $$area=xy=?$$

(1) Each diagonal of R has length 5 --> as the diagonals in a rectangle are the hypotenuses for the sides then: $$x^2+y^2=5^2$$, but we can not get the value of $$xy$$ from this info. Not sufficient.

(2) The perimeter of R is 14 --> $$P=2(x+y)=14$$ --> $$x+y=7$$. Again we can not get the value of $$xy$$ from this info. Not sufficient.

(1)+(2) We have $$x^2+y^2=25$$ and $$x+y=7$$. Square the second expression: $$x^2+2xy+y^2=49$$, as $$x^2+y^2=5^2$$ then $$25+2xy=49$$ --> $$xy=12$$. Sufficient.

OPEN DISCUSSION OF THIS QUESTION IS HERE: http://gmatclub.com/forum/what-is-the-a ... 66186.html

_________________
Re: What is the area of rectangular region R? 1. Each diagonal &nbs [#permalink] 01 Jul 2018, 21:13
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®.