GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 18 Feb 2020, 23:40 ### 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.  # Is the surface area of a rectangular carpet larger than 1000 square fe

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 61286
Is the surface area of a rectangular carpet larger than 1000 square fe  [#permalink]

### Show Tags

2
1 00:00

Difficulty:   45% (medium)

Question Stats: 66% (01:37) correct 34% (01:43) wrong based on 140 sessions

### HideShow timer Statistics

Competition Mode Question

Is the surface area of a rectangular carpet larger than 1000 square feet?

(1) The carpet measures fifty feet diagonally.
(2) One side of the carpet measures twenty five feet.

Are You Up For the Challenge: 700 Level Questions

_________________
Director  D
Joined: 07 Mar 2019
Posts: 688
Location: India
GMAT 1: 580 Q43 V27
WE: Sales (Energy and Utilities)
Re: Is the surface area of a rectangular carpet larger than 1000 square fe  [#permalink]

### Show Tags

1
Is the surface area of a rectangular carpet larger than 1000 square feet?
Let sides are a and b.
So, Area = a * b > 1000 ?

(1) The carpet measures fifty feet diagonally.
Possible Sides are
1, 49.9~ Area > 1000 NO
30, 40 Area > 1000 YES

INSUFFICIENT.

(2) One side of the carpet measures twenty five feet.
Possible sides are
25, 1 Area > 1000 NO
25, 41 Area > 1000 YES

INSUFFICIENT.

Together 1 and 2
Sides possible are
25, 43.3~ Area > 1000 YES

SUFFICIENT.

_________________
Ephemeral Epiphany..!

GMATPREP1 590(Q48,V23) March 6, 2019
GMATPREP2 610(Q44,V29) June 10, 2019
GMATPREPSoft1 680(Q48,V35) June 26, 2019
VP  V
Joined: 20 Jul 2017
Posts: 1321
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: Is the surface area of a rectangular carpet larger than 1000 square fe  [#permalink]

### Show Tags

2
(1) The carpet measures fifty feet diagonally.
Minimum area is close to zero (when length is close to 50 and breadth close to 0)

Maximum area is possible when rectangle is a square
—> Max. Area = $$1/2(diagonal)^2 = 1/2*50*50 = 1250$$

Two outcomes are possible.—> Insufficient

(2) One side of the carpet measures twenty five feet.
—> We do not know about the other side. No definite value
—> Insufficient

Combining (1) &(2),
—> other side = $$\sqrt{50^2 - 25^2}$$
= $$\sqrt{3*25^2}$$
—> Other side = $$25\sqrt{3}$$

Area = $$25*25\sqrt{3}$$
—> A definite value
—> Sufficient

IMO Option C

Posted from my mobile device
GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 5931
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Is the surface area of a rectangular carpet larger than 1000 square fe  [#permalink]

### Show Tags

Is the surface area of a rectangular carpet larger than 1000 square feet?

(1) The carpet measures fifty feet diagonally.
(2) One side of the carpet measures twenty five feet.

#1
diagonal - 50
the rectangle can be square ;
so side = 25√2
area = 1250 as value of area may be< 1250 as well
insufficient
#2
One side of the carpet measures twenty five feet.
other can be <25 or =25 or >25
we get yes and no
insufficient
from 1&2
one side know and digonal value know
third side can be determined
IMO C

Originally posted by Archit3110 on 04 Nov 2019, 00:48.
Last edited by Archit3110 on 05 Nov 2019, 02:27, edited 1 time in total.
Senior Manager  G
Joined: 23 Nov 2018
Posts: 253
GMAT 1: 650 Q49 V28 GPA: 4
Re: Is the surface area of a rectangular carpet larger than 1000 square fe  [#permalink]

### Show Tags

2(L+B) >1000?

is L+B>500?

(1) The carpet measures fifty feet diagonally.
L^2+B^2= 225
L^2>L
B^2>B

therefore L+B<500- A is sufficient!

(2) One side of the carpet measures twenty five feet.
Option B is insufficient

option A is the correct option!
_________________
Manager  S
Joined: 30 Nov 2017
Posts: 62
GMAT 1: 690 Q49 V35
Re: Is the surface area of a rectangular carpet larger than 1000 square fe  [#permalink]

### Show Tags

1
Is the surface area of a rectangular carpet larger than 1000 square feet?

(1) The carpet measures fifty feet diagonally.
Therefore L*L+B*B=50*50
Scenario 1:
B=1, L=Sqrt(2499)=apx 50. Ans No
Scenario 2:
Maximum area is when L=B therefore, L=B=50/sqrt2, area= L*B=2500/2=1250. Ans Yes.

Insufficient

(2) One side of the carpet measures twenty five feet. Other side could be much greater or much smaller. Insufficient.

Together, we can find the third side and hence, the area. Sufficient. Ans: C
CR Forum Moderator P
Joined: 18 May 2019
Posts: 706
Re: Is the surface area of a rectangular carpet larger than 1000 square fe  [#permalink]

### Show Tags

1
We are to determine if the surface area of a rectangular carpet is larger than 1000sq.ft.

Statement 1: The carpet measures 50ft diagonally.
Insufficient. If the length and breadth of the carpet are l and b respectively, then l^2 + b^2 = 2500
Now if l=1ft, then b<50, and surface area, l*b < 50, and the answer is No.
however, if l=30, then b=40 and l*b = 1200, implying the answer is Yes.

Statement 2: One side of the carpet measures twenty-five feet.
Clearly insufficient. This is because the other side can be 10ft, in which case surface area is 250sq.ft, implying the answer is No.
However, if the other side is 100ft, then the surface area is 2500sq.ft, implying the answer is Yes.

1+2
This sufficient. We are able to determine the length of the other side from the equation \sqrt{(2500-625)}. From this, we can deduce that the surface area (1083sq.ft) is more than 1000sq.ft.

VP  P
Joined: 24 Nov 2016
Posts: 1207
Location: United States
Re: Is the surface area of a rectangular carpet larger than 1000 square fe  [#permalink]

### Show Tags

1
Quote:
Is the surface area of a rectangular carpet larger than 1000 square feet?

(1) The carpet measures fifty feet diagonally.
(2) One side of the carpet measures twenty five feet.

(1) The carpet measures fifty feet diagonally. insufic.

$$x^2+y^2=50^2…x^2+y^2=2500$$
$$x=20:x^2+y^2=50^2…y^2=2500-400=2100…y=10\sqrt{21}=aprox(46)…xy<1000$$
$$x=40:x^2+y^2=50^2…y^2=2500-1600=900…y=30…xy=40*30>1000$$

(2) One side of the carpet measures twenty five feet. insufic.

(1 & 2) sufic.
$$x=25:x^2+y^2=50^2…y^2=2500-625=1875…y=\sqrt{1875}=25\sqrt{3}…xy=aprox(625*1.7)>1000$$

Senior Manager  P
Joined: 01 Mar 2019
Posts: 438
Location: India
Concentration: Strategy, Social Entrepreneurship
Schools: Ross '22, ISB '20, NUS '20
GPA: 4
Re: Is the surface area of a rectangular carpet larger than 1000 square fe  [#permalink]

### Show Tags

1
(1) The carpet measures fifty feet diagonally.

The max area will be for a square....so if 50 is diagonal of a square then each side will be 25sqrt(2).....so max area will be 1250....from which we cannot say where its greater or less than 1000....so insufficient

(2) One side of the carpet measures twenty five feet.

clearly alone is not sufficient by knowing only one side

Combing both we can get the other side, from which we can get the area...

OA: C
Manager  G
Joined: 31 Oct 2015
Posts: 95
Re: Is the surface area of a rectangular carpet larger than 1000 square fe  [#permalink]

### Show Tags

1
Question : Is lb > 1000

a) Diagonal is 50
The sides of the triangle that fulfill Diagonal 50 could be 49 & 9,95ish(In this case answer is no to above Question) or 30 &40(the answer is Yes)
A is insufficient

B) One of the sides is 25
Insufficient since 25x2 = 50 (the answer to above Question is No) and 25x50=1250(The answer is Yes)

Both statements together, we can see that we can calculate the other side of rectangle. Sufficient.

Current Student G
Joined: 11 Feb 2013
Posts: 274
Location: United States (TX)
Schools: Neeley '21 (A\$)
GMAT 1: 490 Q44 V15 GMAT 2: 690 Q47 V38 GPA: 3.05
WE: Analyst (Commercial Banking)
Re: Is the surface area of a rectangular carpet larger than 1000 square fe  [#permalink]

### Show Tags

I would go for A.
From the given diagonal, we can have maximum area if rectangle Is a square.
So, if the diagonal of the square is 50, maximum surface area is 100*root 2.=141
So, we have max surface area which is lower than 1000.
Sufficient.
Statement 2 provides no info about other side.
Senior Manager  P
Joined: 21 Jun 2017
Posts: 412
Location: India
Concentration: Finance, Economics
Schools: IIM
GMAT 1: 620 Q47 V30
GPA: 3
WE: Corporate Finance (Commercial Banking)
Is the surface area of a rectangular carpet larger than 1000 square fe  [#permalink]

### Show Tags

sampriya wrote:
2(L+B) >1000?

is L+B>500?

(1) The carpet measures fifty feet diagonally.
L^2+B^2= 225
L^2>L
B^2>B

therefore L+B<500- A is sufficient!

(2) One side of the carpet measures twenty five feet.
Option B is insufficient

option A is the correct option!

You are wrongly rephrasing the stem...

it shd be L.B > 1000
Manager  S
Joined: 30 Oct 2019
Posts: 108
Location: United Kingdom
Concentration: General Management, Technology
GPA: 4
Is the surface area of a rectangular carpet larger than 1000 square fe  [#permalink]

### Show Tags

1
ShankSouljaBoi wrote:
sampriya wrote:
2(L+B) >1000?

is L+B>500?

(1) The carpet measures fifty feet diagonally.
L^2+B^2= 225
L^2>L
B^2>B

therefore L+B<500- A is sufficient!

(2) One side of the carpet measures twenty five feet.
Option B is insufficient

option A is the correct option!

You are wrongly rephrasing the stem...

it shd be L.B > 1000

Thanks man, this was bugging me for 5 minutes and was contemplating whether to point out the error or not. Thanks for doing this, else it would have bothered me for a long loooong time. Is the surface area of a rectangular carpet larger than 1000 square fe   [#permalink] 30 Dec 2019, 02:01
Display posts from previous: Sort by

# Is the surface area of a rectangular carpet larger than 1000 square fe  