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

Question

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.

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unraveled · Answer

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.

IMO Answer C.

CareerGeek · Answer

(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

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Archit3110 · Answer

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

sampriya · Answer

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!

vg18 · Answer

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

eakabuah · Answer

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.

The answer is therefore C.

exc4libur · Answer

(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

Answer (C)

madgmat2019 · Answer

(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

suchithra · Answer

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.

C is the Answer.

BelalHossain046 · Answer

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.

ShankSouljaBoi · Answer

You are wrongly rephrasing the stem...

it shd be L.B > 1000

AnirudhaS · Answer

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.

sameerm22 · Answer

Technically, Root2 is an irrational number! So, you cannot have any side such 25\sqrt{2}! Also, it's not possible to have a side "close to 0". There is not such thing defined..."close to 0". It can be 0.001 or 0.000001....in all such cases diagonal is not 50 accurately! If the Question was asking approximate, then those options are possible.

So, with how Q is worded, option should be A!

So, with how Q is worded, option should be A!

Bunuel · Answer

The length can be irrational. For example, a square with side length of 1, will have its diagonal equal to  \sqrt{2} .

Louis14 · Answer

Wouldn't a fixed length of the diagonal fix the length and breadth?

VeritasKarishma   IanStewart

IanStewart · Answer

For a square, yes, but for a rectangle, no, not at all. If you have a diagonal, say, of length 10, you might have sides of 6 and 8, or you might have sides of 5 and 5√3, or you might have a square with sides of 5√2 and 5√2, among many other possibilities.

I assume this is just a badly-written question, and the solutions above are probably all correctly guessing its intended meaning. But "surface area" is a 3-dimensional concept. To find the "surface area" of this carpet, we'd need to add the areas of both sides of the carpet, along with any small area we get around the edges because of the carpet's height. I doubt that's what the question means -- it probably just means to ask about ordinary "area" -- but the answer is C no matter how you interpret it.

Louis14 · Answer

Thanks for your prompt response. You're always extremely helpful, sir!

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

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