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

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

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04 Nov 2019, 00:52
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71% (01:34) correct 29% (01:38) wrong based on 72 sessions

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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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Re: Is the surface area of a rectangular carpet larger than 1000 square fe  [#permalink]

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04 Nov 2019, 01:36
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.

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Re: Is the surface area of a rectangular carpet larger than 1000 square fe  [#permalink]

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04 Nov 2019, 01:42
1
(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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Is the surface area of a rectangular carpet larger than 1000 square fe  [#permalink]

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Updated on: 05 Nov 2019, 03:27
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, 01:48.
Last edited by Archit3110 on 05 Nov 2019, 03:27, edited 1 time in total.
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Re: Is the surface area of a rectangular carpet larger than 1000 square fe  [#permalink]

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04 Nov 2019, 01:51
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!
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Re: Is the surface area of a rectangular carpet larger than 1000 square fe  [#permalink]

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04 Nov 2019, 01:52
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
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Re: Is the surface area of a rectangular carpet larger than 1000 square fe  [#permalink]

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04 Nov 2019, 04:38
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.

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Re: Is the surface area of a rectangular carpet larger than 1000 square fe  [#permalink]

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04 Nov 2019, 04:54
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.
$$x=25:x^2+y^2=50^2…y^2=2500-625=1875…y=\sqrt{1875}=25\sqrt{3}…xy=aprox(625*1.7)>1000$$

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Re: Is the surface area of a rectangular carpet larger than 1000 square fe  [#permalink]

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04 Nov 2019, 05:05
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
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Re: Is the surface area of a rectangular carpet larger than 1000 square fe  [#permalink]

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04 Nov 2019, 15:18
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.

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Re: Is the surface area of a rectangular carpet larger than 1000 square fe  [#permalink]

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04 Nov 2019, 18:14
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.
Re: Is the surface area of a rectangular carpet larger than 1000 square fe   [#permalink] 04 Nov 2019, 18:14
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