Is the value of the perimeter of rectangle R greater than

Question

Is the value of the perimeter of rectangle R greater than the value of its area?

(1) The width of rectangle R is 2 inches.

(2) The area of rectangle R is 200 square inches.

kp1811 · Answer

stmnt1 - 
area = l*w = 2l
perimeter = 2  = 2l + 4. So perimeter is always greater than Area. hence Suff

stmnt2-
Area= l*w = 200
here l can be 20 and w= 10 giving perimeter as 2(20+10) = 60. So perimeter is less than Area

now lets consider l = 200 and w=1 giving Area = 200 and perimeter as 2(100+1) = 202. So perimeter value is greater than Area value. 
No single answer. hence insuff

Ans A

fozzzy · Answer

Really Tricky! good question...

Bunuel · Answer

Is the value of the perimeter of rectangle R greater than the value of its area?

Is 2(L+W)>LW ?

(1) The width of rectangle R is 2 inches --> W=2. The question becomes: is 2(L+2)>2L? --> is 2>0? The answer is YES. Sufficient.

(2) The area of rectangle R is 200 square inches --> LW=200. The question becomes: is 2(L+W)>200? --> is L+W>100. We don't know that. Not sufficient.

Answer: A.

GittinGud · Answer

Bunuel  Is the length of a rectangle always greater than the width? If so, then A is the answer, else, the answer would be C. Thanks!

TestPrepUnlimited · Answer

Is 2(L+W) > LW ?

1) W=2. Then the question becomes
Is 2(L+2) > 2L?
Is L+2 > L?
Is 2 > 0?
Yes.

2) If LW=200, we can substitute into the original question:
Is 2(L+W) > LW ?
Is 2(L+W) > 200 ?
Is L+W > 100 ?
We need information about L and W. Insufficient.

OA: A

GittinGud · Answer

That is only true if L>W. If W=2 and L=1, then A=2 and P=6 --> A<P

TestPrepUnlimited · Answer

You raise a valid point, theoretically speaking. Practically, however, I do not recall seeing any official GMAT questions in which width > length.

Bunuel · Answer

Yes. The length of a rectangle is the measure of its longest side. So, the length is never smaller than the width. For example, check here: https://mathworld.wolfram.com/Length.html

prabsahi · Answer

Nice question.

Let l be the length and b be the width.

Note: Its not comparing the perimeter and area..Its comparing the value of those things. 
 
Given b= 2

area=  2*x

perimiter= 2(l+b)= 2(x+2) =  2l+ 4

Clearly 4l+2 will always be greater than 2l

So statement 1 is sufficient.

STAT2:

Now area= 200
implies l*b = 200

We have no information about l or b .

Say when l=200 and B=1 area=200 and perimeter is 402 So here area< perimeter
Say when l=20 and B=10 area=200 and perimeter is 60 So here area> perimeter

So statement 2 is insufficient.

Therfore,I would chose A.

Hope it helps!!

Is the value of the perimeter of rectangle R greater than

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Is the value of the perimeter of rectangle R greater than

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