If a rectangular region has perimeter P inches and area A sq

Question

If a rectangular region has perimeter P inches and area A square inches, is the region square?

(1) P = 4/3*A
(2) P = 4√A

hassan233 · Answer

It is a square iff the four sides are the same.
This means that if it is a square, the perimeter should be 4 * length of one side and that the area should be one of the equal sides squared.
This means the area of a square must be (P/4)^2
A = (P/4)^2
Now, let us take the statements and see if we can make either one of them look like A = (P/4)^2
Statement 1: P = 4/3 A => (3/4)P = A... this doesn't look right
Statement 2: P = 4*sqrt(A) => p/4 = sqrt(A) => A = (p/4)^2... this works!
Therefore, only statement one is will tell you the right answer.

Someone confirm my method?

hassan233 · Answer

upon further investigation of my own work, this will NOT work!
What I wrote for statement 1 shows that it is possible for it NOT to be a square, but does not show whether it CAN be a square. I need to do a 2-way proof (that is, show that with that equation it CAN be a square and can also NOT be a square). I did half of that. Not good enough because if it is NOT a square, it would still be sufficient since I would be able to answer the question. I need to prove that it does NOT have the potential to become a square, not just proof that it is possible that it is not a square.

For statement one, the work I showed still makes it clear that it can only be a square, since the four parameters would HAVE to be the same for the equation to work.

Aarav2706 · Answer

In statement 2; if all we have proved is x=y , then it could be a rhombus too right? Without knowing if the angles are 90 degrees, how can we be certain?

Bunuel · Answer

We are told that the region is a rectangle. So, angles are 90 degrees. A rhombus with 90 degrees angles is a square.

jabhatta2 · Answer

Hi  avigutman  - i know this was discussed on quantreasoning.com

While I do understand this problem - i am still un-easy with my steps.

Whenever I feel this, i try to create a 'variation' of the original problem, to get a deeper understanding of the concept

But i am struggling to create a version of this problem

Can you perhaps think of one ? i want to see if i can have truly understood the concept of this problem

If you can't think of a variation, thats totally fine, no worries

Thank you

avigutman · Answer

jabhatta2  Can you articulate what your steps are? That should help you get a deeper understanding of the concept. 
And if you mess it up, that'll be a good learning opportunity.

jabhatta2 · Answer

hI  avigutman  - here is what i did for S1

For S1 - attached is what I did for S1 . Found that the length of the region (represented by 'a' can be  zero  or can be  three .

Now
-- a =  zero . That too me doesnt make sense and thus "a"=  zero  can be dropped as a possible value of 'a' 
-- Thus a = three only.

In Yes /No question - S1 should work for every value of "a". S1 only works when a = 3

Thus, Not sufficient.

jabhatta2 · Answer

My question was on S2

avigutman  - For S2, here is what I did

I am not sure what Zero = Zero represents (Specifically, how is zero=zero, different from a = zero, which is what i got in S1 and rejected)

I was not getting a value of "A" unlike in S1.

I think i was struggling because from S2 -- i was not getting values of "A"

Thus i wasnt sure what to make from S2 with regards to zero = zero.

avigutman · Answer

jabhatta2

Are you using the question as if it were a statement (assuming the answer to the question is YES, and using that as if it were known?), and then testing what that means for S1?
If so, that's data validation, not data sufficiency.

I'm not sure what you mean. The statements are always truthful. Again, seems like you're using the question to validate the statement.

Why is that not sufficient?

jabhatta2 · Answer

Hi  avigutman  - Yes, i think i was doing what you mentioned in the yellow

I am taking the question itself as 'TRUE' --> inserting it into the statements --> validating the statement instead  True  or  False ]

In the Case of validating S1 = i got  True   when length is 3 only. In case length was some other length, statement 1 would be  FALSE .  
 In case of the validating S2 -- I got S2 as  True , irrespective of the value of the length of the square

Do you mind discusing my process (regarding what i did) in the next AMA (if you believe this mistake is perhaps usefull for the class to know about) - validating statements.  Why is that not a legitimate strategy  - uneven results / perhaps an analogy for a question WHERE it wont work ?

Below is a simpler example and the process i followed

I think i thought like this because i followed   some version of    this process in another  quant question

jabhatta2 · Answer

Here is how i had solved S2 in the referenced question and i think i picked up this DS strategy because of this question

I think given i was allowed to do some version of 'going backwards' i thought i could do the same in the original question

avigutman · Answer

Now that we've discussed in the AMA, would you like to try to explain here the errors in your approach and how you'd attack the problem differently now,  jabhatta2 ?

jabhatta2 · Answer

Hi  avigutman  - last session on quantreasoning.com was very helpful. Here was my mistakes / insights from just this one problem

(a) my mistake was assuming the question as 'True'. Then plugging that information INTO S1 & S2 - That was a mistake. It should be the other way around

(b) The process should be instead
info from statement + free information == Can you proove the question

jabhatta2 · Answer

What i found interesting were the following insights

jabhatta2 · Answer

In fact  avigutman  --- i can make up a new problem and figure out whether the statement is sufficient

It is this kind of amazing insights that make quant reasoning AMA's unparallel in terms of building logic for prospective students

Arnaud6775 · Answer

It is given that it's a rectangular region, so we know it has 90-degree angles

Snehaaaaa · Answer

Let's assume the sides of the region as 2 and 2. If any of the equations satisfy we can consider that the rectangular region is a square
Perimeter = 2(2+2) = 8
Area =l*b = 2*2 = 4

1) P=4/3*A
8 = 4/3 * 4
24 is not equal to 16

2) P = 4\sqrt{A}
8 = 4\sqrt{4}
8 = 4*2
8=8
Correct Answer is B

mallika227 · Answer

Hi  Bunuel , Can you share more of such question types as you have done for various other question types ?

bumpbot · Answer

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If a rectangular region has perimeter P inches and area A sq

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If a rectangular region has perimeter P inches and area A sq

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