Least possible problem - Tough numbers problem

[just4myself]

The sides of a square region measured to the nearest centimeters, are 6 centimeters long. The least possible value of the actual area of the square region is :
A) 36.00 sq. cm
B) 35.00 sq. cm
C) 33.75 sq. cm
D) 30.25 sq. cm
E) 25.00 sq. cm

Please write your explanation...

Will post the OA tomo...

Thank you

[pepeprepa]

Well like that, I would have answered 5.6*5.6 because when we say "to the nearest " centimer, 5.5 is as close as 5 as to 6. The question is badly wrote for me and should say"rounded to the centimer" if they want us to find 5.5*5.5
But anyway you don't have 5.6*5.6
so it is 5.5*5.5=30.25

[parallel_chase]

Rounded to the nearest 6 cms
least possible value = 5.5

Least possible area = 5.5*5.5 =30.25

D

[pepeprepa]

Chase, you don't make difference between rounded to and nearest ?
I think there was a question which was based on it.

[just4myself]

Yes D is the right answer...
But did u eliminate the possibility of the side being 5.9 cm, just by looking at the answer choices?

[parallel_chase]

pepeprepa you are absolutely right i meant rounded to 6cm
least possible value =5.5 cms

I didnt looked at 5.9

I calculated 5.6 first, then realized 5.5 can also be rounded to 6.

[pepeprepa]

But do you think the question is wrong?

[Ian Stewart]

But do you think the question is wrong?

There is nothing wrong with the question, as written. When you write this:

Well like that, I would have answered 5.6*5.6 because when we say "to the nearest " centimer, 5.5 is as close as 5 as to 6.

you are correct that 5.5 is as close to 5 as it is to 6. Still, even if you do not accept that 5.5 should round off to 6, the length of a side can be as close to 5.5 as you like; there is no reason to assume we have one decimal point precision here. The length of each side could be

5.500000000000000000000000001

for example.

[pepeprepa]

The point I noticed from the following https://www.beatthegmat.com/x-and-y-t15125.html

Am I wrong on this difference between closest/rounded ?
closest integer of x+y is 4
3.5<x+y<4.5
x+y rounded to the unit gives 4
3.5 <= x+y <= 4.5

I understand the least possible value can be "5.500000000000000000000000001", very close to 5, but I don't understand the result question gives the feeling it is exactly 5.5 and not an approximation...