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Least possible problem - Tough numbers problem

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Least possible problem - Tough numbers problem

by just4myself » Mon Aug 25, 2008 8:57 am
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
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by pepeprepa » Mon Aug 25, 2008 9:04 am
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
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by parallel_chase » Mon Aug 25, 2008 9:05 am
Rounded to the nearest 6 cms
least possible value = 5.5

Least possible area = 5.5*5.5 =30.25

D
Last edited by parallel_chase on Mon Aug 25, 2008 9:23 am, edited 1 time in total.
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by pepeprepa » Mon Aug 25, 2008 9:11 am
Chase, you don't make difference between rounded to and nearest ?
I think there was a question which was based on it.
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by just4myself » Mon Aug 25, 2008 9:13 am
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?
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by parallel_chase » Mon Aug 25, 2008 9:15 am
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.
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by pepeprepa » Mon Aug 25, 2008 9:22 am
But do you think the question is wrong?
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by Ian Stewart » Mon Aug 25, 2008 11:52 am
pepeprepa wrote:But do you think the question is wrong?
There is nothing wrong with the question, as written. When you write this:
pepeprepa wrote: 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.
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by pepeprepa » Mon Aug 25, 2008 1:34 pm
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...
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