The sides of a square region, measured to the nearest centimeter, are

Question

The sides of a square region, measured to the nearest centimeter, 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

PS50750.02

Archit3110 · Accepted Answer

least of 6cm value rounded off at 5.5 cm
so area of 5.5 sided square = (5.5)^2 ; 30.25 cm^2
OPTION D:

GMATinsight · Answer

Screenshot 2020-04-23 at 6.32.21 PM.png

rahulbhusan · Answer

As the questions is asking for   least possible area of the square region   
so, Min side length of square= 5.5 cm  
Least area = (5.5)^2
=> 30.25 CM^2
 (Option D)

Nipunh1991 · Answer

Measured to the nearest centimetre 6 cm long could be a value rounded in the range of 5.5 cm- 6.4cm (All of value from 5.5 to 6.4 when rounded will be considered 6)

Since we want the least area of the square, we will consider the lowest value i.e 5.5

Area of Square = side^2
= 5.5 ^2
= 30.25 sq cm

ScottTargetTestPrep · Answer

The least side length of the square is 5.5 cm long (notice that 5.5 cm can be rounded to 6 cm when rounded to the nearest centimeter), so the least possible value of the area of the square is 5.5^2 = 30.25 sq cm.

Answer: D

perfectreview · Answer

Here tests the concepts of rounding off.

The possible values are

5.5 when rounded of it is 6
5.6 when rounded of it is 6
5.7 when rounded of it is 6
5.8 when rounded of it is 6
5.9 when rounded of it is 6

If the area has to be least then the possible value has to be least.

So the least possible value is 5.5 cm.

least area of a square =  (5.5)^{2}  =  30.25

Therefore answer is  Options D

SimplyBrilliant · Answer

To minimize the area, minimize the length of the side of the square so that when rounded to the nearest cm, the side is 6cm. That minimum length is 5.5cm.

So the least possible area is 5.5 x 5.5 cm ^2 . Yes, it's 55 x 55, then move the decimal twice to the left, but this is a perfect example of the kind of calculation that can be done more easily with fractions.

(\frac{11}{2})^2 = \frac{121}{4} = 30\frac{1}{4} = 30.25

Answer D

99.9% of the time, the GMAT is not going to make you prove you can do long multiplication or long division!

CrackverbalGMAT · Answer

SOLUTION :

A NEW OG 2021 QUESTION

As the side is exactly NOT 6,the area is exactly NOT 36 too and hence (A) can be eliminated.

Any number greater than or equal to 5.5 can be rounded off to 6.

=>The minimum side length to check for is 5.5.

(5.5)^2 = 30.25 is the minimum area with minimum side length of 5.5 (OPTION D)

Hope this helps

Devmitra Sen (Math)

CEdward · Answer

Rounding rules. 6 is the result of x rounded to the nearest cm which means x is as small as 5.5.

5.5^2 = 30.25

Answer is D.

GMATinsight · Answer

Answer: Option D

Video solution by  GMATinsight

https://www.youtube.com/watch?v=GnqsRCEU8M0

leonkarsten · Answer

Remember side x side = area, or rather side x side = side^2

The question is asking which (of the) alternatives'  roots  can be rounded to 6.0cm & then would be the the least of the squares.

So, option E (25) has a root of 5, meaning 5x5=25. As 5.0 cannot be rounded to 6.0cm, it will not be considered. We only need to focus on options A, B, C or D.

Option D (30.25) has a root of 5.5cm - this can be rounded to 6.0cm, so we can consider it. It is also the least (possible) value, so D is the answer.

Thib33600 · Answer

I understand perfectly but how do you do 5.5^2 without a calculator?

Bunuel · Answer

There are many ways. One you can do 55^2 and move decimal place of the result two places to the left. Or you can do (11/2)^2 = 121/4, or (5 + 0.5)^2 =5^2 + 5 + 0.5^2. Finally you can approximate.

There are many ways to do 5.5^2 without a calculator. One way is to do 55^2 and then move the decimal place in the result two places to the left. Or you can do (11/2)^2 = 121/4, or (5 + 0.5)^2 = 5^2 + 250.5 + 0.5^2. You can also simply approximate the value.

bumpbot · Answer

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The sides of a square region, measured to the nearest centimeter, are

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