The sides of a square region, measured to the nearest centimeter, are : Problem Solving (PS)

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gmatt1476

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The sides of a square region, measured to the nearest centimeter, are [#permalink]

20 Apr 2020, 12:51

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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

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Re: The sides of a square region, measured to the nearest centimeter, are [#permalink]

21 Apr 2020, 11:24

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gmatt1476 wrote:

The sides of a square region, measured to the nearest centimeter, are 6 centimeters long. The least possible 8 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

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:

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Re: The sides of a square region, measured to the nearest centimeter, are [#permalink]

23 Apr 2020, 06:07

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gmatt1476 wrote:

The sides of a square region, measured to the nearest centimeter, are 6 centimeters long. The least possible 8 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

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rahulbhusan

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Re: The sides of a square region, measured to the nearest centimeter, are [#permalink]

22 Apr 2020, 06:25

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gmatt1476 wrote:

The sides of a square region, measured to the nearest centimeter, are 6 centimeters long. The least possible 8 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

As the questions is asking for least possible area of the square region
so, Min side length of square= 5.5 cm [As 6 is the side length rounded to the nearest centimetre]
Least area = (5.5)^2
=> 30.25 CM^2
(Option D)

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Nipunh1991

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Re: The sides of a square region, measured to the nearest centimeter, are [#permalink]

29 Apr 2020, 14:00

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gmatt1476 wrote:

The sides of a square region, measured to the nearest centimeter, are 6 centimeters long. The least possible 8 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

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

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ScottTargetTestPrep

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Re: The sides of a square region, measured to the nearest centimeter, are [#permalink]

30 Apr 2020, 03:44

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gmatt1476 wrote:

The sides of a square region, measured to the nearest centimeter, are 6 centimeters long. The least possible 8 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

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
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perfectreview

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Re: The sides of a square region, measured to the nearest centimeter, are [#permalink]

01 Jun 2020, 07:49

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

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Re: The sides of a square region, measured to the nearest centimeter, are [#permalink]

06 Jun 2020, 19:09

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gmatt1476 wrote:

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

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!

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CrackverbalGMAT

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The sides of a square region, measured to the nearest centimeter, are [#permalink]

12 Feb 2021, 03:42

Top Contributor

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)
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CEdward

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Re: The sides of a square region, measured to the nearest centimeter, are [#permalink]

12 Feb 2021, 23:49

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.
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Re: The sides of a square region, measured to the nearest centimeter, are [#permalink]

27 May 2021, 08:22

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gmatt1476 wrote:

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

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leonkarsten

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Re: The sides of a square region, measured to the nearest centimeter, are [#permalink]

09 Sep 2023, 01:15

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.

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Thib33600

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Re: The sides of a square region, measured to the nearest centimeter, are [#permalink]

28 Jan 2024, 18:54

Archit3110 wrote:

gmatt1476 wrote:

The sides of a square region, measured to the nearest centimeter, are 6 centimeters long. The least possible 8 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

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:

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

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Bunuel

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Re: The sides of a square region, measured to the nearest centimeter, are [#permalink]

29 Jan 2024, 00:05

Expert Reply

Thib33600 wrote:

Archit3110 wrote:

gmatt1476 wrote:

The sides of a square region, measured to the nearest centimeter, are 6 centimeters long. The least possible 8 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

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:

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

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.
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