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PS(Geometry)

by rintoo22 » Sat Apr 06, 2013 12:20 pm
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

How to approach such questions ?
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by Brent@GMATPrepNow » Sat Apr 06, 2013 1:02 pm
rintoo22 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

How to approach such questions ?
The key information here is measured to the nearest centimeter.
So, the sides do not necessarily have length 6.
In fact 5.5 < (length of 1 side) < 6.5

We want the smallest possible area. This will occur when the side lengths are minimized.
The shortest length of each side is 5.5 cm.
So, the smallest possible area = (5.5)(5.5) = [spoiler]30.25 = D[/spoiler]

Cheers,
Brent
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by srcc25anu » Sat Apr 06, 2013 1:14 pm
SIde of square measured to nearest integer = 6
therefore the size could range from 5.5 - 6.4
for area of this square to be the smalles we should consider the smallest number which is 5.5
and if side = 5.5, area of square = 5.5 * 5.5 = 30.25
Hence D
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by bharat.bondalapati » Sun Apr 07, 2013 5:02 am
30.25

Key info is "measured to the nearest cm". Since, we need the least area possible for the square the least side length possible is 5.5. Hence, least area possible is 30.25cm^2
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by Brent@GMATPrepNow » Sun Apr 07, 2013 5:16 am
As an aside, notice that the question requires us to find (5.5)^2
This is the same as squaring 55 to get 3025 and then moving the decimal over 2 spaces to get 30.25

If anyone is interested, there's a 3-second technique for squaring numbers ending in 5. To learn this technique, watch our free video: https://www.gmatprepnow.com/module/gmat- ... ts?id=1024

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