PS(Geometry)

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rintoo22: Senior | Next Rank: 100 Posts; Posts: 73; Joined: Sun May 06, 2012 2:19 am; Location: Cape Town; Thanked: 6 times

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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Source: Beat The GMAT — Problem Solving | Sat Apr 06, 2013 12:20 pm

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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

Brent Hanneson - Creator of GMATPrepNow.com

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srcc25anu: Master | Next Rank: 500 Posts; Posts: 423; Joined: Fri Jun 11, 2010 7:59 amFollowed by: 2 members; Location: Seattle, WA; Thanked: 86 times

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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bharat.bondalapati: Junior | Next Rank: 30 Posts; Posts: 14; Joined: Fri Apr 05, 2013 11:56 pm; Thanked: 3 times

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

Best,
Bharat

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GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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