the cube in inches?

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Mon Oct 24, 2011 3:54 am

Volume of a cube is x cubic yards and its surface area is y square feet. If x = y, what is the length of each edge of the cube in inches?
(A) 54
(B) 216
(C) 432
(D) 864
(E) 1944

Last edited by sanju09 on Mon Oct 24, 2011 4:44 am, edited 1 time in total.

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Source: Beat The GMAT — Problem Solving | Mon Oct 24, 2011 3:54 am

neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 amFollowed by: 52 members; Location: Utrecht, The Netherlands; Thanked: 318 times

by neelgandham » Mon Oct 24, 2011 4:24 am

1 yard = 3 feet
1 cubic yard = 27 cubic feet

Say, the side of the cube = a,
Volume = a*a*a = x Cubic Yards = x*27 Cubic feet -(1)
Surface area = 6*a*a = y Cubic feet = x Cubic feet(x=y) -(2)

from 1 and 2

(a*a*a)/(6*a*a) = x*27/x => a/6 = 27 => a = 27*6 = 162 feet = [spoiler]162*12 inches = 1944[/spoiler]

:banghead: where did I go wrong ??

Edited: Relaxed now

Last edited by neelgandham on Mon Oct 24, 2011 4:50 am, edited 1 time in total.

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Mon Oct 24, 2011 4:46 am

neelgandham wrote:1 yard = 3 feet
1 cubic yard = 27 cubic feet

Say, the side of the cube = a,
Volume = a*a*a = x Cubic Yards = x*27 Cubic feet -(1)
Surface area = 6*a*a = y Cubic feet = x Cubic feet(x=y) -(2)

from 1 and 2

(a*a*a)/(6*a*a) = x*27/x => a/6 = 27 => a = 27*6 = 162 feet = 162*12 inches = 1944

:banghead: where did I go wrong ??

Don't bang head, you are correct, choices edited, thanks

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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mankey: Legendary Member; Posts: 627; Joined: Thu Jun 23, 2011 9:12 amFollowed by: 1 member; Thanked: 4 times

by mankey » Mon Oct 24, 2011 6:27 am

On solving it gives: B.

What is the OA?

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Oct 24, 2011 6:58 am

sanju09 wrote:Volume of a cube is x cubic yards and its surface area is y square feet. If x = y, what is the length of each edge of the cube in inches?
(A) 54
(B) 216
(C) 432
(D) 864
(E) 1944

Let e = the length of each edge in YARDS.
Volume in CUBIC YARDS = eÂ³.

Since 1 yard = 3 feet, the length of each edge in FEET = 3e.
Surface area in SQUARE FEET = 6(3e)Â² = 54eÂ².

Since the volume in CUBIC YARDS = the surface area in SQUARE FEET:
eÂ³ = 54eÂ²
e = 54 yards.

Since 1 yard = 36 inches, the length of each edge in INCHES = 54*36 = 1944.

The correct answer is E.

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