MGMAT cube

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rommysingh: Master | Next Rank: 500 Posts; Posts: 112; Joined: Thu Mar 22, 2012 9:33 amFollowed by: 1 member; Thanked: 1 times

by rommysingh » Thu Sep 10, 2015 3:28 pm

What is the ratio of the surface area of a cube to the surface area of a rectangular solid identical to the cube in all ways except that its length has been doubled?

1/4

3/8

1/2

3/5

2

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Source: Beat The GMAT — Problem Solving | Thu Sep 10, 2015 3:28 pm

MartyMurray: Legendary Member; Posts: 2135; Joined: Mon Feb 03, 2014 9:26 amFollowed by: 140 members; Location: https://martymurraycoaching.com/; Thanked: 955 times; GMAT Score:800

by MartyMurray » Thu Sep 10, 2015 3:35 pm

rommysingh wrote:What is the ratio of the surface area of a cube to the surface area of a rectangular solid identical to the cube in all ways except that its length has been doubled?

The cube has six equal sides.

A rectangular solid identical to a cube in all ways except that its length has been doubled is basically the same shape as two of the cubes stacked with their sides lining up. So the rectangular solid has the same surface area that two of the cubes would, except that two of the twelve sides of the two cubes are buried in the middle of the rectangular solid. So effectively the rectangular solid has 12 - 2 = 10 cube sides.

So the cube has 6 cube sides.

The rectangular solid has the equivalent of 10 cube sides.

So the ratio of cube's surface area to rectangular solid's surface area is 6/10 = 3/5.

Choose D.

Marty Murray
Perfect Scoring Tutor With Over a Decade of Experience
MartyMurrayCoaching.com
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by [email protected] » Thu Sep 10, 2015 7:10 pm

Hi rommysingh,

This question can be solved by TESTing VALUES. You would likely find it helpful to physically draw the cube and solid.

Since the answer choices do not include variables, we can use whatever values we'd like for the dimensions of the cube and for the rectangular solid (as long as we follow the Facts described in the prompt). Given the one specific rule (the length of the rectangular solid is double the length of the cube), I'll TEST the easiest VALUES that I can think of...

Cube = (1)(1)(1)
Solid = (1)(1)(2)

Surface Area of Cube = 6(1) = 6
Surface Area of Solid = 2(1) + 4(2) = 10

Thus, the ratio of the two Surface Areas is 6:10 = 3:5

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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