A rectangular solid box is $x$ inches long, $y$ inches wide, and $z$ inches tall, where $x, y,$ and $z$ are

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by M7MBA » Fri Jul 24, 2020 7:26 am

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A rectangular solid box is $x$ inches long, $y$ inches wide, and $z$ inches tall, where $x, y,$ and $z$ are positive integers, exactly two of which are equal. What is the total surface area of the box?

(1) One face of the box has an area of 9 square inches.

(2) One face of the box has an area of 81 square inches.

[spoiler]OA=E[/spoiler]

Source: Manhattan GMAT

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Source: Beat The GMAT — Data Sufficiency | Fri Jul 24, 2020 7:26 am

dashingnightmare: Senior | Next Rank: 100 Posts; Posts: 31; Joined: Fri Jul 24, 2020 9:40 pm

Re: A rectangular solid box is $x$ inches long, $y$ inches wide, and $z$ inches tall, where $x, y,$ and $z$ ar

by dashingnightmare » Fri Jul 24, 2020 10:51 pm

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deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

Re: A rectangular solid box is $x$ inches long, $y$ inches wide, and $z$ inches tall, where $x, y,$ and $z$ ar

by deloitte247 » Sat Jul 25, 2020 10:03 pm

Given that length = x inches, width = y inches and height = z inches.
* Exactly tow of the length, width and height are equal,
Target question: What is the total surface area?
Surface area of a solid box = 2(h*w) + 2(h*l) + 2(w*l)

Statement 1 => One face of the box has an area of 9 square inches.
We do not know if the face is rectangular or square. Also, the length and breadth of the face in question is either 3x3 or 9x1, and we cannot relate this to the length, width, or height of the entire box as it could be any value.
So, therefore, statement 1 is NOT SUFFICIENT.

Statement 2 => One face of the box has an area of 81 square inches.
we do not know if the face is rectangular or square. So, the length and breadth of the given face can be 9x9, 27x3, 81x1. And at that, we cannot relate it to the length, width, or height of the entire box as it could be any value. So, statement 2 is NOT SUFFICIENT.

Combining both statements together:
None of the statements gives a definite value for the length, width, or height, so, the surface area cannot be evaluated. Therefore, both statements combined together are NOT SUFFICIENT.

Answer = option E

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