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EMPOWERgmat Instructor V
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If the length of a rectangular solid is 7, then what is its surface  [#permalink]

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EMPOWERgmat DS Series:
Block 1, Question 1

If the length of a rectangular solid is 7, then what is its surface area?

1) The rectangular solid is a cube
2) One face of the solid has an area of 49

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Originally posted by EMPOWERgmatRichC on 23 Sep 2019, 21:09.
Last edited by EMPOWERgmatRichC on 26 Sep 2019, 14:20, edited 1 time in total.
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GMAT 1: 720 Q50 V37 Re: If the length of a rectangular solid is 7, then what is its surface  [#permalink]

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1
Solution
Given that the length of a rectangular solid is 7
Question: Find the surface area of the rectangular solid

Statement 1: The rectangular solid is a cube
If the rectangular solid is a cube and given that the length of one side of the rectangular solid is 7, then we CAN find the surface area. Sufficient
Surface area = 6x$$side^2$$. You do not need to find the surface area. It's enough to just know that surface area could be found.

Statement 2: One face of the solid has an area of 49
If one face of the solid has an area of 49 and the length of a rectangular solid is 7, then the other side of THAT surface is 7 units. However, we have no other information about the sides. Various side lengths will result in various surface areas, for the remaining sides. Not Sufficient

Therefore, the correct answer is option A.
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EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
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Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
If the length of a rectangular solid is 7, then what is its surface  [#permalink]

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OFFICIAL EXPLANATION

Hi All,

We're told that the LENGTH of a rectangular solid is 7. We're asked for the surface area of this solid. This question is based on some standard Geometry rules (although you do NOT actually need to do a lot of 'math' to answer this question).

To start, a 'rectangular solid' is essentially a 'box' - with a length, width and height. To find the surface area, we either need the exact values of the 3 dimensions or the individual areas of all 6 sides of the box.

1) The rectangular solid is a CUBE.

When it comes to rectangular solids, cubes are special - all 3 dimensions (the length, width AND height) are the SAME. We already know that the length of the solid is 7, so with the information in Fact 1, we also know that the width and height are ALSO each 7. At this point, we could calculate the total surface area (although we do not actually have to do that math), so we can answer the question that is asked.

If you're interested though, each individual surface would be (7)(7) = 49, so the total surface area would be 6(49) = 294
Fact 1 is SUFFICIENT

2) One face of the solid has an area of 49.

With the area of one surface, we know what the product of 2 of the dimensions would be... but we do NOT know which two dimensions and we do NOT know the actual dimensions.

IF...the 49 is the length x width, then we know that the length is 7 and the width is 7... but we know NOTHING about the height (meaning that the surface area could be any positive number).
IF...the 49 is the width x height, then those two dimensions MIGHT be 7 and 7, meaning that a 7x7x7 solid has a surface area of 294. However, those dimensions might be 1 and 49, meaning that we have a 7x1x49 solid which would have a surface area of 798.
Fact 2 is INSUFFICIENT

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Rich
_________________ If the length of a rectangular solid is 7, then what is its surface   [#permalink] 26 Sep 2019, 14:34
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