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
Final Answer:
GMAT assassins aren't born, they're made,
Rich
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