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What is the length of the sides of a given cube?

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by Max@Math Revolution » Thu Aug 23, 2018 1:06 am

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[Math Revolution GMAT math practice question]

What is the length of the sides of a given cube?

1) The surface area of the cube is 150
2) The volume of the cube is 125
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Thu Aug 23, 2018 7:28 am
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

What is the length of the sides of a given cube?

1) The surface area of the cube is 150
2) The volume of the cube is 125
IMPORTANT: For geometry Data Sufficiency questions, we are typically checking to see whether the statements "lock" a particular angle, length, or shape into having just one possible measurement. This concept is discussed in much greater detail in the following video: https://www.gmatprepnow.com/module/gmat ... /video/884

This technique can save a lot of time.

Target question: What is the length of the sides of a given cube?

Statement 1: The surface area of the cube is 150
There are infinitely many cubes. Each cube has different surface area.
So, we COULD go to our workshop and start making millions and millions of cubes of different sizes.
Once we make a cube, we measure its surface area.
We keep doing this until we find the ONE cube that has a surface area of 150.
When we eventually find that cube, we COULD measure its side length (which is what the target question is asking for)
Since there is only 1 cube in the universe that has a surface area of 150, then statement 1 must LOCK us in to exactly one shape.
Therefore, statement 1 is SUFFICIENT

Statement 2: The volume of the cube is 125
We can use the same approach here, since each different cube has a different volume.
Since there's only 1 cube in the universe with a volume of 125, then statement 2 must LOCK us in to exactly one shape.
Therefore, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Max@Math Revolution » Sun Aug 26, 2018 5:17 pm
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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since a cube is uniquely determined by its side length, we have only one variable. So, we should consider each of the conditions on their own first.

Condition 1)
Let x be the side-length of the cube. Then condition 1) tells us that 6x^2 = 150. Solving this equation yields x = 5.
Condition 1) is sufficient.

Condition 2)
Let x be the side-length of the cube. Then condition 2) tells us that x^3 = 125. Solving this equation yields x = 5.
Condition 2) is sufficient.

Therefore, D is the answer.
Answer: D

If the original condition includes "1 variable", or "2 variables and 1 equation", or "3 variables and 2 equations" etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
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