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# What is the volume of cube C ?

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What is the volume of cube C ?  [#permalink]

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08 Sep 2017, 06:49
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Difficulty:

15% (low)

Question Stats:

85% (00:33) correct 15% (00:51) wrong based on 55 sessions

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What is the volume of cube C ?

(1) The total surface area ofCis 54 square inches.
(2) The area of each face of C is 9 square inches.

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Re: What is the volume of cube C ?  [#permalink]

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08 Sep 2017, 08:15
1) 6a^2 = 54 -->. Get the value of 'a'
2) a^2 = 9 --> get value of 'a'

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Re: What is the volume of cube C ?  [#permalink]

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09 Sep 2017, 22:01
What is the volume of cube C ?

(1) The total surface area of C is 54 square inches.
(2) The area of each face of C is 9 square inches.

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

The cube has only one variable with VA(Variable Approach) method. So we need 1 equation. D is the answer most likely.

Assume a is the length of an edge.

Condition 1)
We have $$6a^2 = 54$$ or $$a^2 = 9$$.
Thus the volume of the cube is $$a^3 = 27$$ since $$a = 3$$.
This is sufficient.

Condition 2)
We have $$a^2 = 9$$ or $$a = 3$$.
Thus the volume of the cube is $$a^3 = 27$$ too.
This is also sufficient.

-> For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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Re: What is the volume of cube C ?   [#permalink] 09 Sep 2017, 22:01
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