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On each face of a cube, one of 1, 2 or 3 is written. The number of 1’s on a face is a, the number of 2’s is b, and the

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On each face of a cube, one of 1, 2 or 3 is written. The number of 1’s on a face is a, the number of 2’s is b, and the

by Max@Math Revolution » Wed Jan 22, 2020 11:48 pm
[GMAT math practice question]

On each face of a cube, one of 1, 2 or 3 is written. The number of 1’s on a face is a, the number of 2’s is b, and the number of 3’s is c. What is c?

1) a = 2 and b = 3.
2) The probability of throwing the two identical cubes and getting a sum of 3 is 1/3.
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Source: — Data Sufficiency |
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Re: On each face of a cube, one of 1, 2 or 3 is written. The number of 1’s on a face is a, the number of 2’s is b, and

by Max@Math Revolution » Mon Jan 27, 2020 6:16 pm
=>

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.
Visit https://www.mathrevolution.com/gmat/lesson for details.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

We have 3 variables and 1 equation. However, we should check condition 1) alone first, since it has 2 equations.

Condition 1)
Since we have a + b + c = 6, a = 2 and b = 3, we have 2 + 3 + c = 6, 5 + c = 6, and c = 1.
Since condition 1) yields a unique solution, it is sufficient.

Condition 2)
Condition 2) tells us that c/6 + c/6 = 1/3, (2c)/6 = 1/3, c/3 = 1/3, c = 3/3. Then we have c = 1.
Since condition 2) yields a unique solution, it is sufficient.

Therefore, D is the answer.
Answer: D
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