What is the value of abc?

[Max@Math Revolution]

[GMAT math practice question]

What is the value of abc?

1) a + 4/b = 1
2) b + 1/c = 4

[Max@Math Revolution]

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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.
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.

Since we have 3 variables (a, b, and c) and 0 equations, E is most likely the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.
The question --------- is equivalent to ----------- for the following reason

Conditions 1) & 2)

When we multiply both sides of the equation a + 4/b = 1 by b, we have ab + 4 = b.
When we multiply both sides of the equation b + 1/c = 4 by c, we have bc + 1 = 4c or bc = 4c – 1.
When we multiply both sides of the equation ab + 4 = b by c, we have abc + 4c = bc.
When we replace bc of the equation abc + 4c = bc by 4c – 1, we have abc + 4c = 4c – 1 or abc = -1.

Since both conditions together yield a unique solution, they are sufficient.

Therefore, C is the answer.
Answer: C

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B, or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C, or D.