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Is ax + 2y - 3 = 4x + by + 5 an equation of a line on the xy

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by Max@Math Revolution » Sun Nov 24, 2019 11:34 pm
[GMAT math practice question]

Is ax + 2y - 3 = 4x + by + 5 an equation of a line on the xy-plane?

1) a ≠ 4.
2) b ≠ 2.
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Source: — Data Sufficiency |
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by Max@Math Revolution » Wed Nov 27, 2019 2:57 am
=>

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.
ax + 2y - 3 = 4x + by + 5
=> (a - 4)x + (2 - b)y - 8 = 0.

If we have a = 4 and b = 2, then the equation is equivalent to -8 = 0, which is not an equation of a line.

So, each condition alone is sufficient.

Therefore, D is the answer.
Answer: D
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