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What is the value of x?

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What is the value of x?

by Max@Math Revolution » Sun Sep 29, 2019 11:18 pm
[GMAT math practice question]

What is the value of x?

1) [x, y, z]=xy+yz+zx
2) [1, x, 2]=[4, -3, 2].
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Source: — Data Sufficiency |
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by Max@Math Revolution » Tue Oct 01, 2019 11:42 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.
Visit https://www.mathrevolution.com/gmat/lesson for details.

Since we have 3 variables (x, y, and z) 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.

Conditions 1) & 2)
Condition 2) tells us that [1, x, 2]=[4, -3, 2]. Substituting 1, x, 2 into xy + yz + zx and then substituting 4, -3, 2, into xy + yz + zx gives us (1)(x) + (x)(2) + (2)(1) = (4)(-3) + (-3)(2) + (2)(4), which simplifies to x + 2x + 2 = -12 - 6 + 8 or 3x = -12.
So, we have x = -4, and both conditions together are sufficient.

Therefore, C is the answer.
Answer: C
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