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x, y and y are positive numbers satisfying x < y < z.

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by Max@Math Revolution » Fri May 31, 2019 12:12 am

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[GMAT math practice question]

x, y and y are positive numbers satisfying x < y < z. Is x < 5?

1) x^2 + y^2 + z^2 = 125
2) y^2 = 25
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Source: — Data Sufficiency |
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by Max@Math Revolution » Sun Jun 02, 2019 4:49 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.

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.

Condition 1)
If x ≥ 5, then x^2 + y^2 + z^2 > x^2 + x^2 + x^2 > 3x^2 > 3*52 = 125.
Thus, we must have x < 5. Condition 1) is sufficient since it yields the unique answer, 'yes'.

Condition 2)
Since x^2 < y^2 = 25, and x and y are positive numbers, x < y = 5.
Thus, x < 5. Condition 2) is sufficient since it yields the unique answer, 'yes'.

Therefore, D is the answer.
Answer: D
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