In the right triangle above, is c less than 10? (1) b < 8 (2) c > 9

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.
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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 the equation \(c^2 = b^2 + 6^2 = b^2 + 36\).
Then \(c = \sqrt{b^2+36} < \sqrt{8^2+36} = \sqrt{100} = 10\) from condition 1)
Since condition 1) yields a unique solution, it is sufficient.

Condition 2)
In inequality questions, the law “Question is King” tells us that if the solution set of the question includes the solution set of the condition, then the condition is sufficient
However, the solution set of the question does not include that of the condition 2), it is not sufficient.

Therefore, A is the answer.

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