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

Question

https://gmatclub.com/forum/download/file.php?id=54136 In the right triangle above, is c less than 10? (1) b < 8 (2) c > 9 GMAT.jpg

GMATinsight · Answer

In the triangle  6^2+b^2 = c^2 
But  6^2+8^2 = 10^2

so if b ≥6 then c ≥ 10

Question: is c less than 10?

Question REPHRASED: is b less than 8?

Statement 1: b < 8 
i.e. YES

SUFFICIENT

Statement 2: c > 9 
i.e. c may be 9.5 or 10.5 which may be less than or greater than 10 hence

NOT SUFFICIENT

ANswer: Option A

GMATWhizTeam · Answer

Solution Step 1: Analyse Question Stem We need to find whether c is less than 10 or not. Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE Statement 1: b < 8 • c^2 = 6^2+b^2 = 36 + b^2 • c^2 < 6^2+8^2 • c< 10 Hence, statement 1 is sufficient, we can eliminate answer options B, C, and E.Statement 2: c > 9 • Case I: If c = 11, then c > 10• Case II: If c = 9.99, then c < 10 o We are not getting a unique answer. Hence, statement 2 is not sufficient, the correct answer is Option A.

MathRevolution · Answer

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

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