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a, b and X are positive numbers where a > b and n is a positive integer

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by Max@Math Revolution » Fri May 01, 2020 2:46 am

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A

B

C

D

E

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[GMAT math practice question]

a, b and X are positive numbers where a > b and n is a positive integer. What is the value of \(\left(\sqrt{X}-\sqrt{X-1}\right)^{\frac{1}{n}}\) ?

1) \(X=\frac{\left(a^n+b^n\right)^2}{ }\)
2) ab = 1.
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Source: — Data Sufficiency |
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Re: a, b and X are positive numbers where a > b and n is a positive integer

by Max@Math Revolution » Sun May 03, 2020 7:27 pm
=>

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 4 variables (a, b, X, and n) 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)
5.1DS(A).png
Since there many possible values of b, both conditions together do not yield a unique solution, and they are not sufficient.

Therefore, E is the answer.
Answer: E

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B, or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2) when taken together. Obviously, there may be occasions on which the answer is A, B, C, or D.
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