Question: If x = \(^5\sqrt{-37}\) then which of the following must be true?

​A. \(\sqrt{-x} > 2\)

B. x > −2

C.\(x^2\) < 4

​D. \(x^3\)<-8

​E. \(x^4\) >32

Answer: D

Solution and Explanation:

Approach Solution 1:

Since the GMAT solely deals with Real Numbers, even roots from negative numbers are undefined on the exam. For instance, the number \(\sqrt{-25}\) is undefined on both the GMAT and the GRE.

The sign of odd roots is the same as the root's base. For instance, \(\sqrt{125}=5\) and\( \sqrt{-64}\) = - 4.

Returning to the original query:

As\( -2^5\)= - 32 then x must be somewhat less than -2, leading to x=\(\sqrt{-37}\approx -2.1 < 2\). Consequently, \(x^3 \approx(-2.1)^3\approx -8\).something < -8, therefore D must be accurate.

As for the further choices:

2. \(\sqrt{-x} =\sqrt{-(-2.1)} = \sqrt{2.1} < 2\) does not hold true for\( \sqrt{-x} > 2\)
3. Since x\(\approx\)-2.1 < -2 so x > -2 is also false.

2. \(x^2 \approx(-2.1)^2 = 4.something > 4, thus x^2 < 4\) is also not true.

D is the correct answer.

Approach Solution 2:

Given that the value of x is \(^5\sqrt{-37}\)

x =\(^5\sqrt{-37}\)

\(x^5 = -37\)

\((-x)^5 = 37 > 32 = 2^5\)

-x > 2

\(x^3 < -8\)

D is the correct answer.

“If x = \(^5\sqrt{-37}\) then which of the following must be true?" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.

To understand GMAT Club tests questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude for reasoning and mathematics. The GMAT Quantitative Test's Club Test Phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The problem-solving section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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