For a Certain Set of Numbers, If x is in the Set, Then Both –x^2 and −x^3 GMAT Problem Solving

Question: For a certain set of numbers, if x is in the set, then both –x^2 and −x^3 are also in the set. If the number ½ is in the set, which of the following must also be in the set?

1. −1/64
2. 1/64
3. 1/3√2

1. I only
2. II only
3. III only
4. I and II only
5. I, II and III

Correct Answer: D
Solution and Explanation:
There is only one approach to this problem.
Approach Solution 1:

The problem statement states that:

Given:

• For a certain set of numbers, if x is in the set, then both –x^2 and −x^3 are also in the set.

Asked:

• If the number ½ is in the set, which of the following must also be in the set?

Since it is stated in the question that 1/2 is in the set, then it must be:
−x^2 equals −1/4;
−x^3 equals −1/8.

Since −1/4 is in the set, then it must be:
−x^3 equals 1/64

Since −1/8 is in the set, then it must be:
−x^2 equals −1/64

The only number we cannot get is 1/3√2.
Hence, the only option I and II satisfies the conditions of the question. Therefore, the answer is option D.

“For a certain set of numbers, if x is in the set, then both –x^2 and −x^3”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. This question has been taken from the book “GMAT Official Guide Quantitative Review 2022”. To solve the GMAT Problem Solving questions, the candidates must have basic knowledge of mathematics to evaluate the information in the questions. The candidates can follow GMAT Quant practice papers to analyse several sorts of questions that will help them to improve their mathematical understanding.

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