Question: Which of the following is a non-repeating and non-terminating decimal?

A. 1/3
B. ¼
C. 1/3.5
D. √(1/3)
E. √(1/4)

Answer: D

Solution and Explanation:

Approach Solution 1:
To answer this GMAT question, apply the data provided in the question. These issues pertain to many different branches of mathematics. This query relates to basic mathematics. Because of how the options are set up, it is hard to choose the best one. Applicants must be able to understand the proper strategy for getting the desired response. There is only one correct answer out of the five options offered.
Elimination method:

1. ⅓ = 0.3333 repeating and non-terminating number
2. ¼ = 0.25 non-repeating and terminating.
3. 1/(3.5) = 2/7 = 0.285714285714 repeating
4. √(1/3) = non-repeating and non-terminating
5. √(1/4) = +- ½ = terminating

Correct option: D

Approach Solution 2:
To answer this GMAT question, apply the data provided in the question. These issues pertain to many different branches of mathematics. This query relates to basic mathematics. It is challenging to choose the best option due to the way the options are presented. Applicants must be able to understand the proper strategy for getting the desired response. There is only one correct answer out of the five options offered.
the value of ⅓ = 0.3, where three is repeated after the decimal point.
¼ = 0.25 this is not repeating
1/(3.5) = 2/7 = 0.285714 This is also repeating.
√(1/3) = √(0.333)
This value, when calculated, will be non-repeating and non-terminating.
√(1/4) = √(0.25) = +- 0.5. This value is non-repeating and terminating.
Only choice (D) is non-repeating and non terminating.
Correct option: D

Approach Solution 3:
This GMAT question requires an application of the information given. These problems are relevant to a wide range of mathematical disciplines. This is a really elementary mathematical question. It's difficult to select the optimal solution due to the structure of the available alternatives. Candidates need to know how to formulate an approach that will yield the best results. Out of the five choices provided, only one is the right response.
The only option among the given choices that is a non-repeating and non-terminating decimal is D. √(1/3).
To see why, let's calculate the decimal representations of the fractions:

1. 1/3 = 0.33333... (repeating)
2. 1/4 = 0.25 (terminating)
3. 1/3.5 = 0.28571... (repeating)
4. √(1/3) = 0.57735... (non-repeating, non-terminating)
5. √(1/4) = 0.5 (terminating)

So, the only option that fits the criteria of being a non-repeating and non-terminating decimal is D. √(1/3).
Correct option: D

“Which of the following is a non-repeating and non-terminating decimal?" - 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 Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving 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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