In the Decimal Notation of Number (2/23)^3. What is the Third Digit GMAT Problem Solving

Question: In the decimal notation of the number (2/23)^3. What is the third digit to the right of the decimal point?

1. 0
2. 1
3. 2
4. 4
5. 8

“In the decimal notation of number (2/23)^3. what is the third digit to the right of the decimal point?" - 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 GMAT Quant topic's problem-solving section comprises highly calculative mathematical problems that must be solved using the appropriate mathematical facts.

Solution and Explanation:

Approach Solution 1:

A number is given in the question - (2/23)^3
It has asked to find out the third digit to the right of decimal point.
Notice that (2/23) ^3 < (2/20)^3
Now, (2/20)^3 = (1/10)^3 = 0.001 (2/20)^3 = (1/10)^3 = 0.001.
Finally, since (22/3)^3 < 0.001(2/23)^3 < 0.001, the third digit to the right of the decimal point of (2/23)^3 is 0 because anything less than 0.001 will be of the form 0.000xyz
The third digit from the decimal point will be 0.

Hence, A is the correct answer.

Correct Answer: A

Approach Solution 2:

Simple and quickest approach:

(2/23) will be of the form -> (0.0x..) no need to calculate after x
Now we have to cube this number.
We get,
(2/23)^3 = (0.0x)^3
(0.0x..)^3 will surely be of the for (0.000z....) (one 0 will multiply 3 times when cubed)
Therefore, the third digit after the decimal point is 0. Hence, A is the correct answer.

Correct Answer: A

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