A Terminating Decimal is Defined as a Decimal GMAT Data Sufficiency

Question: A terminating decimal is defined as a decimal that has a finite number of nonzero digits. Examples of terminating decimals are 0.24, 52, and 6.0314. x and y are positive integers. If x/y is expressed as a decimal, is it a terminating decimal?

(1) 40 < x < 45
(2) y = 8

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are not sufficient.

‘A terminating decimal is defined as a decimal that has a finite number of nonzero digits’ - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Solution and Explanation:

Approach Solution 1: 

It's tough to picture a decimal terminating when the denominator is so huge, such as DWG's example of 43/256. This process will help the candidates to think about the basic patterns:

1/2^1 = 0.5
1/2^2 = 0.25
1/2^3 = 0.125
1/2^4 = 0.0625
1/2^5 = 0.03125
1/2^6 = 0.015625
1/2^7 = 0.0078125

1/5^1 = 0.2
1/5^2 = 0.04
1/5^3 = 0.008
1/5^4 = 0.0016
1/5^5 = 0.00032
1/5^6 = 0.000064
1/5^7 = 0.0000128

Every one of these terminates, and the pattern indicates that would continue to be true for higher powers. The number of decimal places increases along with the powers of 2 or 5, but the number of decimal places will always be finite.

In contrast, any factors other than 2 or 5 in the denominator can quickly be shown to be non-terminating, even for the most basic case (exponent of 1). 
Higher powers would be even messier:
1/3 = 0.33333(3 repeating)
1/6 = 0.16666(6 repeating)
1/7 = 0.142857(142857 repeating)
1/9 = 0.11111(1 repeating)

In original question statement (2) says that denominator equals to 2^3=8, hence x/8 will be terminating decimal no matter what the value of x is.
Hence, B is the correct answer. 

Correct Answer: B

Approach Solution 2: 

We will check each statement one by one. 

Statement 1) we don't know anything about y, so Insufficient

Statement 2) when you divide anything by 8 the answer will be either an integer, a fraction of a multiple of 0.125. For example 201/8 = 25.125 and 203/8 = 25.375

So in any case, this will always lead to a terminating decimal. Sufficient.

Hence, B is the correct answer. 

Correct Answer: B

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