SudiptoGmat wrote:

Is r/s^2 a terminating decimal?

1. s=225

2. r=81f t 5r y t5

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient

Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient

EACH statement ALONE is sufficient

Statements (1) and (2) TOGETHER are NOT sufficient

Statement (1) by itself is insufficient. Knowing only without is not enough information to answer the question.

Statement (2) by itself is insufficient. Knowing only without is not enough information to answer the question.

Statements (1) and (2) combined are sufficient. We know both and , so we can calculate the given expression.

The correct answer is C.

But I think answer is A. ST 1 is sufficient. Any comment ??

Several questions have been posted about terminating decimals lately. Below is the theory about this issue:

Theory:Reduced fraction \(\frac{a}{b}\) (meaning that fraction is already reduced to its lowest term) can be expressed as terminating decimal

if and only \(b\) (denominator) is of the form \(2^n5^m\), where \(m\) and \(n\) are non-negative integers. For example: \(\frac{7}{250}\) is a terminating decimal \(0.028\), as \(250\) (denominator) equals to \(2*5^3\). Fraction \(\frac{3}{30}\) is also a terminating decimal, as \(\frac{3}{30}=\frac{1}{10}\) and denominator \(10=2*5\).

Note that if denominator already has only 2-s and/or 5-s then it doesn't matter whether the fraction is reduced or not.

For example \(\frac{x}{2^n5^m}\), (where x, n and m are integers) will always be the terminating decimal.

We need reducing in case when we have the prime in denominator other then 2 or 5 to see whether it could be reduced. For example fraction \(\frac{6}{15}\) has 3 as prime in denominator and we need to know if it can be reduced.

Now:

For (1) \(\frac{r}{s^2}=\frac{r}{225^2}=\frac{r}{9^2*5^4}\), we can not say whether this fraction will be terminating, as 9^2 can be reduced or not.

(2) is clearly insufficient.

(1)+(2) \(\frac{r}{s^2}=\frac{9^2}{9^2*5^4}=\frac{1}{5^4}\), as denominator has only 5 as prime, hence this fraction is terminating decimal.

Answer: C.

As per the theory if the denominator can be expressed in the form of 2^m*5^n, then the numerator is a terminating decimal. However, in the question above after reducing the fraction we are left only with 5^n and hence not sure why in theory we are mentioning 2^n when any integer when divided by 5 will always be terminating. I might be asking a very stupid question but really now want to understand what is the missing link here.