carcass wrote:

Is x/y a terminating decimal?

(1) x is a multiple of 2

(2) y is a multiple of 3

I do not know how to evaluate this question. I mean: for me 1 and 2 are insuff because we do not know alternatively of the other variable. Together we do not have the information that we want ok E is the answer

BUT if we have \(\frac{4}{9}\) we know that 9 is not in the form\(2^n * 5^m\) so is not a terminating decimal ok ------->\(\frac{18}{24}\) reduced is \(\frac{3}{4}\) and

neither 4 is in the aforementioned form here the OA explanation. may be is late in my TM but I'm confused

**Quote:**

Statement 1 indicates that x is a multiple of 2, which has nothing to do with

terminating or non-terminating property of decimals. For instance 2/4 is a

terminating decimal while 4/6 is a non terminating decimal. So, NOT SUFFICIENT.

Statement 2 says that y is a multiple of 3, but gives no information about the

common factors of x and y if any, and what is x/y in lowest terms. For instance, 2/3

is non-terminating while 9/12 is terminating. So, NOT SUFFICIENT.

Taking statements 1 and 2 together, 4/9 which satisfies both the statements is non-

terminating, while 18/24 is a terminating decimal. So NOT SUFFICIENT.

The correct answer is E

Actually \(4=2^2*5^0\), thus \(\frac{3}{4}=0.75\) is a terminating decimal.

If the denominator has only 2-s and/or 5-s then the fraction always will be a terminating decimal (in this case it also doesn't matter whether the fraction is reduced or not).Is x/y a terminating decimal? (1) x is a multiple of 2. Not sufficient since no info about y.

(2) y is a multiple of 3. Not sufficient since no info about x.

(1)+(2) If \(x=2\) and \(y=3\), then \(\frac{x}{y}=\frac{2}{3}=0.666...\) which is NOT a terminating decimal, but if \(x=6\) and \(y=12\), then \(\frac{x}{y}=0.5\) which is a terminating decimal. Not sufficient.

Answer: E.

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 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.)

Hope it helps.

I did not know (or notice) the red part albeit I read the theory in the gmatclub math book