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Is x/y a terminating decimal?

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Is x/y a terminating decimal? [#permalink]

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New post 03 Oct 2012, 18:27
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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
[Reveal] Spoiler: OA

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Re: Is x/y a terminating decimal? [#permalink]

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New post 03 Oct 2012, 19:44
Explanation seems clear to me...its presenting 2 cases (4/9 and 18/24) which are both multiples of 2 and 3. 4/9=.444 repeating (non terminating) and 18/24=.75 (terminating).

Not sure I follow your question, but if n=2, m=0, then it would satisfy your logic?

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Re: Is x/y a terminating decimal? [#permalink]

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New post 04 Oct 2012, 03:37

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Re: Is x/y a terminating decimal? [#permalink]

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New post 04 Oct 2012, 03:51
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.
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Re: Is x/y a terminating decimal? [#permalink]

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New post 04 Oct 2012, 04:28
Bunuel wrote:
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

Thanks
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Re: Is x/y a terminating decimal? [#permalink]

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New post 31 Aug 2017, 22:36
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Re: Is x/y a terminating decimal?   [#permalink] 31 Aug 2017, 22:36
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