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# Is x/y a terminating decimal?

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Joined: 01 Sep 2010
Posts: 3310
Is x/y a terminating decimal?  [#permalink]

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03 Oct 2012, 17:27
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Difficulty:

35% (medium)

Question Stats:

53% (00:33) correct 47% (00:20) wrong based on 253 sessions

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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

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

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03 Oct 2012, 18:44
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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04 Oct 2012, 02:37
Sorry but 24 is in the form of $$2^3*3$$and not $$2^3*5$$
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Re: Is x/y a terminating decimal?  [#permalink]

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04 Oct 2012, 02:51
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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04 Oct 2012, 03:28
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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02 Nov 2018, 04:48
carcass wrote:
Is x/y a terminating decimal?

(1) x is a multiple of 2
(2) y is a multiple of 3

CONCEPT: A ration x/y will be Terminating when in its least form the denominator has NO PRIME FACTOR OTHER THAN 2 and 5

Question: Is x/y a terminating decimal?

Statement 1: x is a multiple of 2
No information about y hence
NOT SUFFICIENT

Statement 2: y is a multiple of 3
No information about y hence
NOT SUFFICIENT

Combining the two statements
using both statements as well we have no idea what will be the least form of x/y hence
NOT SUFFICIENT

Answer: Option E
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Re: Is x/y a terminating decimal? &nbs [#permalink] 02 Nov 2018, 04:48
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# Is x/y a terminating decimal?

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