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# Is x/y a terminating decimal?

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Is x/y a terminating decimal? [#permalink]  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 form2^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.

[Reveal] Spoiler: OA

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

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Re: Is x/y a terminating decimal? [#permalink]  04 Oct 2012, 03:37
Sorry but 24 is in the form of 2^3*3and not 2^3*5
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Re: Is x/y a terminating decimal? [#permalink]  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 form2^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.

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.

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]  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 form2^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.

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.

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] 04 Oct 2012, 04:28
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