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# Is r/s^2 a terminating decimal?

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Is r/s^2 a terminating decimal? [#permalink]  23 Feb 2010, 13:23
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Is r/s^2 a terminating decimal?

(1) s=225
(2) r=81

[Reveal] Spoiler:
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.

But I think answer is A. ST 1 is sufficient. Any comment ??
[Reveal] Spoiler: OA

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Re: DS - MAth 3 [#permalink]  23 Feb 2010, 13:37
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SudiptoGmat wrote:
Is r/s^2 a terminating decimal?

1. s=225
2. r=81

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.

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

Hi dude... long time.....

Yes correct is C.....

Any fraction can only be a terminating decimal if it has the denominator in the form of $$2^m*5^n$$ where $$m\geq 0$$ & $$n\geq 0$$

Ques: Is $$\frac{r}{s^2}$$ a terminating decimal?

S1: s = 225 = $$3^2 * 5^2$$... Therefore deno = $$3^4 * 5^4$$.. Not SUff.... as If the numerator is divisible by $$3^4$$.. then it would be terminating... else it would not be!

S2: r = 81... gives no idea about denominator... so... Not SUFF...

Together....

SUFF.... as now the denominator $$3^4$$ cancels out the numerator 81... and hence the fraction can be terminating.

Hence C...
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Is r/s^2 a terminating decimal? [#permalink]  23 Feb 2010, 13:49
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Expert's post
2
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SudiptoGmat wrote:
Is r/s^2 a terminating decimal?

1. s=225
2. r=81

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.

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

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.

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Re: DS - MAth 3 [#permalink]  23 Feb 2010, 14:17
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Thanks for the elaborate theory. I was such a stupid.
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is r/s2 is a terminating decimal [#permalink]  12 Mar 2010, 13:57
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Is r/s2 a terminating decimal? (s2 = square of s)

s = 225
r = 81

--------------

I chose A but the OA is C...This question is from gmatclub test # 02 in which I got 35/37 correct. I think any fraction with denominator ending with 2, 4, 5, 10 always is a terminating decimal, so I chose A.
Pls help me to understand.
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Re: is r/s2 is a terminating decimal [#permalink]  12 Mar 2010, 14:03
xyztroy wrote:
Is r/s2 a terminating decimal? (s2 = square of s)

s = 225
r = 81

to have a terminating decimal, the denominator should be of hte form 2^n * 5^m after the given expression is broken down.

st 1) s = 225 = 3^2 * 5^2
we dont know about r and where it has 3^4 as a factor ... only in this case, it would be terminating or else it wont
not sufficient
st 2) r=81=3^4
dont know about denominator .. so cannot say
not sufficient

combinng the expression will become 1/5^4 and this is terminating

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Re: is r/s2 is a terminating decimal [#permalink]  12 Mar 2010, 14:13
the denominator is factored to ( 3^2 * 5^2 ) ^2 which is 3^4 *5^4. numerator is 81 , 81 is 3^4 , so the fraction reduced to 1 / 5^4 , powers of 5 is a terminating decimel.
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Re: is r/s2 is a terminating decimal [#permalink]  13 Mar 2010, 11:08
Isn't any number ending in 5 a terminating decimal? I can't think of number that is divided by 5 that doesn't terminate. Can someone explain why the numerator is necessary?
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Re: is r/s2 is a terminating decimal [#permalink]  15 Mar 2010, 15:21
Example of non terminating decimal when divided by 5:

$$sqrt2/5$$
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Re: is r/s2 is a terminating decimal [#permalink]  16 Mar 2010, 07:56
Touche` Marco - I did not consider square roots. Thanks.
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Re: is r/s2 is a terminating decimal [#permalink]  05 Oct 2011, 21:44
Since denominator is of the form 3^2 * 5^2. So numerator is also required to determine whether it is terminating or not.
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Re: Is r/s^2 a terminating decimal? 1. s=225 2. r=81 Statement [#permalink]  25 Nov 2011, 05:08
Thanks Bunuel for the formula. Is there an similar concept/formula for a recurring decimals . Something like 0.77634563456... ?
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Re: Is r/s^2 a terminating decimal? 1. s=225 2. r=81 Statement [#permalink]  25 Nov 2011, 10:56
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Re: DS - MAth 3 [#permalink]  13 Feb 2013, 22:54
Bunuel wrote:
SudiptoGmat wrote:
Is r/s^2 a terminating decimal?

1. s=225
2. r=81

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.

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

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 $$2*5^2$$. 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.

Hi Bunuel,
From what I can understand from the above,
The denominator should have only 2 and or 5 for the fraction to be terminating. Please correct me if I am wrong.
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Re: DS - MAth 3 [#permalink]  14 Feb 2013, 01:42
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Expert's post
Sachin9 wrote:
Bunuel wrote:
SudiptoGmat wrote:
Is r/s^2 a terminating decimal?

1. s=225
2. r=81

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 $$2*5^2$$. 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.

Hi Bunuel,
From what I can understand from the above,
The denominator should have only 2 and or 5 for the fraction to be terminating. Please correct me if I am wrong.

If the fraction is already reduced to its lowest term then yes.

For example, $$\frac{6}{15}$$ has extra 3 in the denominator but this fraction will still be terminating decimal, since that 3 can be reduced: $$\frac{6}{15}=\frac{2}{5}$$.

Questions testing this concept:
does-the-decimal-equivalent-of-p-q-where-p-and-q-are-89566.html
any-decimal-that-has-only-a-finite-number-of-nonzero-digits-101964.html
if-a-b-c-d-and-e-are-integers-and-p-2-a3-b-and-q-2-c3-d5-e-is-p-q-a-terminating-decimal-125789.html
700-question-94641.html
is-r-s2-is-a-terminating-decimal-91360.html
pl-explain-89566.html
which-of-the-following-fractions-88937.html
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Is r/s^2 a terminating decimal? [#permalink]  16 Nov 2014, 10:47
Bunuel wrote:
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.

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

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.

Hey Bunuel,

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.
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Re: Is r/s^2 a terminating decimal? [#permalink]  16 Nov 2014, 11:25
Expert's post
davidfrank wrote:
Bunuel wrote:
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.

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

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.

Hey Bunuel,

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.

The denominator should be in the form of 2^m*5^n, where $$m$$ and $$n$$ are non-negative integers. Thus n and m could be 0, meaning that the denominator could have only 2's, only 5's or both.

For more check Terminating and Recurring Decimals Problems in our Special Questions Directory.

Hope it helps.
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Re: Is r/s^2 a terminating decimal?   [#permalink] 16 Nov 2014, 11:25
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