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Is r/s^2 a terminating decimal? [#permalink]
23 Feb 2010, 13:49
4
This post received KUDOS
Expert's post
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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.
The correct answer is C.
But I think answer is A. ST 1 is sufficient. Any comment ??
Several questions have been posted about terminating decimals lately. Below is the theory about this issue:
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.
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.
The correct answer is C.
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... _________________
Cheers! JT........... If u like my post..... payback in Kudos!!
|Do not post questions with OA|Please underline your SC questions while posting|Try posting the explanation along with your answer choice| |For CR refer Powerscore CR Bible|For SC refer Manhattan SC Guide|
is r/s2 is a terminating decimal [#permalink]
12 Mar 2010, 13:57
1
This post received KUDOS
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.
Several questions have been posted about terminating decimals lately. Below is the theory about this issue:
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.
Answer: C.
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: \(\frac{6}{15}=\frac{2}{5}\).
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
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.
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?
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.
The correct answer is C.
But I think answer is A. ST 1 is sufficient. Any comment ??
Several questions have been posted about terminating decimals lately. Below is the theory about this issue:
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.
Answer: C.
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. _________________
hope is a good thing, maybe the best of things. And no good thing ever dies.
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.
The correct answer is C.
But I think answer is A. ST 1 is sufficient. Any comment ??
Several questions have been posted about terminating decimals lately. Below is the theory about this issue:
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.
Answer: C.
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.
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.
The correct answer is C.
But I think answer is A. ST 1 is sufficient. Any comment ??
Several questions have been posted about terminating decimals lately. Below is the theory about this issue:
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.
Answer: C.
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.
You are not reading carefully...
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.
Re: Is r/s^2 a terminating decimal? [#permalink]
17 Nov 2015, 20:00
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