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# If r is a prime number and s is a positive integer, is

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If r is a prime number and s is a positive integer, is  [#permalink]

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Updated on: 20 Jan 2016, 04:52
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75% (hard)

Question Stats:

35% (01:32) correct 65% (01:30) wrong based on 51 sessions

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If r is a prime number and s is a positive integer, is $$\frac{r^3}{s}$$ a terminating decimal?

(1) r $$\geq$$ 5
(2) s = 75

Originally posted by naumyuk on 20 Jan 2016, 00:15.
Last edited by naumyuk on 20 Jan 2016, 04:52, edited 1 time in total.
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Joined: 02 Aug 2009
Posts: 6810
Re: If r is a prime number and s is a positive integer, is  [#permalink]

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20 Jan 2016, 01:04
2
1
naumyuk wrote:
If r is a prime number and s is a positive integer, is a $$\frac{r^3}{c}$$ terminating decimal?

(1) r $$\geq$$ 5
(2) s = 75

c in $$\frac{r^3}{c}$$ must be 's'..

so we have to find if $$\frac{r^3}{s}$$ is a terminating decimal...
the value depends on the denominator in its simplified form..

lets see the statements..

(1) r $$\geq$$ 5
it just tell us that r cannot br 2 and 3 nothing else..
insuff

(2) s = 75
the denominator is 75...
if the numerator is 3 it will be a terminating decimal, otherwise not...
insuff..

combined we know numerator does not have 3, so it will not be a terminating decimal, as we have 3 in denominator..
suff
C
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: If r is a prime number and s is a positive integer, is  [#permalink]

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10 Apr 2017, 04:58
chetan2u wrote:
naumyuk wrote:
If r is a prime number and s is a positive integer, is a $$\frac{r^3}{c}$$ terminating decimal?

(1) r $$\geq$$ 5
(2) s = 75

c in $$\frac{r^3}{c}$$ must be 's'..

so we have to find if $$\frac{r^3}{s}$$ is a terminating decimal...
the value depends on the denominator in its simplified form..

lets see the statements..

(1) r $$\geq$$ 5
it just tell us that r cannot br 2 and 3 nothing else..
insuff

(2) s = 75
the denominator is 75...
if the numerator is 3 it will be a terminating decimal, otherwise not...
insuff..

combined we know numerator does not have 3, so it will not be a terminating decimal, as we have 3 in denominator..
suff
C

I am sorry I am slightly confused with the explanation. As far as my understanding goes, if the denominator has any other prime number in prime factorisation other than 2 and 5 and if that prime number can be cancelled with the numerator, then the fraction is terminating, otherwise not.

Here, the numerator is >or = to 5 i.e. it could also be 6 or 9 or 12 and those cases the 3 in the denominator will get cancelled. Therefore, there is no way to know what the value of r could be. Hence, my answer was E.

Kindly explain.
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Re: If r is a prime number and s is a positive integer, is  [#permalink]

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10 Apr 2017, 05:07
ashikaverma13 wrote:

I am sorry I am slightly confused with the explanation. As far as my understanding goes, if the denominator has any other prime number in prime factorisation other than 2 and 5 and if that prime number can be cancelled with the numerator, then the fraction is terminating, otherwise not.

Here, the numerator is >or = to 5 i.e. it could also be 6 or 9 or 12 and those cases the 3 in the denominator will get cancelled. Therefore, there is no way to know what the value of r could be. Hence, my answer was E.

Kindly explain.

The prompt says that r is PRIME number. So it can't be 6 or 9 or 12.
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Joined: 02 Sep 2009
Posts: 49496
Re: If r is a prime number and s is a positive integer, is  [#permalink]

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10 Apr 2017, 05:10
ashikaverma13 wrote:
chetan2u wrote:
naumyuk wrote:
If r is a prime number and s is a positive integer, is a $$\frac{r^3}{c}$$ terminating decimal?

(1) r $$\geq$$ 5
(2) s = 75

c in $$\frac{r^3}{c}$$ must be 's'..

so we have to find if $$\frac{r^3}{s}$$ is a terminating decimal...
the value depends on the denominator in its simplified form..

lets see the statements..

(1) r $$\geq$$ 5
it just tell us that r cannot br 2 and 3 nothing else..
insuff

(2) s = 75
the denominator is 75...
if the numerator is 3 it will be a terminating decimal, otherwise not...
insuff..

combined we know numerator does not have 3, so it will not be a terminating decimal, as we have 3 in denominator..
suff
C

I am sorry I am slightly confused with the explanation. As far as my understanding goes, if the denominator has any other prime number in prime factorisation other than 2 and 5 and if that prime number can be cancelled with the numerator, then the fraction is terminating, otherwise not.

Here, the numerator is >or = to 5 i.e. it could also be 6 or 9 or 12 and those cases the 3 in the denominator will get cancelled. Therefore, there is no way to know what the value of r could be. Hence, my answer was E.

Kindly explain.

Notice that we are told that r is a prime number, so it cannot be any multiple of 3 apart from 3 itself but r = 3 is ruled out with the first statement.
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Re: If r is a prime number and s is a positive integer, is &nbs [#permalink] 10 Apr 2017, 05:10
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