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Intern  Joined: 18 Apr 2015
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If r and s are positive integers, can the fraction r/s be expressed as  [#permalink]

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Hi

In the question p/q, how can we be sure whether this can be reduced or it is already reduced

Also, if the first option would have been a multiple of 100 then the option would have been insufficient right? Since we could have any other prime factor
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GMAT 1: 660 Q48 V33 GMAT 2: 740 Q50 V40 If r and s are positive integers, can the fraction r/s be expressed as  [#permalink]

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kirtivardhan wrote:
Hi
In the question p/q, how can we be sure whether this can be reduced or it is already reduced

If we have only this information, we can't say nothing about state of this fraction.
And if we have information only about $$r$$ or about $$q$$ it's the same: we can't say nothing about reducing of this fraction.

I think I've got your previous question. Yes this task is exception about reducing factors:
because in this case we need to know if denominator contain any other factors except $$2$$ and $$5$$.
and we already have information that denominator is a factor of $$100$$, so we know that denominator doesn't conatain any factors except $$2$$ and $$5$$ and we don't need to reduce fraction.

kirtivardhan wrote:
Also, if the first option would have been a multiple of 100 then the option would have been insufficient right? Since we could have any other prime factor

Absolutely right.
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Re: If r and s are positive integers, can the fraction r/s be expressed as  [#permalink]

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''as a decimal with only a finite number of nonzero digits'' what does it exactly mean? Are 3.05, 9.002 etc under this category or sth else?
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Re: If r and s are positive integers, can the fraction r/s be expressed as  [#permalink]

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oishik wrote:
''as a decimal with only a finite number of nonzero digits'' what does it exactly mean? Are 3.05, 9.002 etc under this category or sth else?

Yes, because there is a finite number, respectively 2 and 3, of nonzero digits after the decimal point. For example, 1/3 = 0.33333... is not a decimal with only a finite number of nonzero digits, because 3's there goes infinitely.
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Re: If r and s are positive integers, can the fraction r/s be expressed as  [#permalink]

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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If r and s are positive integers, can the fraction r/s be expressed as

If r and s are positive integers, can the fraction r/s be expressed as a decimal with only a finite number of nonzero digits?

(1) s is a factor of 100
(2) r is a factor of 100

This is a commonly tested type of question.
If we modify the question, we get a decimal with only a finite number of nonzero digits=terminating decimal. So, it is referring to things such as 0.2=1/5, 0.5=1/2, 0.21=21/(2^2)(5^2). But in order to become a terminating decimal, the denominator has to have 2 or 5 as their prime factors; as the question asks whether the prime factor of s is composed of only 2 or 5 in r/s, we only need to know the value of s.
In condition 1, 100=(2^2)(5^2). The prime factors only include 2 or 5, so the condition is sufficient and the answer becomes (A).

Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.
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Re: If r and s are positive integers, can the fraction r/s be expressed as  [#permalink]

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The question asks if r/s can be expressed as a decimal with only a finite number of nonzero digits. So, it's asking if r/s can be expressed with a finite number of nonzero digits and nothing else (therefore, there can be no zeroes in the decimal). So, 10, for example, would not work (there's a zero in 10).

Or are we supposed to read the "only" to refer only to the "finite number" part of the question?
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Re: If r and s are positive integers, can the fraction r/s be expressed as  [#permalink]

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momonmoprob wrote:
The question asks if r/s can be expressed as a decimal with only a finite number of nonzero digits. So, it's asking if r/s can be expressed with a finite number of nonzero digits and nothing else (therefore, there can be no zeroes in the decimal). So, 10, for example, would not work (there's a zero in 10).

Or are we supposed to read the "only" to refer only to the "finite number" part of the question?

"Only" refers to finite, only.
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If r and s are positive integers, can the fraction r/s be expressed as  [#permalink]

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Bunuel wrote:
momonmoprob wrote:
The question asks if r/s can be expressed as a decimal with only a finite number of nonzero digits. So, it's asking if r/s can be expressed with a finite number of nonzero digits and nothing else (therefore, there can be no zeroes in the decimal). So, 10, for example, would not work (there's a zero in 10).

Or are we supposed to read the "only" to refer only to the "finite number" part of the question?

"Only" refers to finite, only.

I find that a bit confusing, is there some way I can avoid this confusion in the future? To me the wording is pretty clear, the decimal should only have a finite number of nonzero digits, in which case there should be a finite number of nonzero digits and nothing else (no zeroes).

How are we supposed to know during the test what they mean?

EDIT: Further, if they meant for the "only" to refer to "finite," only, then they simply should have wrote the question as "...can r/s can be expressed as a decimal with a finite number of nonzero digits?" That would have gotten the intended message across.
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GMAT 1: 660 Q48 V33 GMAT 2: 740 Q50 V40 Re: If r and s are positive integers, can the fraction r/s be expressed as  [#permalink]

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Top Contributor
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momonmoprob wrote:
Bunuel wrote:
momonmoprob wrote:
The question asks if r/s can be expressed as a decimal with only a finite number of nonzero digits. So, it's asking if r/s can be expressed with a finite number of nonzero digits and nothing else (therefore, there can be no zeroes in the decimal). So, 10, for example, would not work (there's a zero in 10).

Or are we supposed to read the "only" to refer only to the "finite number" part of the question?

"Only" refers to finite, only.

I find that a bit confusing, is there some way I can avoid this confusion in the future? To me the wording is pretty clear, the decimal should only have a finite number of nonzero digits, in which case there should be a finite number of nonzero digits and nothing else (no zeroes).

How are we supposed to know during the test what they mean?

EDIT: Further, if they meant for the "only" to refer to "finite," only, then they simply should have wrote the question as "...can r/s can be expressed as a decimal with a finite number of nonzero digits?" That would have gotten the intended message across.

Hello momonmoprob

The phrases "with only a finite number of nonzero digits" and "with a finite number of nonzero digits" are equal.

"To me the wording is pretty clear, the decimal should only have a finite number of nonzero digits"
this is not correct because the word "only" can not modify words and do not stand next to them:

"with only a finite number of nonzero digits" - here word "only" modifies "finite number"
"with a finite number of only nonzero digits" - here word "only" modifies "nonzero digits"
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Re: If r and s are positive integers, can the fraction r/s be expressed as  [#permalink]

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What if r=25 and s=25

Then 25/25=1

It has no decimal point in this case.

Posted from my mobile device
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Re: If r and s are positive integers, can the fraction r/s be expressed as  [#permalink]

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Goindanij wrote:
What if r=25 and s=25

Then 25/25=1

It has no decimal point in this case.

Posted from my mobile device

An integer IS a decimal with a finite number of nonzero digits. For example, integer 1 has 1 (finite) number of digits.
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Re: If r and s are positive integers, can the fraction r/s be expressed as  [#permalink]

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Quote:
1)S is a factor of 100. So S cannot have more than two 2s and two 5s. Any number divisible be 2 or 5 gives a finite decimal. Since R and S are both positive integers, there can be no 0s in the decimal places either. So Sufficient

MacFauz
If r=1, 1/100 is a possible answer as 100 is factor of 100.
1/100= 0.01 which has a zero in a decimal place.
Hence, your conclusion doesn't work 100% times. Am I right?
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Re: If r and s are positive integers, can the fraction r/s be expressed as  [#permalink]

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I have trouble understanding "a decimal with only a finite number of nonzero digits".
0.01=1/100, but there is a zero in the decimal digits.
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Re: If r and s are positive integers, can the fraction r/s be expressed as  [#permalink]

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After reading explanations from Bunuel, it takes only few seconds to answer these types of questions. Thank you for all your work..
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Re: If r and s are positive integers, can the fraction r/s be expressed as  [#permalink]

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- r and s are positive integers,
the fraction r/s be expressed as a decimal with only a finite number of nonzero digits, if s is a multiple of 2 or 5 or both.

(1) s is a factor of 100
Yes! s is a multiple of 2 or 5 or both.
SUFFICIENT

(2) r is a factor of 100
We don't know what number s is
NOT SUFFICIENT

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Re: If r and s are positive integers, can the fraction r/s be expressed as  [#permalink]

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Shouldn't the answer be 'E'?
In A it is given that s is a factor of 100. But there is no information about r. If r is an unterminating number i.e 0.33333...., then r/s will not be terminating decimal.

Experts, is my reasoning correct? Please do reply.

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If r and s are positive integers, can the fraction r/s be expressed as  [#permalink]

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himanshurajawat wrote:
Shouldn't the answer be 'E'?
In A it is given that s is a factor of 100. But there is no information about r. If r is an unterminating number i.e 0.33333...., then r/s will not be terminating decimal.

Experts, is my reasoning correct? Please do reply.

Hi,

The question clearly states that if r and s are positive integers..., then either r or s must not be a fraction, be it unterminating fraction (i.e. 0.333...) or terminating fraction (i.e. 0.25) If r and s are positive integers, can the fraction r/s be expressed as   [#permalink] 27 Aug 2019, 09:41

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