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

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

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New post 26 Apr 2015, 12:24
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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Re: If r and s are positive integers, can the fraction r/s be expressed as  [#permalink]

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New post 05 Nov 2015, 04:36
''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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New post 05 Nov 2015, 11:22
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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New post 08 Nov 2015, 06:32
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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New post 24 Jul 2016, 04:42
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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New post 24 Jul 2016, 08:07
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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New post 24 Jul 2016, 09:29
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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Re: If r and s are positive integers, can the fraction r/s be expressed as  [#permalink]

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New post 24 Jul 2016, 12:52
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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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