GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 18 Mar 2019, 10:48

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Intern
Joined: 18 Apr 2015
Posts: 19
If r and s are positive integers, can the fraction r/s be expressed as  [#permalink]

### Show Tags

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
Retired Moderator
Joined: 06 Jul 2014
Posts: 1228
Location: Ukraine
Concentration: Entrepreneurship, Technology
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]

### Show Tags

26 Apr 2015, 12:48
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.

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.
_________________
Intern
Joined: 06 May 2015
Posts: 14
Location: United States
Concentration: Operations, Other
GPA: 3.39
Re: If r and s are positive integers, can the fraction r/s be expressed as  [#permalink]

### Show Tags

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?
Math Expert
Joined: 02 Sep 2009
Posts: 53657
Re: If r and s are positive integers, can the fraction r/s be expressed as  [#permalink]

### Show Tags

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.
_________________
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7086
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: If r and s are positive integers, can the fraction r/s be expressed as  [#permalink]

### Show Tags

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.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only \$149 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Intern
Joined: 21 Jul 2016
Posts: 4
Re: If r and s are positive integers, can the fraction r/s be expressed as  [#permalink]

### Show Tags

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?
Math Expert
Joined: 02 Sep 2009
Posts: 53657
Re: If r and s are positive integers, can the fraction r/s be expressed as  [#permalink]

### Show Tags

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.
_________________
Intern
Joined: 21 Jul 2016
Posts: 4
If r and s are positive integers, can the fraction r/s be expressed as  [#permalink]

### Show Tags

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.
Retired Moderator
Joined: 06 Jul 2014
Posts: 1228
Location: Ukraine
Concentration: Entrepreneurship, Technology
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]

### Show Tags

24 Jul 2016, 12:52
Top Contributor
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"
_________________
Intern
Joined: 02 Sep 2018
Posts: 1
Re: If r and s are positive integers, can the fraction r/s be expressed as  [#permalink]

### Show Tags

13 Jan 2019, 17:57
What if r=25 and s=25

Then 25/25=1

It has no decimal point in this case.

Posted from my mobile device
Math Expert
Joined: 02 Sep 2009
Posts: 53657
Re: If r and s are positive integers, can the fraction r/s be expressed as  [#permalink]

### Show Tags

13 Jan 2019, 21:16
1
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.
_________________
Intern
Joined: 03 Dec 2018
Posts: 5
Re: If r and s are positive integers, can the fraction r/s be expressed as  [#permalink]

### Show Tags

28 Feb 2019, 02:25
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?
Intern
Joined: 23 Feb 2019
Posts: 1
Location: China
Re: If r and s are positive integers, can the fraction r/s be expressed as  [#permalink]

### Show Tags

02 Mar 2019, 09:59
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.
Re: If r and s are positive integers, can the fraction r/s be expressed as   [#permalink] 02 Mar 2019, 09:59

Go to page   Previous    1   2   [ 33 posts ]

Display posts from previous: Sort by

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

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.