Aug 20 08:00 PM PDT  09:00 PM PDT EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299) Aug 20 09:00 PM PDT  10:00 PM PDT Take 20% off the plan of your choice, now through midnight on Tuesday, 8/20 Aug 22 09:00 PM PDT  10:00 PM PDT What you'll gain: Strategies and techniques for approaching featured GMAT topics, and much more. Thursday, August 22nd at 9 PM EDT Aug 24 07:00 AM PDT  09:00 AM PDT Learn reading strategies that can help even nonvoracious reader to master GMAT RC Aug 25 09:00 AM PDT  12:00 PM PDT Join a FREE 1day verbal workshop and learn how to ace the Verbal section with the best tips and strategies. Limited for the first 99 registrants. Register today! Aug 25 08:00 PM PDT  11:00 PM PDT Exclusive offer! Get 400+ Practice Questions, 25 Video lessons and 6+ Webinars for FREE.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 57155

Question Stats:
60% (01:15) correct 40% (01:48) wrong based on 141 sessions
HideShow timer Statistics
\(m\) and \(n\) are positive integers. What is the smallest possible value of integer \(m\) if \(\frac{m}{n}\) = 0.3636363636...? A. 3 B. 4 C. 7 D. 13 E. 22
Official Answer and Stats are available only to registered users. Register/ Login.
_________________



Math Expert
Joined: 02 Sep 2009
Posts: 57155

Re D0108
[#permalink]
Show Tags
16 Sep 2014, 00:11
Official Solution:\(m\) and \(n\) are positive integers. What is the smallest possible value of integer \(m\) if \(\frac{m}{n}\) = 0.3636363636...? A. 3 B. 4 C. 7 D. 13 E. 22 We are dealing with a repeating decimal in this question. It's helpful to know that there's a way to write these kinds of decimals as a fraction. For example, the repeating decimal 0.444444444(4) may be written as \(\frac{4}{9}\). So, \(\frac{5}{9}\), \(\frac{7}{9}\) and \(\frac{8}{9}\) will all be repeating decimals. You might check it in your calculator. In order to make two decimal points repeat, you have to divide the two digit number by 99. For example, \(\frac{23}{99} = 0.232323232323(23)\). Similarly, \(\frac{36}{99} = \frac{4}{11} = 0.36363636(36)\). Now it's clear that the minimum value of \(m = 4\). Alternate Solution: In case you did not know the formula for the repeating decimal (most probably did not), there is another approach to solving this question  backsolving. This is not a typical backsolving question, however, since both of the variables are unknown and we have to make some assumptions to get to the solution. 1. Looking at the repeating decimal  0.36....  the ratio between m and n has to be slightly less than 1:3. 2. Let's run through the answer choices: A. 3  the number that's slightly less than 3*3 is 8. \(\frac{3}{8} = 0.375\). Does not work. B. 4  the number that's slightly less than 3*4 is 11. \(\frac{4}{11} = 0.3636\). Works! C. 7 D. 13 E. 22 We could continue going through answer choices C, D, and E, but the question asks us for the smallest possible value of m, and 4 is the smallest of the ones that work (even if multiple do) so there is no value to check others. Answer: B
_________________



Intern
Joined: 01 Jun 2014
Posts: 44
Concentration: General Management, International Business
Schools: Haas '18, Tuck '18, Yale '18, Duke '18, Darden '18, Kelley '18, KenanFlagler '18, LBS '18, ISB '18, Goizueta '18, Rotman '18, Olin '18 (S), IE '19

Re: D0108
[#permalink]
Show Tags
01 Dec 2014, 02:36
When you look at the question , it does strike that 0.3636.. is 4 * 0.0909.. . I think from there on it becomes very simple.



Intern
Joined: 27 Nov 2014
Posts: 44

m and n are positive integers. What is the smallest possible value of integer m if \frac{m}{n} = 0.3636363636...?
A. 3 B. 4 C. 7 D. 13 E. 22 
it is easy to memorize that n will be 11 because if we choose any other value smaller than 11 it will not give 2 repeating non terminating values in return.
for eg. 1/3 = .3333...(1 repeating decimal) 1/7 = .142857 142857. ... (6 repeating decimals) 1/9 = .11111... (1 repeating decimals) 1/11= .090909 (2 repeating decimals) > this is wat we willl pick
Now look at the ans choices a. 3 upon dividing with 11 will not yield .363636... out b. 4 upon dividing with 11 will yield .363636 ... correct
Hence B ans!
Regards SG



Intern
Joined: 11 Aug 2012
Posts: 2

Re: D0108
[#permalink]
Show Tags
01 Dec 2014, 07:40
Bunuel wrote: Official Solution:
\(m\) and \(n\) are positive integers. What is the smallest possible value of integer \(m\) if \(\frac{m}{n}\) = 0.3636363636...?
A. 3 B. 4 C. 7 D. 13 E. 22
We are dealing with a repeating decimal in this question. It's helpful to know that there's a way to write these kinds of decimals as a fraction. For example, the repeating decimal 0.444444444(4) may be written as \(\frac{4}{9}\). So, \(\frac{5}{9}\), \(\frac{7}{9}\) and \(\frac{8}{9}\) will all be repeating decimals. You might check it in your calculator. In order to make two decimal points repeat, you have to divide the two digit number by 99. For example, \(\frac{23}{99} = 0.232323232323(23)\). Similarly, \(\frac{36}{99} = \frac{4}{11} = 0.36363636(36)\). Now it's clear that the minimum value of \(m = 4\). Answer: B Alternatively, \(\frac{m}{n}\) = 0.363636...  Eq 1 100\(\frac{m}{n}\) = 36.363636...  Eq 2 (Multiplied by 100 as we have 2 repeating decimals, in case of 3 repeating decimals we'd multiply by 1000 and so on) Subtract equation1 from 2 99\(\frac{m}{n}\) = 36 \(\frac{m}{n}\) = \(\frac{4}{11}\) Smallest possible value of m is 4. It can be used in the similar way for any number of repeating decimals.



Senior Manager
Joined: 23 Sep 2015
Posts: 371
Location: France
GMAT 1: 690 Q47 V38 GMAT 2: 700 Q48 V38
WE: Real Estate (Mutual Funds and Brokerage)

Re: D0108
[#permalink]
Show Tags
25 Nov 2015, 04:24
It is easy to spot the answer once we know that 1/11 yields 0,0909
_________________



Manager
Joined: 11 Oct 2013
Posts: 102
Concentration: Marketing, General Management

Re D0108
[#permalink]
Show Tags
18 Dec 2015, 07:43
I think this is a highquality question and I agree with explanation.
_________________



Manager
Joined: 11 Oct 2013
Posts: 102
Concentration: Marketing, General Management

Re: D0108
[#permalink]
Show Tags
18 Dec 2015, 07:47
james2329 wrote: Bunuel wrote: Official Solution:
\(m\) and \(n\) are positive integers. What is the smallest possible value of integer \(m\) if \(\frac{m}{n}\) = 0.3636363636...?
A. 3 B. 4 C. 7 D. 13 E. 22
We are dealing with a repeating decimal in this question. It's helpful to know that there's a way to write these kinds of decimals as a fraction. For example, the repeating decimal 0.444444444(4) may be written as \(\frac{4}{9}\). So, \(\frac{5}{9}\), \(\frac{7}{9}\) and \(\frac{8}{9}\) will all be repeating decimals. You might check it in your calculator. In order to make two decimal points repeat, you have to divide the two digit number by 99. For example, \(\frac{23}{99} = 0.232323232323(23)\). Similarly, \(\frac{36}{99} = \frac{4}{11} = 0.36363636(36)\). Now it's clear that the minimum value of \(m = 4\). Answer: B Alternatively, \(\frac{m}{n}\) = 0.363636...  Eq 1 100\(\frac{m}{n}\) = 36.363636...  Eq 2 (Multiplied by 100 as we have 2 repeating decimals, in case of 3 repeating decimals we'd multiply by 1000 and so on) Subtract equation1 from 299\(\frac{m}{n}\) = 36 \(\frac{m}{n}\) = \(\frac{4}{11}\) Smallest possible value of m is 4. It can be used in the similar way for any number of repeating decimals. This is exactly how Bunuel's formula is derived.
_________________



Intern
Joined: 16 Sep 2015
Posts: 3

Re: D0108
[#permalink]
Show Tags
14 Jul 2016, 02:16
1. Looking at the repeating decimal  0.36....  the ratio between m and n has to be slightly less than 1:3. Could you please explain how did we arrive at this when we know 0.36> 0.33 how is it that the ratio is slightly less than 1:3. Could you please clarify this point. Thanks



Senior Manager
Joined: 31 Mar 2016
Posts: 375
Location: India
Concentration: Operations, Finance
GPA: 3.8
WE: Operations (Commercial Banking)

Re D0108
[#permalink]
Show Tags
20 Aug 2016, 04:55
I think this is a highquality question and I agree with explanation.



Intern
Joined: 11 Oct 2017
Posts: 11

Re: D0108
[#permalink]
Show Tags
02 Jan 2018, 09:07
all 'repeating decimals" can be written as a fraction with a denominator that is made up of only 9s i.e. 9, 99, 999. below is an explanation how. but before that, an interesting fact to know is that when the repeating digits are 0 and 1, then the nominator is ALWAYS 1 and the denominator is ALWAYS made up of 9s. i.e. 0.11111.... = 1/9 0.010101.... = 1/99 0.001001001..... = 1/999 i.e note that for every additional 9 in the denominator in addition to the first 9, a 0 is added before and after the 1s. except the first 9. (see above) now, knowing this simple fact, you can tackle all such questions.
0.363636.... = 0.36 + 0.0036 + 0.000036 +...... = 36 (0.01 + 0.0001 + 0.000001 + .....) = 36 (0.010101......) = 36 (1/99) = 36/99 = 4/11



Manager
Joined: 26 Feb 2018
Posts: 51
Location: India
GPA: 3.9
WE: Web Development (Computer Software)

Re D0108
[#permalink]
Show Tags
07 May 2018, 03:32
I think this is a highquality question and I agree with explanation.



Intern
Joined: 12 Nov 2017
Posts: 18

Re: D0108
[#permalink]
Show Tags
18 Apr 2019, 04:51
The most simple way to solve it: 0.36363636 here 36 repeats. For such a number to convert to fraction : We know 0.36 = 36/100, but since 36 repeats deduct 1 from the denominator. In this case 1001= 99 So, this fraction is 36/99. Now we need the smallest possible value of integer m. Therefore, simplify 36/99 = 4/11 So the answer is m=4.



Intern
Joined: 25 Apr 2018
Posts: 12
Location: India
Concentration: Strategy, Finance

Re: D0108
[#permalink]
Show Tags
03 Aug 2019, 09:38
x=0.3636.. (1) 10x=3.6363 100x=36.3636 (2) Subtracting (2) & (1) we get, 99x=36 x=4/11 therefore m/n=4/11 Smallest value of m is 4.
_________________
Gmat aspirant Target score 750 !










