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

 It is currently 22 Sep 2018, 00:24

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

D01-08

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49300

Show Tags

16 Sep 2014, 00:11
1
12
00:00

Difficulty:

45% (medium)

Question Stats:

63% (00:50) correct 37% (01:19) wrong based on 192 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

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 49300

Show Tags

16 Sep 2014, 00:11
1
8
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.

_________________
Intern
Joined: 01 Jun 2014
Posts: 45
GMAT 1: 660 Q48 V34

Show Tags

01 Dec 2014, 02:36
1
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.
Manager
Joined: 27 Nov 2014
Posts: 51

Show Tags

01 Dec 2014, 03:39
2
1
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

Show Tags

01 Dec 2014, 07:40
15
4
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 $$m = 4$$.

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.
Retired Moderator
Joined: 23 Sep 2015
Posts: 385
Location: France
GMAT 1: 690 Q47 V38
GMAT 2: 700 Q48 V38
WE: Real Estate (Mutual Funds and Brokerage)

Show Tags

25 Nov 2015, 04:24
It is easy to spot the answer once we know that 1/11 yields 0,0909
_________________

New Application Tracker : update your school profiles instantly!

Manager
Joined: 11 Oct 2013
Posts: 111
Concentration: Marketing, General Management
GMAT 1: 600 Q41 V31

Show Tags

18 Dec 2015, 07:43
I think this is a high-quality question and I agree with explanation.
_________________

Its not over..

Manager
Joined: 11 Oct 2013
Posts: 111
Concentration: Marketing, General Management
GMAT 1: 600 Q41 V31

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 $$m = 4$$.

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.

This is exactly how Bunuel's formula is derived.
_________________

Its not over..

Intern
Joined: 16 Sep 2015
Posts: 3

Show Tags

14 Jul 2016, 02:16
1
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: 395
Location: India
Concentration: Operations, Finance
GMAT 1: 670 Q48 V34
GPA: 3.8
WE: Operations (Commercial Banking)

Show Tags

20 Aug 2016, 04:55
I think this is a high-quality question and I agree with explanation.
Intern
Joined: 11 Oct 2017
Posts: 11

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: 53
Location: India
GMAT 1: 560 Q41 V27
WE: Web Development (Computer Software)

Show Tags

07 May 2018, 03:32
I think this is a high-quality question and I agree with explanation.
Re D01-08 &nbs [#permalink] 07 May 2018, 03:32
Display posts from previous: Sort by

D01-08

Moderators: chetan2u, Bunuel

Events & Promotions

 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®.