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

It is currently 14 Dec 2019, 03:16

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

If n is one of the numbers in 1/3, 3/16, 4/7, 3/5 then what

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Director
Director
User avatar
Joined: 03 Sep 2006
Posts: 609
GMAT ToolKit User
If n is one of the numbers in 1/3, 3/16, 4/7, 3/5 then what  [#permalink]

Show Tags

New post 24 Jan 2012, 09:52
2
5
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

59% (02:50) correct 41% (02:34) wrong based on 237 sessions

HideShow timer Statistics

If n is one of the numbers in \(\frac{1}{3}\), \(\frac{3}{16}\), \(\frac{4}{7}\), \(\frac{3}{5}\) then what is the value of n?

(1) \(\frac{5}{16}<n<\frac{7}{12}\)

(2) \(\frac{7}{13}<n<\frac{19}{33}\)
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59722
Re: DS If n is one of the numbers  [#permalink]

Show Tags

New post 24 Jan 2012, 11:04
2
4
LM wrote:
If n is one of the numbers in \(\frac{1}{3}\), \(\frac{3}{16}\), \(\frac{4}{7}\), \(\frac{3}{5}\) then what is the value of n?

1. \(\frac{5}{16}<n<\frac{7}{12}\)

2. \(\frac{7}{13}<n<\frac{19}{33}\)


If n is one of the numbers in \(\frac{1}{3}\), \(\frac{3}{16}\), \(\frac{4}{7}\), \(\frac{3}{5}\) then what is the value of n?

The method of cross multiplication:
Suppose we want to know which positive fraction is greater \(\frac{4}{7}\) or \(\frac{7}{12}\). Cross-multiply --> \(4*12=48\) and \(7*7=49\) --> \(48<49\). Now, ask yourself, which fraction contributed nominator for the larger value? \(\frac{7}{12}\)! Thus \(\frac{4}{7}<\frac{7}{12}\).


(1) \(\frac{5}{16}<n<\frac{7}{12}\) --> \(\frac{5}{16}<(\frac{1}{3}=\frac{5}{15})<\frac{7}{12}\), hence \(\frac{1}{3}\) is obviously in the given range (notice also that \(\frac{1}{2}<\frac{7}{12}\)). Next, from our example above we know that \(\frac{4}{7}<\frac{7}{12}\) so \(\frac{4}{7}\) is also in the given range. Not sufficient.


(2) \(\frac{7}{13}<n<\frac{19}{33}\) --> only two values might be in this range: \(\frac{4}{7}\approx{5.7}\) and \(\frac{3}{5}=0.6\) (other possible values of n are less than 1/2 and are clearly out of the range). As the second one is larger, then let's compare it with \(\frac{19}{33}\) (the upper limit of the range). So we are comparing \(\frac{19}{33}\) and \(\frac{3}{5}\): cross-multiply --> \(3*33=99\) and \(19*5=95\) --> \(99>95\). Which fraction contributed nominator for the larger value? \(\frac{3}{5}\)! Thus \(\frac{3}{5}>\frac{19}{33}\), which means that \(\frac{3}{5}\) is out of the range. \(n\) can only be \(\frac{4}{7}\). Sufficient.

Answer: B.

Hope it's clear.
_________________
General Discussion
Director
Director
User avatar
Joined: 25 Apr 2012
Posts: 651
Location: India
GPA: 3.21
WE: Business Development (Other)
Reviews Badge
Re: If n is one of the numbers in 1/3, 3/16, 4/7, 3/5 then what  [#permalink]

Show Tags

New post 25 Jun 2013, 10:36
1
LM wrote:
If n is one of the numbers in \(\frac{1}{3}\), \(\frac{3}{16}\), \(\frac{4}{7}\), \(\frac{3}{5}\) then what is the value of n?

(1) \(\frac{5}{16}<n<\frac{7}{12}\)

(2) \(\frac{7}{13}<n<\frac{19}{33}\)



I find it easier to convert the fractions into decimal form
1/3= 0.3333
3/16= 0.1875 ( Easier way to do this will be, we know 1/8 = 0.125 and so 1/16 = 0.0625 ----> 0.0625*3= 0.1875)
4/7 = 0.568 ( 1/7 = 0.142857...consider only 0.142 as the given options are not so close)
3/5 = 0.6

From st 1 we have 5/16< n< 7/12 can be converted to 0.3125 < n < 0.583...

we see that 2 values are possible ie 1/3 or 4/7 and hence st 1 ruled out

st 2 7/13< n< 19/33 -----> 0.49<n< 0.577

Another way to look at it will be , Since the largest fraction is 3/5 which is 0.6,we can calculate 60% of 33 which is 19.8 but since the numerator in the fraction (19/33) is 19 which is less than 19.8 and thus we will have only one value in the range Only 1 value that is 4/7 is in this range
_________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59722
Re: If n is one of the numbers in 1/3, 3/16, 4/7, 3/5 then what  [#permalink]

Show Tags

New post 24 Jun 2013, 03:17
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13740
Re: If n is one of the numbers in 1/3, 3/16, 4/7, 3/5 then what  [#permalink]

Show Tags

New post 26 Mar 2019, 14:51
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Bot
Re: If n is one of the numbers in 1/3, 3/16, 4/7, 3/5 then what   [#permalink] 26 Mar 2019, 14:51
Display posts from previous: Sort by

If n is one of the numbers in 1/3, 3/16, 4/7, 3/5 then what

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne