Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 02 Aug 2015, 16:29

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:
Director
Joined: 03 Sep 2006
Posts: 884
Followers: 6

Kudos [?]: 309 [0], given: 33

If n is one of the numbers in 1/3, 3/16, 4/7, 3/5 then what [#permalink]  24 Jan 2012, 08:52
1
This post was
BOOKMARKED
00:00

Difficulty:

85% (hard)

Question Stats:

56% (03:29) correct 44% (02:09) wrong based on 130 sessions
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) $$\frac{7}{13}<n<\frac{19}{33}$$
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 28782
Followers: 4595

Kudos [?]: 47530 [2] , given: 7123

Re: DS If n is one of the numbers [#permalink]  24 Jan 2012, 10:04
2
KUDOS
Expert's post
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.

Hope it's clear.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 28782
Followers: 4595

Kudos [?]: 47530 [0], given: 7123

Re: If n is one of the numbers in 1/3, 3/16, 4/7, 3/5 then what [#permalink]  24 Jun 2013, 02:17
Expert's post
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

All DS Fractions/Ratios/Decimals questions: search.php?search_id=tag&tag_id=36
All PS Fractions/Ratios/Decimals questions: search.php?search_id=tag&tag_id=57

_________________
Moderator
Joined: 25 Apr 2012
Posts: 734
Location: India
GPA: 3.21
Followers: 30

Kudos [?]: 445 [1] , given: 723

Re: If n is one of the numbers in 1/3, 3/16, 4/7, 3/5 then what [#permalink]  25 Jun 2013, 09:36
1
KUDOS
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.”

Re: If n is one of the numbers in 1/3, 3/16, 4/7, 3/5 then what   [#permalink] 25 Jun 2013, 09:36
Similar topics Replies Last post
Similar
Topics:
5 What is the two-digit number N? 8 03 Nov 2012, 07:48
3 If m and n are two numbers on number line, what is the value 6 06 Nov 2011, 07:19
1 If N & S are two numbers on the number line then what is 3 08 Jan 2011, 13:18
1 What is the number of members of Club X who are at least 35 2 23 Jul 2010, 19:11
If a is equal to one of the numbers 5/11, 7/12,9/13 what is 3 06 Apr 2010, 00:36
Display posts from previous: Sort by