It is currently 17 Jan 2018, 10:25

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If m, p, s and v are positive, and m/p < s/v, which of the following

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

Hide Tags

Manager
Manager
avatar
B
Joined: 03 May 2014
Posts: 167

Kudos [?]: 20 [0], given: 126

Location: India
WE: Sales (Mutual Funds and Brokerage)
Re: If m, p, s and v are positive, and m/p < s/v, which of the following [#permalink]

Show Tags

New post 01 Oct 2017, 04:19
Picking nos is the best approach.
m,p,s & v are +ve.
m/p<s/v.
Let m/p=1/2=0.5 ie m=1, p=2
and s/v=4/5=0.8 ie s=4 and v=5
0.5<0.8
Plugin the values in the answer choices.
I. (m+s)/(p+v)=(1+4)/(2+5)=5/7=0.71 this is between 0.5 and 0.8
II. ms/pv=4/10=0.4 not between 0.5 and 0.8
III. s/v−m/p=4/5-1/2=0.3 again not between 0.5 and 0.8.

Kudos [?]: 20 [0], given: 126

Expert Post
Target Test Prep Representative
User avatar
S
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2014

Kudos [?]: 1083 [0], given: 4

Location: United States (CA)
Re: If m, p, s and v are positive, and m/p < s/v, which of the following [#permalink]

Show Tags

New post 08 Dec 2017, 10:28
imhimanshu wrote:
If m, p, s and v are positive, and \(\frac{m}{p} <\frac{s}{v}\), which of the following must be between \(\frac{m}{p}\) and \(\frac{s}{v}\)

I. \(\frac{m+s}{p+v}\)
II. \(\frac{ms}{pv}\)
III. \(\frac{s}{v} - \frac{m}{p}\)

A. None
B. I only
C. II only
D. III only
E. I and II both


Let’s analyze each statement using specific values for the variables.

We can let m = 2, s = 3, p = 4, and v = 5. Thus:

m/p = 2/4 = 0.5 and s/v = 3/5 = 0.6.

Notice that m/p = 0.5 is less than s/v = 0.6. Now let’s analyze each statement.

I. (m+s)/(p+v)

(2 + 3)/(4 + 5) = 5/9 = 0.555… is between m/p = 0.5 and s/v = 0.6.

II. (ms)/(pv)

(2 x 3)/(4 x 5) = 6/20 = 0.3 is NOT between 0.5 and 0.6.

III. s/v - m/p

3/5 - 2/4 = 0.6 - 0.5 = 0.1 is NOT between 0.5 and 0.6.

From the above, we see that only statement I is true. However, this was illustrated by using one set of numbers (m = 2, s = 3, p = 4, and v = 5). It’s possible that it could be false when we use another set of values for m, s, p, and m.

However, we can prove that (m+s)/(p+v) is between m/p and s/v; that is, we can prove that m/p < (m+s)/(p+v) < s/v regardless of the values we use for m, s, p, and m, as long as the values are positive.

Notice that m/p < (m+s)/(p+v) < s/v means m/p < (m+s)/(p+v) and (m+s)/(p+v) < s/v. Also, keep in mind that we are given that m/p < s/v, which is equivalent to mv < ps.

Let’s prove that m/p < (m+s)/(p+v):

m/p < (m+s)/(p+v) ?

m(p+v) < p(m + s) ?

mp + mv < mp + ps?

mv < ps ? (YES)

Since mv < ps is true, m/p < (m+s)/(p+v) is true. Finally, let’s prove that (m+s)/(p+v) < s/v:

(m+s)/(p+v) < s/v ?

v(m+s) < s(p+v)?

mv + sv < sp + sv ?

mv < ps ? (YES)

Again, since mv < ps is true, (m+s)/(p+v) < s/v is true. Thus we have shown that m/p < (m+s)/(p+v) < s/v is always true.

Answer: B
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 1083 [0], given: 4

Manager
Manager
avatar
B
Joined: 29 Jun 2017
Posts: 223

Kudos [?]: 12 [0], given: 518

Re: If m, p, s and v are positive, and m/p < s/v, which of the following [#permalink]

Show Tags

New post 22 Dec 2017, 08:29
imhimanshu wrote:
If m, p, s and v are positive, and \(\frac{m}{p} <\frac{s}{v}\), which of the following must be between \(\frac{m}{p}\) and \(\frac{s}{v}\)

I. \(\frac{m+s}{p+v}\)

II. \(\frac{ms}{pv}\)

III. \(\frac{s}{v} - \frac{m}{p}\)


A. None
B. I only
C. II only
D. III only
E. I and II both


THIS IS HARD
the point tested here is that we need to change from ratio from to factor form
m/p<s/v
multiple two sides with s.v
mv<sp

from this point you can solve the problem.

Kudos [?]: 12 [0], given: 518

Intern
Intern
avatar
B
Joined: 24 Oct 2017
Posts: 17

Kudos [?]: 0 [0], given: 91

Re: If m, p, s and v are positive, and m/p < s/v, which of the following [#permalink]

Show Tags

New post 07 Jan 2018, 05:02
One very easy way to make I correct is as below
Any number can be expressed in form of A/1 (lets say --3/2 it can be written as 1.5/1)
so basically if you see option 1 is asking us A/1 < (A+B)/(2) < B/1

The average is always in btw A & B

II & III can simply be rejected by taking values 1,2,3,4.

Kudos [?]: 0 [0], given: 91

Re: If m, p, s and v are positive, and m/p < s/v, which of the following   [#permalink] 07 Jan 2018, 05:02

Go to page   Previous    1   2   [ 24 posts ] 

Display posts from previous: Sort by

If m, p, s and v are positive, and m/p < s/v, which of the following

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


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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®.