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

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Manager
Joined: 03 May 2014
Posts: 167

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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]

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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

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
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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]

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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.

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Manager
Joined: 29 Jun 2017
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Kudos [?]: 12 [0], given: 518

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

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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
Joined: 24 Oct 2017
Posts: 17

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

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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

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