gprep-4 ps-2

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gprep-4 ps-2

by GMATGuruNY » Tue Jul 22, 2014 2:54 am
If m, p, s and v are positive, and m/p < s/v, which of the following must be between m/p and s/v?

I. (m+s)/(p+v)
II. ms/pv
III. s/v - m/p

A. None
B. I only
C. II only
D. III only
E. I and II both
Case 1: m=1, p=2, s=1 and v=1
In this case, m/p = 1/2 and s/v = 1/1 = 1.
Eliminate any statement that does not yield a value between 1/2 and 1.

I: (m+s)/(p+v) = (1+1)/(2+1) = 2/3.
Since 2/3 is between 1/2 and 1, hold onto I.

II: ms/pv = (1*1)/(2*1) = 1/2.
Since 1/2 is NOT between 1/2 and 1, eliminate any answer choice that includes II.
Eliminate C and E.

III: s/v - m/p = 1/1 - 1/2 = 1/2.
Since 1/2 is NOT between 1/2 and 1, eliminate any remaining answer choice that includes III.
Eliminate D.

Test whether Statement I holds true when m/p and s/v are VERY CLOSE.
Case 2: m=9, p=10, s=1, and v=1
In this case, m/p = 9/10 = 9/10 and s/v = 1/1 = 1.

I: (m+s)/(p+v) = (9+1)/(10+11) = 10/11.
Since 10/11 is between 9/10 and 1, statement I holds true.

Since statement 1 holds true even when the distance between m/p and s/v is extremely small, we should be satisfied:
Statement I must yield a value between m/p and s/v.

The correct answer is B.
Last edited by GMATGuruNY on Thu Sep 07, 2017 3:13 pm, edited 1 time in total.
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by abhasjha » Tue Jul 22, 2014 3:14 am
Dear mitch ,

I have a question . you have written - Case 1: m=1, p=2, s=1 and v=1 ...

if the question has given different variables - namely s and V then is it prudent to substitute same value for s and v which is equal to 1 .

if varaibales are different should we not take different values for the variable ?

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by GMATGuruNY » Tue Jul 22, 2014 3:31 am
abhasjha wrote:Dear mitch ,

I have a question . you have written - Case 1: m=1, p=2, s=1 and v=1 ...

if the question has given different variables - namely s and V then is it prudent to substitute same value for s and v which is equal to 1 .

if varaibales are different should we not take different values for the variable ?
Just the opposite.
Since we are not told that the values must be distinct, we should consider the consequences of making them equal to one another.
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