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
What properties can we use to find the right option quickly? What happen if the numbers are negative?
Which of the following options must be truth?
This topic has expert replies
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Case 1: m=1, p=2, s=1 and v=1If 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
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.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Rule:Vincen wrote: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)
If a/b < c/d and all four values are positive, then a/c < b/d.
Below is an algebraic proof for Statement I, given that m/p < s/v and that all four values are positive.
Given condition:
m/p < s/v
Applying the rule in blue, we get:
m/s < p/v
Since Statement I refers to m+s and p+v, we want to add s to the value of m on the left side and v to the value of p on the right side.
To this end, add s/s to the left side and v/v to the right side, the equivalent of adding 1 to each side:
m/s + s/s < p/v + v/v
Put each side over a common denominator:
(m+s)/s < (p+v)/v
Applying the rule in blue, we get:
(m+s)/(p+v) < s/v.
Given condition, rephrased:
s/v > m/p
Applying the rule in blue, we get:
s/m > v/p
Since Statement I refers to m+s and p+v, we want to add m to the value of s on the left side and p to the value of v on the right side.
To this end, add m/m to the left side and p/p to the right side, the equivalent of adding 1 to each side:
s/m + m/m > v/p + p/p
Put each side over a common denominator:
(m+s)/m > (p+v)/p
Applying the rule in blue, we get:
(m+s)/(p+v) > m/p.
Thus:
m/p < (m+s)/(p+v) < s/v.
Last edited by GMATGuruNY on Fri Sep 08, 2017 5:07 am, edited 1 time in total.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
GMAT/MBA Expert
- Jay@ManhattanReview
- GMAT Instructor
- Posts: 3008
- Joined: Mon Aug 22, 2016 6:19 am
- Location: Grand Central / New York
- Thanked: 470 times
- Followed by:34 members
Given that m, p, s, and v are positive, and m/p < s/v.Vincen wrote: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
What properties can we use to find the right option quickly? What happen if the numbers are negative?
We have to find out of the following must be between m/p and s/v.
Let's take each of them one by one.
Statement I: (m+s)/(p+v)
We know that m/p < s/v
Multiplying both the sides by p/s, we get m/s < p/v
Adding '1' to both the sides, we have
m/s + 1 < p/v + 1
(m + s)/s < (p + v)/v
By cross-mutiplying, we get (m + p)/(s + v) < s/v
We are not yet sure wether (m + p)/(s + v) > m/p.
Again, we know that m/p < s/v
Multiplying both the sides by p/s, we get m/s < p/v
Taking the reciprocal of above inequality
We have s/m > v/p
Adding '1' to both the sides, we have
s/m + 1 > v/p + 1
(s+m)/m > (v+p)/p
By cross-multiplying, we get (m+s)/(p+v) > m/p
Thus, m/p < (m+s)/(p+v) < s/v. Statement 1 is correct.
Statement II: (ms)/(pv)
We know that m/p < s/v
Multiplying above inequality by s/v, we get ms/pv < (s/v)^2
If s/v > 1, then (s/v)^2 > s/v, and then either ms/pv < s/v or ms/pv > s/v. This is a Could be true type of situation and not a Must be true type.
Statement III: s/v - m/p
We know that m/p < s/v
Transposing m/p, we have, 0 < s/v - m/p. The value of (s/v - m/p) may or may not be between m/p and s/v.
Say s/v = 3 and m/p = 2, then s/v - m/p = 1. The value of (s/v - m/p) does not lie between m/p and s/v.
The correct answer: B
Hope this helps!
Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide
-Jay
_________________
Manhattan Review GMAT Prep
Locations: New York | Jakarta | Nanjing | Berlin | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.