1) IF m < p, mv < pv if v > 0.
For eg -3 < -2 and if v = +1, inequality remains so. But if v = -1, inequality is inverted. Hence v has to be greater than 0.
2) if mv < 0, and m < 0. Then v is greater than 0 else mv would change sign and be greater than 0.
BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course
Redeem
Featured Course
Target Test Prep GMAT OnDemand
Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.
- 715+ score guarantee — highest in the industry (99th percentile)
- 52 chapters · 1,500+ lessons · 4,000+ practice questions
- 400 hours of video · 1,500+ instructor-led HD smartboard lessons
- 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
- 24/7 live support + weekly Zoom office hours with GMAT instructors
- TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
- 1,200+ flashcards + AI-powered study assistant & daily calendar
- OnDemand, LiveTeach & GMAT Bootcamp formats available
- Also: GRE, SAT Math & Executive Assessment courses
- MBA Admissions Consulting now available
- 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
- 200,000+ students served
- 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★
5.0
(559 reviews)
130-pt guarantee
$0 to start
then $127/mo
Inequalities
Source: Beat The GMAT — Data Sufficiency |
I) m < pAkansha wrote:If mv < pv < 0, is v > 0?
a. m < p
b. m < 0
OA is D
m -p < 0
mv < pv
v(m-p)<0
as, m-p<0
So,v>0
Sufficient.
II)m<0
as,mv<0 and m<0
So,v>0
Sufficient.
D it is.
mv<pv<0
(m-p)v<0
thus either v<0 or m<p
a) m<p now if both m,p are positive, to satisfy mv<0, v <0 but then mv<pv won't be satisfied
if both m and p are -ve, v>0 possible
Also both m and p should be of same sign (as mv,pv are both <0)
Thus A is sufficient (m and p should be <0 and v is greater than 0)
b)m<0 to satisfy mv<0, v should be greater than 0.
sufficient.
IMO D
(m-p)v<0
thus either v<0 or m<p
a) m<p now if both m,p are positive, to satisfy mv<0, v <0 but then mv<pv won't be satisfied
if both m and p are -ve, v>0 possible
Also both m and p should be of same sign (as mv,pv are both <0)
Thus A is sufficient (m and p should be <0 and v is greater than 0)
b)m<0 to satisfy mv<0, v should be greater than 0.
sufficient.
IMO D
-
aftableo2006
- Senior | Next Rank: 100 Posts
- Posts: 99
- Thanked: 1 times
mv<pv<0
this means,v(m-p)<0
so either v<0or m-p<0 which means m<p
a.m<p this implies v<0.so this condition alone is sufficient
b.m<0means v>0 so this condition alone is also sufficient.
hence the answer is D
this means,v(m-p)<0
so either v<0or m-p<0 which means m<p
a.m<p this implies v<0.so this condition alone is sufficient
b.m<0means v>0 so this condition alone is also sufficient.
hence the answer is D
