If mv

Question

If mv < pv < 0, is v > 0?

(1) m < p
(2) m < 0

Bunuel · Answer

If mv < pv< 0, is v > 0? Given: mv two cases: If v>0 then when dividing by v we would have: mp>0 (flip the sign when dividing by negative value). (1) m < p --> we have the first case, so v>0 . Sufficient. (2) m < 0 --> we have the first case, so v>0 . Sufficient. Answer: D. Hope it's clear.

KarishmaB · Answer

You can solve such questions easily by re-stating '< 0' as 'negative' and '> 0' as 'positive'. mv < pv < 0 implies both 'pv' and 'mv' are negative and mv is more negative i.e. has greater absolute value as compared to pv. Since v will be equal in both, m will have a greater absolute value as compared to p. When will mv and pv both be negative? In 2 cases: Case 1: When v is positive and m and p are both negative. Case 2: When v is negative and m and p are both positive. So how will we know whether v is positive? If we know that at least one of m and p is negative, then v must be positive. If at least one of m and p is positive, then v must be negative. Now that we understand the question and the implications of the given data, we go on to the statements. Stmnt 1: m < p m has greater absolute value as compared to p but it is still smaller than p. This means m must be negative. If m is negative, p must be negative too which implies that v must be positive. Sufficient. Stmnt 2: m < 0 Very straight forward. m and p both must be negative and v must be positive. Sufficient. Answer (D) Check this post for a very similar question: if-zy-xy-0-is-x-z-x-z-101210.html#p1098097

flower07 · Answer

I am sorry but I somehow still dont understand. I chose B, which I know is incorrect.

Well, let me tell you why I do not understand the Stmt. 1 is sufficient.

Given: mv<pv<0. It is given that MV and PV ARE -ve. This means, When V is -ve, M,P are +ve and vice versa.

I tabulated as below:

m v p mv pv
+ - + - -
- + - - -

Now, statement 1 says m < p. It does not say if they are negative or positive.

So, it is possible that:

3 < 5 (m=3 and p=5) and this means V is -ve

OR

-3 < -1 (m=-3 and p=-1) and this means V is +ve

Different answers so stmt 1 should be insufficient. What I am missing?

Thank you!

Bunuel · Answer

Ask yourself: if m=3 and p=5 and v is negative, say -1, does mv < pv< 0 hold true?

flower07 · Answer

Aha!! I get it now. So, when m=3, p=5 and v is -ve, mv (-3) becomes > pv (-5) making the given condition void. So, Stmt 1 is sufficient. Great learning for the day. (This makes me wanna repeat to myself - When you pick numbers, quickly plug in to see if they are correct) I also figured this just now: mv < pv < 0 (mv-pv) <0 v(m-p)<0 If v is +ve, m

p So, the answer is D. Thank you!!

shankyGMAT · Answer

Statement 1 : Since m

0 SUFFICIENT Statement 2: Given m<0 Since mv<0 therefore v > 0 SUFFICIENT Hence (D)

HKD1710 · Answer

I understood Bunuel's explanation for statement-1 but following values makes statement-1 insufficient. Please help me understand this:

(1) m<p

lets take v=1, m=-3, p=-2 it gives mv=-3, pv=-2 and hence does not violate mv<pv<0 as -3<-2<0, so v is +ve here
lets take v=-1, m=3, p=2 it gives mv=-3, pv=-2 and hence does not violate mv<pv<0 as -3<-2<0 but v is -ve here

Thanks

Bunuel · Answer

m = 3 and p = 2 violate the first statement, which says that m < p.

BrainLab · Answer

(1) means both  m  and  p  are negative, so in order   mv   and   pv   to be < 0,   v   must be greater than zero. (If it's -ve mv will > 0)
(2) same is in (1) m<0 means   m   is -ve, and in order  mv  to be negative  v  must be greater than zero.
Answer D

anairamitch1804 · Answer

I believe it is D.

Case 1) m < p 
mv < pv < 0
mv - pv < pv - pv < -pv . Subtract pv
v(m-p) < 0 < -pv

Since m < p OR (m - p) < 0 Therefore, v must be positive. SUFF

Case 2) m < 0
Since mv < 0 (given), v must be positive. SUFF

Hence D.

dabaobao · Answer

Main Topic Inequalities Rule: Multiplying/dividing inequalities by + variable: Don't flip sign - variable: Flip sign Divide by v If v = +, then m < p < 0 If v = -, then m > p > 0 1) Implies v = +. Sufficient. 2) Implies v = +. Sufficient. ANSWER: D

MathRevolution · Answer

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. Visit https://www.mathrevolution.com/gmat/lesson for details. The first step of the VA (Variable Approach) method is to modify the original condition and the question. Then we recheck the question. We should simplify conditions if necessary. mv < pv ⇔ mv - pv < 0 ⇔ v(m-p) < 0 Since the original condition is equivalent to v(m-p) < 0 , the question is equivalent to m - p < 0 or m < p . This is same as condition 1). Thus condition 1) is sufficient. Condition 2) When we consider both condition 2), m < 0 and the original condition, mv < 0 , we have v > 0 . Thus condition 2) is also sufficient. Therefore, D is the answer.

tagheueraquaracer · Answer

Damn it's solvable in less than 30 seconds! Never thought it was that easy! Thanks Bunuel!!!

Basshead · Answer

If  mv < pv < 0,  is  v > 0 ?

mv - pv < 0 
 v(m-p) < 0 
 (m - p)  and v must have opposite signs. For v to be positive,  (m - p)  must be negative. We can rephrase the question as: Is  m < p ?

(1)  m < p

Directly answers our question. SUFFICIENT.

(2)  m < 0

Lets look back at the original question prompt:  mv < pv < 0

If m is negative, v  MUST  be negative for the prompt to be true. Otherwise, mv would be greater than 0. SUFFICIENT.

Answer is D.

hassan233 · Answer

Did not really like the solutions I read, so here is mine.
We know mv < pv < 0, so this means we know mv < 0 (aka negative) AND pv < 0 (aka negative).

(1) m < p

Let us say m = -5 and p = -1
Then -5v < -1v < 0 is only true if v is positive
 Say v = 1, then -5 < -1 < 0 TRUE 
Say v = -1, then 5 < 1 < 0 FALSE

Well, what if m = 1 and p = 5, it is still true m < p
Then 1v < 5v < 0
If v is negative, say v = -1 then
-1 < -5 < 0 FALSE so that is not possible
If v is positive, save v = 1 then
1 < 5 < 0 also FALSE

Let us say m = -1 and p = 3, again m < p
Then -1v < 3v < 0
if v is negative, say v = -1 then
1< -3 < 0 FALSE, not possible
if v is positive, say v = 1 then
-1 < 3 < 0 FALSE not positive

So I just proved to you that if m < p, v MUST be positive

(2) m < 0

Remember when I said mv < 0 (aka negative)?

if mv MUST be negative, and m is negative, then that means v MUST be positive since (-)(+) is (-)

So both are sufficient. This is more theory-based than using formulas. It is helpful to know both ways!!

RastogiSarthak99 · Answer

My 2 cents on this: It seems better to not use numbers, since algebraic equations might suffice. I solved it with this logic: Before heading to Statements, we are given mv< pv < 0. I'm quickly able to deduce that mv < 0 and pv < 0. Let's keep this in mind. S1: m

written now as m-p< 0 from main statement, we know mv mv - pv < 0 further written as v(m-p) < 0 Now lets look at v (m-p) < 0 either v < 0 or m-p < 0; from S1 we can confirm m-p< 0 and so v > 0 has to be true. Sufficient. S2: m<0. Ding ding ding! Our initial deduction was mv<0 and if m< 0 v has to be positive. Sufficient. Hence, D.

pnandi3 · Answer

This is such an elegant and simple solution. Your brain really is something else...

bumpbot · Answer

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If mv < pv < 0, is v > 0?

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