gabriel wrote:5) If mv < pv < 0, is v>0 ?
1) m<p
2) m<0

Answer is D. Can understand statement 2, can't understand why 1 is sufficient.

Ok, so we have mv<pv<0 .. that means mv<pv and both mv and pv are <0 ..

the first statement says m<p

there could be 3 cases satisfying this condition ..

1.) m and p are both positive
2.) m is negative and p is positive
3.) m and p are both negative.

consider each case .. u will see that the first 2 cases are not possible ... Why?

if m and p are both positive then v has to be negative bcoz we know that mv and pv <0 ..

so let m = 2, p =3 and v = -1 then mv=-2 and pv=-3 ..but over here mv>pv which contradicts the condition given in the question .. so first case is ruled out ..

the second case is again not possible bcoz to make mv negative v >0 .. but ot make pv negative v<0 .. which is not possible as v cant take 2 different signs ... so the second case is also ruled out ..

the only possiblity according to the conditions given is m<p and both are negative ..

so if m = -3 and p =-2 then v has to be positive to maintain th condition that mv and pv < 0 ... so from the first statement v get v>0 .. so sufficient ..

fantastic. Very clear.