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

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)

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