Solution:

We are given line l and are told that two points, N and Q, are to the right of point M.  We must determine the ratio of the length of QN to the length of MQ.

Statement One Alone:

Twice the length of MN is 3 times the length of MQ.

Using the information in statement one, we see that the length of MN is greater than the length of MQ. Thus, we can insert points N and Q on line l where N is to the right of Q (see the diagram below). We can also label the lengths of MQ and QN as x and y respectively.

Since x = the length of line MQ and x + y = the length of line MN we can create the following equation:

2(x+y) = 3x

2x + 2y = 3x

2y = x

We are asked to determine the ratio of the length of QN to the length of MQ.

Thus, we are asked y/x = ?

Since 2y = x:

y/x = y/(2y) = 1/2

Statement one is sufficient to answer the question. We can eliminate answer choices B, C, and E.

Statement Two Alone:

Point Q is between points M and N.

Because we are given no information about any of the distances between the points Q, M, and N, statement two is not sufficient to answer the question.