Two points, N and Q (not shown)…
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.