AbeNeedsAnswers wrote: ↑Thu Aug 24, 2017 8:33 pm
Two points, N and Q (not shown), lie to the right of point M on line â„“. What is the ratio of the length of QN to the length of MQ?
(1) Twice the length of MN is 3 times the length of MQ.
(2) Point Q is between points M and N.
A
Solution:
Question Stem Analysis:
We need to determine the value of QN/MQ. We can let MQ = x, QN = y. If Q is between M and N, then MN = x + y. If N is between M and Q, then MN = x - y. In any case, we need to determine the value of y/x.
Statement One Alone:
With statement one, we see that N is further to the right of M than Q is. Therefore, Q is between M and N. In that case, MN = x + y and MQ = x, and we have:
2(x + y) = 3x
2x + 2y = 3x
2y = x
y/x = 1/2
Statement one alone is sufficient.
Statement Two Alone:
Knowing only that Q is between M and N is not sufficient to answer the question. For example, if Q is exactly the midpoint of M and N, then the ratio QN/MQ = 1. However, if Q is closer to M than it is to N, then the ratio is greater than 1.
Answer: A
