OG Two points, N and Q

[A AbeNeedsAnswers]

Two points, N and Q (not shown), lie to the right of point M on line ℓ. 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

[MartyMurray]

Statement 1: Twice the length of MN is 3 times the length of MQ.

We know from the question that both N and Q are to the right of M. So, the lengths of MN and MQ are both distances to the right of M.

Translate the statement.

2MN = 3MQ

MN = 1.5MQ

So, we know that N is further from M than Q is. Since both N and Q are to the right of M the sequence is M Q N.

Since MN = 1.5MQ the distance between N and Q is .5MQ.

So QN/MQ = .5

Sufficient.

Statement 2: Point Q is between points M and N.

This statement give us no information about distances or relative distances.

Insufficient.

The correct answer is A.

[Scott@TargetTestPrep]

Two points, N and Q (not shown), lie to the right of point M on line ℓ. 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