If two points Q and R are each placed to the right of point P on the

GMATPrepNow 's method is elegant - and not one about which I'd be sure. So I found PQ's value in relation to PR, got order of variables, and chose values.

If 2PQ = 3PR, then PQ = \(\frac{3}{2}\)PR.

PQ > PR, which means Q and R aren't in alphabetical order, hence: P_____R___Q

(Knowing ordinality sometimes makes it easier to "see" where the points' values fall.)

Assign a few different values, where PQ = \(\frac{3}{2}\)PR

Case 1: Let PR = 2. (\(\frac{3}{2}\)*2) = 3 = PQ.

P___R__Q
0___2__3

Case 2: Let PR = 8. (\(\frac{3}{2}\)*8) = 12 = PQ

P________R_____Q
0________8____12

Case 3: Let PR = 14. (\(\frac{3}{2}\)*14) = 21 = PQ

P_________________R_________Q
0_________________14_______21

Ratio of \(\frac{RQ}{PR}\), where RQ = PQ - PR?

Case 1: PR = 2. PQ = 3. And RQ = (3-2) = 1

\(\frac{RQ}{PR}\) = \(\frac{1}{2}\)

Case 2: PR = 8. PQ = 12. And PR = (12-8) = 4

\(\frac{RQ}{PR}\) = \(\frac{4}{8}\) = \(\frac{1}{2}\)

Case 3: PR = 14. PQ = 21. And RQ = (21-14) = 7

\(\frac{RQ}{PR}\) = \(\frac{7}{14}\) = \(\frac{1}{2}\)

Answer A

Since 2PQ = 3PR
=>R lies between P and Q .

Let PR = 2 , then PQ = 3
RQ = PQ-PR = 3-2 = 1
RQ/PR = 1/2

Answer A

Given PQ/PR = 3/2;

RQ/PR can be rewritten as (PQ-PR)/PR --> further reduced to (PQ/PR)-1 ---> (3/2)-1 => 1/2

answer A.

I always get a bit confused looking at things like "PQ" and "PR" so I usually try to simplify the problem so I don't need to think about pairs of letters stuck together. We really have this situation:

•-----a-----|--b---•

and the one equation we're given just tells us that a is 2/3 of the total length between the two dots. So the ratio of b to a must be 1 to 2. It's really just the same question as: if 2/3 of the people in a room are women, what is the ratio of men to women?

By far, the easiest and understandable approach. Kudos to ya!

Ratio is 1/2 option A.
Sequence of points PRQ,for which the ratio RQ/PR can be written as (PQ-PR)/PR. Substitute PQ in terms of PR using PQ=3/2PR

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