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

Question

https://gmatclub.com/forum/download/file.php?id=36243 If two points Q and R are each placed to the right of point P on the line above such that 2PQ = 3PR, what will be the value of RQ/PR? (A) 1/2 (B) 2/5 (C) 2/3 (D) 3/2 (E) cannot be determined 2017-07-13_1355.png

BrentGMATPrepNow · Answer

Let's make things easy on ourselves and say that P, R and Q are on the number line AND point P is at zero. 
So, where do we need to place R and Q so that 2PQ = 3PR? 
One option is R = 2 and Q = 3 
In this case, RQ/PR = 1/2

Another option is R = 4 and Q = 6 
In this case, RQ/PR = 2/4 = 1/2

Another option is R = 10 and Q = 15 
In this case, RQ/PR = 5/10 = 1/2

etc...

Answer:  A

sarathyishere · Answer

PQ > PR So, line is P-----R------Q
PQ=1.5PR. Let PR =1 then PQ =1.5 => RQ=0.5
Then RQ/PR = 0.5/1=1/2

generis · Answer

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

Skywalker18 · Answer

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

JTR · Answer

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.

IanStewart · Answer

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?

Blackbox · Answer

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

FB2017 · Answer

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

PietroCavallo · Answer

How are we supposed to know that with 2PQ or 3PR we mean the distance between the two points and not just a simple multiplication? It would need the proper notation with a line on top of the letters... am i wrong?

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

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