Bunuel wrote:
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
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
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