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

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

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13 Jul 2017, 02:56
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Difficulty:

45% (medium)

Question Stats:

63% (01:31) correct 37% (02:23) wrong based on 66 sessions

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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

Attachment:

2017-07-13_1355.png [ 1.33 KiB | Viewed 1003 times ]

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Re: If two points Q and R are each placed to the right of point P on the  [#permalink]

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13 Jul 2017, 05:25
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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

Attachment:
2017-07-13_1355.png

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...

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Joined: 30 Jun 2017
Posts: 3
Re: If two points Q and R are each placed to the right of point P on the  [#permalink]

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13 Jul 2017, 06:02
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

Attachment:
2017-07-13_1355.png

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

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13 Jul 2017, 07:21
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

$$\frac{RQ}{PR}$$ = $$\frac{7}{14}$$ = $$\frac{1}{2}$$

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Re: If two points Q and R are each placed to the right of point P on the  [#permalink]

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13 Jul 2017, 08:57
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

Attachment:
2017-07-13_1355.png

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

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Re: If two points Q and R are each placed to the right of point P on the  [#permalink]

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13 Jul 2017, 11:31
1
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

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Re: If two points Q and R are each placed to the right of point P on the  [#permalink]

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13 Jul 2017, 11:46
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?
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Re: If two points Q and R are each placed to the right of point P on the  [#permalink]

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13 Jul 2017, 20:45
JTR wrote:
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

By far, the easiest and understandable approach. Kudos to ya!
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Re: If two points Q and R are each placed to the right of point P on the  [#permalink]

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15 Jul 2017, 11:24
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
Re: If two points Q and R are each placed to the right of point P on the   [#permalink] 15 Jul 2017, 11:24
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