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# 1/2 < r < 1

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Moderator
Joined: 18 Apr 2015
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1/2 < r < 1 [#permalink]  17 Dec 2017, 13:03
Expert's post
00:00

Question Stats:

36% (00:25) correct 63% (00:51) wrong based on 19 sessions
$$\frac{1}{2} < r < 1$$

 Quantity A Quantity B $$2r$$ $$\frac{1}{r}$$

A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal
D. The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Director
Joined: 07 Jan 2018
Posts: 553
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Kudos [?]: 477 [1] , given: 84

Re: 1/2 < r < 1 [#permalink]  10 Jan 2018, 21:42
1
KUDOS
let us plug in two numbers such that 1st is close to 1/2 and another is close to 1
for r=0.6
2r= 2*0.6= 1.2 while 1/r = 1/0.6 =1.67 A<B
for r=0.9
2r=2*0.9=1.8 while 1/r= 1/0.9=1.11 A>B
(D)
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GRE Instructor
Joined: 10 Apr 2015
Posts: 1232
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Kudos [?]: 1113 [1] , given: 7

Re: 1/2 < r < 1 [#permalink]  11 Jan 2018, 15:44
1
KUDOS
Expert's post
Carcass wrote:
$$\frac{1}{2} < r < 1$$

 Quantity A Quantity B $$2r$$ $$\frac{1}{r}$$

We can solve this question using matching operations and testing values
Given:
Quantity A: 2r
Quantity B: 1/r

Since r is POSITIVE, we can safely multiply both quantities by r to get:
Quantity A: 2r²
Quantity B: 1

Divide both quantities by 2 to get:
Quantity A: r²
Quantity B: 1/2

Now let's TEST SOME VALUES

If r = 3/5 then we get:
Quantity A: (3/5)² = 9/25
Quantity B: 1/2
Quantity B is greater

If r = 4/5 then we get:
Quantity A: (4/5)² = 16/25
Quantity B: 1/2
Quantity A is greater

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Re: 1/2 < r < 1   [#permalink] 11 Jan 2018, 15:44
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