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If Rn+1Rn=(1/2)n for positive integers n, which of the following is
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Updated on: 12 Apr 2018, 00:46
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[GMAT math practice question] If \(R_{n+1}R_n=(\frac{1}{2})^n\) for positive integers \(n\), which of the following is true? A. \(R_1>R_3 >R_2\) B. \(R_1>R_2 >R_3\) C. \(R_3 >R_1 >R_2\) D. \(R_2>R_3 >R_1\) E. \(R_3>R_2>R_1\)
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Originally posted by MathRevolution on 06 Apr 2018, 00:03.
Last edited by Bunuel on 12 Apr 2018, 00:46, edited 2 times in total.
Edited the question.



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Re: If Rn+1Rn=(1/2)n for positive integers n, which of the following is
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06 Apr 2018, 01:12
MathRevolution wrote: [GMAT math practice question]
If \(R_{n+1}R_n=(\frac{1}{2})^n\) for positive integers \(n\), which of the following is true?
A. \(R_1>R_3 >R_2\)
B. \(R_1>R_2 >R_3\)
C. \(R_3 >R_1 >R_2\)
D. \(R_2>R_3 >R_1\)
E. \(R_3>R_2>R_1\) I think answer should be A . R2R1=1/2 R3R2=1/4 Adding both equations R3R1=1/4 Therefore, R1>R3>R2 Can you please confirm? Bunuel



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Re: If Rn+1Rn=(1/2)n for positive integers n, which of the following is
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06 Apr 2018, 03:13
the option A should be correct



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If Rn+1Rn=(1/2)n for positive integers n, which of the following is
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Updated on: 25 Jul 2018, 13:19
=> If \(n = 1\), then R 2 – R 1 = \((\frac{1}{2}) < 0\), and we have R 1 > R 2. If \(n = 2\), then R 3 – R 2 = \(\frac{1}{4} > 0\), and we have R 3 > R 2. Furthermore, R 3 – R 1 = ( R 3 – R 2 ) + ( R 2 – R 1 ) = \(\frac{1}{4} + (\frac{1}{2})\) =\(\frac{1}{4} < 0\), and we have R 3 < R 1. Thus R 1 > R 3 > R 2. Therefore, A is the answer. Answer: A
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Re: If Rn+1Rn=(1/2)n for positive integers n, which of the following is
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12 Apr 2018, 00:42
MathRevolution wrote: =>
If \(n = 1\), then R2 – R1 = \((\frac{1}{2}) < 0\), and we have R1 > R2. If \(n = 2\), then R3 – R2 = \(\frac{1}{4} > 0\), and we have R3 > R2. Furthermore, R3 – R1 = ( R3 – R2 ) + ( R2 – R1 ) = \(\frac{1}{4} + (\frac{1}{2})\) =\(\frac{1}{4} < 0\), and we have R3 < R1. Thus R1 > R3 > R2.
Therefore, C is the answer. Answer: C The answer obtained points to Option A and not Option C. Kindly modify the OA.



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Re: If Rn+1Rn=(1/2)n for positive integers n, which of the following is
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20 Jul 2018, 07:15
MathRevolution wrote: =>
If \(n = 1\), then R2 – R1 = \((\frac{1}{2}) < 0\), and we have R1 > R2. If \(n = 2\), then R3 – R2 = \(\frac{1}{4} > 0\), and we have R3 > R2. Furthermore, R3 – R1 = ( R3 – R2 ) + ( R2 – R1 ) = \(\frac{1}{4} + (\frac{1}{2})\) =\(\frac{1}{4} < 0\), and we have R3 < R1. Thus R1 > R3 > R2.
Therefore, C is the answer. Answer: C Dear Moderator , This post needs your attention. The answer obtained is choice A and NOT choice C. Kindly correct the small typo in the post by MathRevolution. Thank you.
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Re: If Rn+1Rn=(1/2)n for positive integers n, which of the following is
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20 Jul 2018, 07:56
R2R1=  0.5 R3R2= 1 So, R3R1= 1.5 There can be a situation when value of R1=3, R2=2.5 R3=1.5 then these values satisfy the above equations. Then R1>R2>R3. Ans.B Is this approach right ??? Sent from my Lenovo K33a42 using GMAT Club Forum mobile app



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Re: If Rn+1Rn=(1/2)n for positive integers n, which of the following is
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20 Jul 2018, 10:16
BARUAH wrote: R2R1=  0.5 R3R2= 1 So, R3R1= 1.5 There can be a situation when value of R1=3, R2=2.5 R3=1.5 then these values satisfy the above equations. Then R1>R2>R3. Ans.B Is this approach right ??? Sent from my Lenovo K33a42 using GMAT Club Forum mobile appHow did you get \(R_3 R_2= 1\) ? \(R_3R_2 = \frac{1}{4}\) because \(R_3R_2\) = \((\frac{1}{2})^2\) Remember the stem \(R _{n+1} R_n = (\frac{1}{2})^n\) So for n= 2 , \((\frac{1}{2})^2\) Hope this helps, please feel free to ask if anything is still unclear.
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Re: If Rn+1Rn=(1/2)n for positive integers n, which of the following is
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25 Jul 2018, 11:37
(I) R2  R1 = 1/2 = 0.50 (II) R3  R2 = +1/4 = +0.25 (III) R3  R1 = 1/4 = 0.25 We can see that R1 > R3 > R2 If it's not clear, you can change the variables for numbers R2 = 0.50 R1 = 1.00 R3 = 0.75 (I) R2  R1 = 1/2 = 0.50 0.5  1.0 = 0.50 (II) R3  R2 = +1/4 = +0.25 0.75  0.50 = +0.25 (III) R3  R1 = 1/4 = 0.25 0.75  1.00 = 0.25 1.00 > 0.75 > 0.50 R1 > R3 > R2 The answer is alternative A
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Re: If Rn+1Rn=(1/2)n for positive integers n, which of the following is &nbs
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