Author 
Message 
TAGS:

Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6363
GPA: 3.82

If Rn+1Rn=(1/2)n for positive integers n, which of the following is
[#permalink]
Show Tags
Updated on: 12 Apr 2018, 01:46
Question Stats:
52% (02:03) correct 48% (02:07) wrong based on 117 sessions
HideShow timer Statistics
[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. \(R_3>R_2>R_1\)
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $99 for 3 month Online Course" "Free Resources30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons  try it yourself"
Originally posted by MathRevolution on 06 Apr 2018, 01:03.
Last edited by Bunuel on 12 Apr 2018, 01:46, edited 2 times in total.
Edited the question.



Director
Joined: 21 May 2013
Posts: 651

Re: If Rn+1Rn=(1/2)n for positive integers n, which of the following is
[#permalink]
Show Tags
06 Apr 2018, 02:12
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



Manager
Joined: 24 Mar 2018
Posts: 89

Re: If Rn+1Rn=(1/2)n for positive integers n, which of the following is
[#permalink]
Show Tags
06 Apr 2018, 04:13
the option A should be correct



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6363
GPA: 3.82

If Rn+1Rn=(1/2)n for positive integers n, which of the following is
[#permalink]
Show Tags
Updated on: 25 Jul 2018, 14:19
=> 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
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $99 for 3 month Online Course" "Free Resources30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons  try it yourself"



Intern
Joined: 27 Aug 2016
Posts: 15

Re: If Rn+1Rn=(1/2)n for positive integers n, which of the following is
[#permalink]
Show Tags
12 Apr 2018, 01:42
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.



Director
Joined: 27 May 2012
Posts: 581

Re: If Rn+1Rn=(1/2)n for positive integers n, which of the following is
[#permalink]
Show Tags
20 Jul 2018, 08:15
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.
_________________
 Stne



Intern
Joined: 25 Nov 2017
Posts: 36
Location: India
GPA: 3.56

Re: If Rn+1Rn=(1/2)n for positive integers n, which of the following is
[#permalink]
Show Tags
20 Jul 2018, 08:56
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



Director
Joined: 27 May 2012
Posts: 581

Re: If Rn+1Rn=(1/2)n for positive integers n, which of the following is
[#permalink]
Show Tags
20 Jul 2018, 11:16
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.
_________________
 Stne



Intern
Joined: 09 May 2018
Posts: 6
Concentration: Finance, Technology

Re: If Rn+1Rn=(1/2)n for positive integers n, which of the following is
[#permalink]
Show Tags
25 Jul 2018, 12:37
(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
_________________
O SeÑoR do DESTINERO




Re: If Rn+1Rn=(1/2)n for positive integers n, which of the following is &nbs
[#permalink]
25 Jul 2018, 12:37






