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# If An+1=120 + (1/4)An for each positive integer n, and A1=150, which o

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Math Revolution GMAT Instructor
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If An+1=120 + (1/4)An for each positive integer n, and A1=150, which o  [#permalink]

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27 Jun 2018, 02:02
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[GMAT math practice question]

If $$A_{n+1}=120 + (\frac{1}{4})A_n$$ for each positive integer $$n$$, and $$A_1=150$$, which of these ranges of values includes $$A_{12}$$?

A. 110-120
B. 120-130
C. 130-140
D. 140-150
E. 150-160

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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Senior Manager Joined: 04 Aug 2010 Posts: 277 Schools: Dartmouth College Re: If An+1=120 + (1/4)An for each positive integer n, and A1=150, which o [#permalink] ### Show Tags 27 Jun 2018, 03:19 1 MathRevolution wrote: [GMAT math practice question] If An+1=$$120 + (\frac{1}{4})$$An for each positive integer $$n$$, and A1=150, which of these ranges of values includes A12? A. 110-120 B. 120-130 C.130-140 D. 140-150 E. 150-160 $$A_2 = 120 + \frac{1}{4}A_1 = 120 + \frac{1}{4}*150 = 120 + 37.5 = 157.5$$ $$A_3 = 120 + \frac{1}{4}A_2 = 120 + \frac{1}{4}*157.5 ≈ 120 + 39 = 159$$ $$A_4 = 120 + \frac{1}{4}A_3 = 120 + \frac{1}{4}*159$$... The terms are increasing in value. Thus, A₁₂ > 159. _________________ GMAT and GRE Tutor Over 1800 followers Click here to learn more GMATGuruNY@gmail.com New York, NY If you find one of my posts helpful, please take a moment to click on the "Kudos" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. BSchool Forum Moderator Joined: 26 Feb 2016 Posts: 3136 Location: India GPA: 3.12 If An+1=120 + (1/4)An for each positive integer n, and A1=150, which o [#permalink] ### Show Tags 27 Jun 2018, 03:24 1 MathRevolution wrote: [GMAT math practice question] If An+1=$$120 + (\frac{1}{4})$$An for each positive integer $$n$$, and A1=150, which of these ranges of values includes A12? A. 110-120 B. 120-130 C.130-140 D. 140-150 E. 150-160 We are given An+1=$$120 + (\frac{1}{4})$$An A2 = $$120 + (\frac{1}{4})*150 = \frac{630}{4}$$ (As A1=150) A3 = $$120 + (\frac{1}{4}$$)A2 = $$120 + (\frac{1}{4} * \frac{630}{4}) = 120 + 37.5 = 157.5$$ (As A2=$$\frac{630}{4}$$) We can repeat this process until A12 and the value will only increase from this value. Therefore, the range of the values that can be a possible value for A12 is Option E(150 - 160) _________________ You've got what it takes, but it will take everything you've got Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6227 GMAT 1: 760 Q51 V42 GPA: 3.82 If An+1=120 + (1/4)An for each positive integer n, and A1=150, which o [#permalink] ### Show Tags 29 Jun 2018, 01:17 => A1 = 150, A2 = $$120 + (\frac{1}{4})150 = 120 + 32.5 = 152.5.$$ As An is increasing, A12 must lie between $$150$$ and $$160$$. Therefore, the answer is E. Answer: E _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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If An+1=120 + (1/4)An for each positive integer n, and A1=150, which o &nbs [#permalink] 29 Jun 2018, 01:17
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# If An+1=120 + (1/4)An for each positive integer n, and A1=150, which o

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