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• ### $450 Tuition Credit & Official CAT Packs FREE December 15, 2018 December 15, 2018 10:00 PM PST 11:00 PM PST Get the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) # If An+1=120 + (1/4)An for each positive integer n, and A1=150, which o  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6639 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 27 Jun 2018, 01:02 00:00 Difficulty: 25% (medium) Question Stats: 78% (02:32) correct 22% (02:58) wrong based on 39 sessions ### HideShow timer Statistics [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 _________________ 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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Re: 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, 02:19
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.

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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, 02:24
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)
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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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29 Jun 2018, 00:17
=>

A1 = 150, A2 = $$120 + (\frac{1}{4})150 = 120 + 32.5 = 152.5.$$ As An is increasing,
A12 must lie between $$150$$ and $$160$$.

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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, 00:17
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