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# Suppose y=2^x^2+2^x+3. Which of these x-values gives the s

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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Suppose y=2^x^2+2^x+3. Which of these x-values gives the s  [#permalink]

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16 Mar 2018, 00:56
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Difficulty:

25% (medium)

Question Stats:

71% (01:25) correct 29% (01:42) wrong based on 98 sessions

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[GMAT math practice question]

Suppose $$y=2^{x^2}+2^{x+3}$$. Which of these $$x$$-values gives the smallest value of $$y$$?

A. -3
B. -2
C. -1
D. 1
E. 2

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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" CEO Joined: 08 Jul 2010 Posts: 2537 Location: India GMAT: INSIGHT WE: Education (Education) Re: Suppose y=2^x^2+2^x+3. Which of these x-values gives the s [#permalink] ### Show Tags 16 Mar 2018, 01:20 MathRevolution wrote: [GMAT math practice question] Suppose $$y=2^{x^2}+2^{x+3}$$. Which of these $$x$$-values gives the smallest value of $$y$$? A. -3 B. -2 C. -1 D. 1 E. 2 A. -3 y = 2^9 + 2^0 = 513 B. -2 y = 2^4 + 2^1 = 17 C. -1 y = 2^1 + 2^2 = 5 D. 1 y = 2^1 + 2^4 = 18 E. 2 y = 2^4 + 2^5 = 48 Answer: option C _________________ Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772 Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6375 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Suppose y=2^x^2+2^x+3. Which of these x-values gives the s [#permalink] ### Show Tags 18 Mar 2018, 23:21 => Since the exponent function $$y=2^x$$ is an increasing function, the smallest value of $$x^2+2x+3$$ gives the smallest value of $$y=2^{x^2}+2^{x+3}$$. Since $$x^2+2x+3 = (x+1)^2 + 2$$, the exponent $$(x+1)^2 + 2$$ has a minimum value when $$x = -1$$. Therefore, the answer is C. Answer : C _________________ 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: Suppose y=2^x^2+2^x+3. Which of these x-values gives the s  [#permalink]

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04 Apr 2018, 04:56
Could someone explain me why 2^(-3)^2 does not equal 2^(-6)?
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Posts: 49968
Re: Suppose y=2^x^2+2^x+3. Which of these x-values gives the s  [#permalink]

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04 Apr 2018, 05:35
PedroBodnar wrote:
Could someone explain me why 2^(-3)^2 does not equal 2^(-6)?

$$a^m^n=a^{(m^n)}$$ and not $$(a^m)^n$$ (if exponentiation is indicated by stacked symbols, the rule is to work from the top down). Thus, $$2^{(-3)^2}=2^{((-3)^2)}=2^9$$ and not $$(2^{(-3)})^2=2^{-6}$$

On the other hand, $$(a^m)^n=a^{mn}$$.

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Re: Suppose y=2^x^2+2^x+3. Which of these x-values gives the s &nbs [#permalink] 04 Apr 2018, 05:35
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