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# A = (2-3+4)^{11}, and B = (-2+3-4)^{11}. What is the value of 2^{A+B}?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42
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A = (2-3+4)^{11}, and B = (-2+3-4)^{11}. What is the value of 2^{A+B}?  [#permalink]

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21 Jan 2019, 23:32
00:00

Difficulty:

5% (low)

Question Stats:

89% (01:07) correct 11% (01:16) wrong based on 48 sessions

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[Math Revolution GMAT math practice question]

$$A = (2-3+4)^{11}$$, and $$B = (-2+3-4)^{11}.$$ What is the value of $$2^{A+B}$$?

$$A. \frac{1}{2048}$$
$$B. \frac{1}{1024}$$
$$C. 1$$
$$D. 1024$$
$$E. 2048$$

_________________

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 $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" RC Moderator Joined: 24 Aug 2016 Posts: 676 Location: Canada Concentration: Entrepreneurship, Operations GMAT 1: 630 Q48 V28 GMAT 2: 540 Q49 V16 Re: A = (2-3+4)^{11}, and B = (-2+3-4)^{11}. What is the value of 2^{A+B}? [#permalink] ### Show Tags 22 Jan 2019, 08:40 1 MathRevolution wrote: [Math Revolution GMAT math practice question] $$A = (2-3+4)^{11}$$, and $$B = (-2+3-4)^{11}.$$ What is the value of $$2^{A+B}$$? $$A. \frac{1}{2048}$$ $$B. \frac{1}{1024}$$ $$C. 1$$ $$D. 1024$$ $$E. 2048$$ $$A = (2-3+4)^{11}$$ = $$A = (3)^{11}$$ = X ( say) Hence , $$B = (-2+3-4)^{11}.$$= $$B = (-3)^{11}.$$ = -X now $$A+B= X+(-X)= 0$$ $$2^{A+B}$$ = $$2^{0}$$ = $$1$$ ...... Answer C _________________ Please let me know if I am going in wrong direction. Thanks in appreciation. VP Joined: 09 Mar 2018 Posts: 1001 Location: India Re: A = (2-3+4)^{11}, and B = (-2+3-4)^{11}. What is the value of 2^{A+B}? [#permalink] ### Show Tags 22 Jan 2019, 09:25 MathRevolution wrote: [Math Revolution GMAT math practice question] $$A = (2-3+4)^{11}$$, and $$B = (-2+3-4)^{11}.$$ What is the value of $$2^{A+B}$$? $$A. \frac{1}{2048}$$ $$B. \frac{1}{1024}$$ $$C. 1$$ $$D. 1024$$ $$E. 2048$$ $$A = (2-3+4)^{11}$$, and $$B = (-2+3-4)^{11}$$ $$A = (3)^{11}$$, and $$B = (-3)^{11}$$ $$2^{A+B}$$ = [m]A = 2^{3^11- 3^11} 2^0 Answer C _________________ If you notice any discrepancy in my reasoning, please let me know. Lets improve together. Quote which i can relate to. Many of life's failures happen with people who do not realize how close they were to success when they gave up. SVP Joined: 18 Aug 2017 Posts: 1887 Location: India Concentration: Sustainability, Marketing GPA: 4 WE: Marketing (Energy and Utilities) Re: A = (2-3+4)^{11}, and B = (-2+3-4)^{11}. What is the value of 2^{A+B}? [#permalink] ### Show Tags 22 Jan 2019, 09:44 MathRevolution wrote: [Math Revolution GMAT math practice question] $$A = (2-3+4)^{11}$$, and $$B = (-2+3-4)^{11}.$$ What is the value of $$2^{A+B}$$? $$A. \frac{1}{2048}$$ $$B. \frac{1}{1024}$$ $$C. 1$$ $$D. 1024$$ $$E. 2048$$ A= 3^11 and B= -3^11 2^A+B => 2^ ( 3-3)^11 =>2^0 =>1 IMO C _________________ If you liked my solution then please give Kudos. Kudos encourage active discussions. Manager Joined: 16 Oct 2011 Posts: 61 GMAT 1: 620 Q37 V38 GMAT 2: 640 Q36 V41 GMAT 3: 650 Q42 V38 GMAT 4: 650 Q44 V36 GMAT 5: 570 Q31 V38 Re: A = (2-3+4)^{11}, and B = (-2+3-4)^{11}. What is the value of 2^{A+B}? [#permalink] ### Show Tags 22 Jan 2019, 09:56 MathRevolution wrote: [Math Revolution GMAT math practice question] $$A = (2-3+4)^{11}$$, and $$B = (-2+3-4)^{11}.$$ What is the value of $$2^{A+B}$$? $$A. \frac{1}{2048}$$ $$B. \frac{1}{1024}$$ $$C. 1$$ $$D. 1024$$ $$E. 2048$$ Note, (-2+3-4) =-1*(2-3+4) Therefore 2^A+B = 2^((2-3+4)^11-1^11(2-3+4)11) = 2^*((2-3+4)^11-(2-3+4)^11) = 2^0 =1 Answer is C Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6978 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: A = (2-3+4)^{11}, and B = (-2+3-4)^{11}. What is the value of 2^{A+B}? [#permalink] ### Show Tags 24 Jan 2019, 05:28 => $$A + B$$ $$= (2-3+4)^{11}+ (-2+3-4)^{11}$$ $$= 3^{11}+ (-3)^{11}$$ $$= 3^{11}- 3^{11}$$ $$= 0.$$ Therefore, $$2^{A+B} = 2^0 = 1.$$ 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$149 for 3 month Online Course"
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Re: A = (2-3+4)^{11}, and B = (-2+3-4)^{11}. What is the value of 2^{A+B}?   [#permalink] 24 Jan 2019, 05:28
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