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

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

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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. 1/2048
B. 1/1024
C. 1
D. 1024
E. 2048

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Max@Math Revolution 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. 1/2048
B. 1/1024
C. 1
D. 1024
E. 2048
A = (2-3+4)¹¹ = 3¹¹
B = (-2+3-4)¹¹ = (-3)¹¹ = -3¹¹
Thus:
A+B = 3¹¹ - 3¹¹ = 0
2^(A+B) = 2⁰ = 1.

The correct answer is C.

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Max@Math Revolution 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. 1/2048
B. 1/1024
C. 1
D. 1024
E. 2048
$$\left. \matrix{
A = {3^{11}} \hfill \cr
B = {\left( { - 3} \right)^{11}} = - {3^{11}} = - A\,\,\, \hfill \cr} \right\}\,\,\,\,\, \Rightarrow \,\,\,\,\,? = {2^{A + \left( { - A} \right)}} = 1$$

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.

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English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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=>

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

_________________

Math Revolution
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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
Email to : info@mathrevolution.com

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