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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

by Max@Math Revolution » Mon Jan 21, 2019 11:16 pm

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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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by GMATGuruNY » Tue Jan 22, 2019 3:23 am
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) = 2� = 1.

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

by fskilnik@GMATH » Tue Jan 22, 2019 5:15 am
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.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
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by Max@Math Revolution » Thu Jan 24, 2019 5:09 am
=>

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
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