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8^16 + 16^13 + 4^24 =

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Math Expert
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8^16 + 16^13 + 4^24 =  [#permalink]

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New post 23 Oct 2018, 03:25
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

64% (01:28) correct 36% (01:25) wrong based on 114 sessions

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Re: 8^16 + 16^13 + 4^24 =  [#permalink]

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New post 23 Oct 2018, 03:38
1
Bunuel wrote:
\(8^{16} + 16^{13} + 4^{24} =\)


A. \((4)*(2^{29}+1)\)

B. \((6)*(2^{48})\)

C. \((9)*(2^{49})\)

D. \((28)*(2^{53})\)

E. \(2^{148}\)


8^16 = 2^(3*16) = 2^48

16^13 = 2^(4*13) = 2^52

4^24 = 2^(2*24) = 2^48

2^48 + 2^52 + 2^48

take 2^48 as a common factor, 2^48 (1 + 2^4 + 1) = 2^48 (2 + 2^4) = 2^48 (18) = 2^48 (2*9) = 2^49 (9)

Answer choice C
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Re: 8^16 + 16^13 + 4^24 =  [#permalink]

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New post 23 Oct 2018, 05:56
Bunuel wrote:
\(8^{16} + 16^{13} + 4^{24} =\)


A. \((4)*(2^{29}+1)\)

B. \((6)*(2^{48})\)

C. \((9)*(2^{49})\)

D. \((28)*(2^{53})\)

E. \(2^{148}\)


\(8^{16} + 16^{13} + 4^{24}\)

= \(2^{48} + 2^{52} + 2^{48}\)

= \(2^{48} ( 1+ 2^{4} + 1)\)

= \(2^{48} *18\)

= \(2^{48} *2*3^2\)

= \(2^{49}*9\), Answer must be (C)
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Re: 8^16 + 16^13 + 4^24 =  [#permalink]

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New post 25 Oct 2018, 08:22
Bunuel wrote:
\(8^{16} + 16^{13} + 4^{24} =\)


A. \((4)*(2^{29}+1)\)

B. \((6)*(2^{48})\)

C. \((9)*(2^{49})\)

D. \((28)*(2^{53})\)

E. \(2^{148}\)


If we re-express each term as a number with a base of 2, we have:

2^48 + 2^52 + 2^48

2^48(1 + 2^4 + 1) = 2^48 x 18 = 2^48 x 2 x 9 = 2^49 x 9

Answer: C
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Re: 8^16 + 16^13 + 4^24 =  [#permalink]

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New post 25 Oct 2018, 13:57
Bunuel wrote:
\(8^{16} + 16^{13} + 4^{24} =\)


A. \((4)*(2^{29}+1)\)

B. \((6)*(2^{48})\)

C. \((9)*(2^{49})\)

D. \((28)*(2^{53})\)

E. \(2^{148}\)

\(?\,\,\,:\,\,\,{\rm{expression}}\)

\(\left. \matrix{
{8^{16}} = {2^{\,3 \cdot 16}} = {2^{\,48}}\, \hfill \cr
{16^{13}} = {2^{\,4 \cdot 13}}\,\, = {2^{\,52}} \hfill \cr
{4^{24}} = {2^{\,2 \cdot 24}} = {2^{\,48}} \hfill \cr} \right\}\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( + \right)} \,\,\,\,\,? = {2^{\,48}}\left[ {\,1 + {2^4} + 1\,} \right] = \,{2^{\,48}} \cdot \left[ {\,2 \cdot \left( {1 + {2^3}} \right)\,} \right]\,\, = \,\,9 \cdot \,{2^{\,49}}\)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: 8^16 + 16^13 + 4^24 = &nbs [#permalink] 25 Oct 2018, 13:57
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