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8×2^100 + 4×2^101 =

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vikasp99
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8×2^100 + 4×2^101 = [#permalink] New post   15 Mar 2017, 06:06
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81% (00:43) correct 19% (01:04) wrong based on 59 sessions
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8×2^100 + 4×2^101 =

A) 2^101

B) 2^102

C) 2^103

D) 2^104

E) 2^105
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D
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Re: 8×2^100 + 4×2^101 = [#permalink] New post   15 Mar 2017, 11:51
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vikasp99 wrote:
8×2^100 + 4×2^101 =

A) 2^101

B) 2^102

C) 2^103

D) 2^104

E) 2^105

\(8*2^{100} + 4*2^{101}\)

= \(2^3*2^{100} + 2^2*2^{101}\)

= \(2^{103} + 2^{103}\)

= \(2^{103} ( 1 + 1 )\)

= \(2^{103}*2\)

= \(2^{104}\)

Thus, answer must be (D) \(2^{104}\)
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Re: 8×2^100 + 4×2^101 = [#permalink] New post   21 Mar 2017, 06:12
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vikasp99 wrote:
8×2^100 + 4×2^101 =

A) 2^101

B) 2^102

C) 2^103

D) 2^104

E) 2^105


Let’s first factor each non-prime integer into primes.

8 = 2^3

4 = 2^2

Thus, we have:

2^3 x 2^100 + 2^2 x 2^101

2^103 + 2^103

Now factor 2^103 from each of the terms, obtaining:

2^103(1 + 1) = 2^103 x 2^1 = 2^104

Answer: D
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Re: 8×2^100 + 4×2^101 = [#permalink] New post   15 Mar 2017, 11:06
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8×2^100 + 4×2^101
2^3 x 2^100 + 2^2 x 2^101
2^103 + 2^103
2^103 ( 1 + 1)
2^103 (2)
2^104

Answer D
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Re: 8×2^100 + 4×2^101 = [#permalink] New post   15 Mar 2017, 12:38
2^3x2^100+2^2x2^101
2^103+2^103
2x2^103
2^104.
Option D is correct

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Re: 8×2^100 + 4×2^101 = [#permalink]
15 Mar 2017, 12:38
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