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What is the range of the prime factors of m, if m = 2^5*3^11 - 9^6 -

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What is the range of the prime factors of m, if m = 2^5*3^11 - 9^6 -  [#permalink]

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New post 17 Dec 2018, 23:39
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E

Difficulty:

  55% (hard)

Question Stats:

57% (01:30) correct 43% (01:50) wrong based on 193 sessions

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Re: What is the range of the prime factors of m, if m = 2^5*3^11 - 9^6 -  [#permalink]

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New post 18 Dec 2018, 04:22
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Bunuel wrote:
What is the range of the prime factors of m, if \(m = 2^5*3^{11} - 9^{6} - 3^{11}\) ?

A. 0
B. 1
C. 2
D. 4
E. 5



\(m = 2^5*3^{11} - 9^{6} - 3^{11}\)

3^11(2^5-3-1)
3^11(28)
3^11(2^2*7)

range would be 7-2 = 5 IMO E
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Re: What is the range of the prime factors of m, if m = 2^5*3^11 - 9^6 -  [#permalink]

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New post 24 Dec 2018, 04:49
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Re: What is the range of the prime factors of m, if m = 2^5*3^11 - 9^6 -  [#permalink]

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New post 28 Dec 2018, 11:25
Archit3110 wrote:
Bunuel wrote:
What is the range of the prime factors of m, if \(m = 2^5*3^{11} - 9^{6} - 3^{11}\) ?

A. 0
B. 1
C. 2
D. 4
E. 5



\(m = 2^5*3^{11} - 9^{6} - 3^{11}\)

3^11(2^5-3-1)
3^11(28)
3^11(2^2*7)

range would be 7-2 = 5 IMO E



Where does the 3-1 come from?
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Re: What is the range of the prime factors of m, if m = 2^5*3^11 - 9^6 -  [#permalink]

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New post 07 Jan 2019, 12:09
lclarios91 wrote:
Archit3110 wrote:
Bunuel wrote:
What is the range of the prime factors of m, if \(m = 2^5*3^{11} - 9^{6} - 3^{11}\) ?

A. 0
B. 1
C. 2
D. 4
E. 5



\(m = 2^5*3^{11} - 9^{6} - 3^{11}\)

3^11(2^5-3-1)
3^11(28)
3^11(2^2*7)

range would be 7-2 = 5 IMO E



Where does the 3-1 come from?


Archit,

We can factor out 3^11 from 2^5*3^11 -(3^2)^6-3^11 ----> 2^5*3^11-3^12-3^11-----> 3^11(2^5-3-1)---->3^11(32-4)--->3^11(28) ---->3^11(2^2*7).
So the range will be 7 - 2 = 5
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Re: What is the range of the prime factors of m, if m = 2^5*3^11 - 9^6 -   [#permalink] 07 Jan 2019, 12:09
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