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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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Math Expert
Joined: 02 Sep 2009
Posts: 59721
What is the range of the prime factors of m, if m = 2^5*3^11 - 9^6 -  [#permalink]

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17 Dec 2018, 23:39
00:00

Difficulty:

55% (hard)

Question Stats:

56% (01:31) correct 44% (01:47) wrong based on 204 sessions

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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

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Joined: 18 Aug 2017
Posts: 5483
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: What is the range of the prime factors of m, if m = 2^5*3^11 - 9^6 -  [#permalink]

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18 Dec 2018, 04:22
2
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
Math Expert
Joined: 02 Sep 2009
Posts: 59721
Re: What is the range of the prime factors of m, if m = 2^5*3^11 - 9^6 -  [#permalink]

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24 Dec 2018, 04:49
1
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

_________________
Intern
Joined: 26 Dec 2018
Posts: 1
Re: What is the range of the prime factors of m, if m = 2^5*3^11 - 9^6 -  [#permalink]

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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?
Manager
Joined: 27 Oct 2017
Posts: 72
Re: What is the range of the prime factors of m, if m = 2^5*3^11 - 9^6 -  [#permalink]

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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
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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