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The function f(x) represents the number of ways that prime numbers can

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Bunuel
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The function f(x) represents the number of ways that prime numbers can [#permalink] New post   04 Dec 2019, 01:01
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The function f(x) represents the number of ways that prime numbers can be uniquely summed to form a certain number x such that x = a + b + c + d… where those summed variables are each prime and a ≤ b ≤ c ≤ d ... For instance f(8) = 3 and the unique ways are 2 + 2 + 2 + 2 and 2 + 3 + 3 and 3 + 5. What is f(12)?

A. 4
B. 5
C. 6
D. 7
E. 8


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D
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rajatchopra1994
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The function f(x) represents the number of ways that prime numbers can [#permalink] New post   Updated on: 04 Dec 2019, 02:03
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Bunuel wrote:
The function f(x) represents the number of ways that prime numbers can be uniquely summed to form a certain number x such that x = a + b + c + d… where those summed variables are each prime and a ≤ b ≤ c ≤ d ... For instance f(8) = 3 and the unique ways are 2 + 2 + 2 + 2 and 2 + 3 + 3 and 3 + 5. What is f(12)?

A. 4
B. 5
C. 6
D. 7
E. 8


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Explanation:
F(12)=
2+2+2+2+2+2------1
2+2+2+3+3-----2
2+2+3+5----3
2+3+7-----4
3+3+3+3-----5
5+7-----6
2+5+5-----7 (Corrected)

Total = 7
F(12)=7

IMO-D

:please Please Give Kudos, If you find my explanation Good Enough :please

Originally posted by rajatchopra1994 on 04 Dec 2019, 01:12.
Last edited by rajatchopra1994 on 04 Dec 2019, 02:03, edited 1 time in total.
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bhaveshshirode
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Re: The function f(x) represents the number of ways that prime numbers can [#permalink] New post   04 Dec 2019, 01:55
One more 5+5+2 , total 7

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YZLIM1994
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Re: The function f(x) represents the number of ways that prime numbers can [#permalink] New post   17 Oct 2021, 01:05
Bunuel

Do you have a faster method to solve this question?
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Re: The function f(x) represents the number of ways that prime numbers can [#permalink] New post   19 Oct 2021, 10:51
Bunuel wrote:
The function f(x) represents the number of ways that prime numbers can be uniquely summed to form a certain number x such that x = a + b + c + d… where those summed variables are each prime and a ≤ b ≤ c ≤ d ... For instance f(8) = 3 and the unique ways are 2 + 2 + 2 + 2 and 2 + 3 + 3 and 3 + 5. What is f(12)?

A. 4
B. 5
C. 6
D. 7
E. 8


The total number of possibilities are :

1-7+5
2-7+3+2
3-5+3+2+2
4-5+5+2
5-2+2+2+2+2+2
6-3+3+3
7-3+2+3+2

Therefore IMO D
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The function f(x) represents the number of ways that prime numbers can [#permalink] New post   19 Oct 2021, 23:35
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YZLIM1994 wrote:
Bunuel

Do you have a faster method to solve this question?


The prime numbers should be summed up to 12, so they should all be less than 12. Note them, they are 2, 3, 5, 7, 11... Can leave out 11 since 11+1 is not possible as 1 is not a prime (neither a composite).

Now start splitting 12...

1. 12 = 6x2. One possibility.
2. 10+2 = 5+5+2 and 2+3+5+2 and 2+3+2+3+2 (don't worry about the ordering). So 3 possibilities.
3. 9+3 = 3x4 + 3 and 2+7+3 and 2+5+2+3 and 2+2+3+2+3... 3 more possibilities.
4. 7+5... this is a repeat of 10+2... so leave it out.

Total possibilities = 1+3+3 = 7
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Re: The function f(x) represents the number of ways that prime numbers can [#permalink] New post   12 Oct 2023, 20:03
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Re: The function f(x) represents the number of ways that prime numbers can [#permalink]
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