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Question Stats:
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56%
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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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A. 4
B. 5
C. 6
D. 7
E. 8
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Posts: 1,052
Updated on: 04 Dec 2019, 01:03
Originally posted by rajatchopra1994 on 04 Dec 2019, 00:12.
Last edited by rajatchopra1994 on 04 Dec 2019, 01:03, edited 1 time in total.
Last edited by rajatchopra1994 on 04 Dec 2019, 01:03, edited 1 time in total.
Bunuel
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 Give Kudos, If you find my explanation Good Enough General Discussion
Posts: 1
One more 5+5+2 , total 7
Posted from my mobile device
Posted from my mobile device
Posts: 938
Bunuel
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
YZLIM1994
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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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)?
12 = 2+2+2+2+2+2 = 2+2+2+3+3 = 3+3+3+3 = 2+2+3+5 = 2+5+5 = 2+3+7 = 5+7
f(12) = 7
IMO D
What is f(12)?
12 = 2+2+2+2+2+2 = 2+2+2+3+3 = 3+3+3+3 = 2+2+3+5 = 2+5+5 = 2+3+7 = 5+7
f(12) = 7
IMO D
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